B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

S. Pironio, L. Masanes, A. Leverrier, and A. Acín, “Security of device-independent quantum key distribution in the bounded-quantum-storage model,” Phys. Rev. X 3, 031007 (2013).

[Crossref]

L. Masanes, S. Pironio, and A. Acín, “Secure device-independent quantum key distribution with causally independent measurement devices,” Nat. Commun. 2, 238 (2011).

[Crossref]

A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98, 230501 (2007).

[Crossref]

M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97, 190502 (2006).

[Crossref]

B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111, 130406 (2013).

[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

[Crossref]

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H.-A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).

[Crossref]

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).

[Crossref]

F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).

[Crossref]

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H.-A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).

[Crossref]

J. Barrett, R. Colbeck, and A. Kent, “Unconditionally secure device-independent quantum key distribution with only two devices,” Phys. Rev. A 86, 062326 (2012).

[Crossref]

J. Barrett, L. Hardy, and A. Kent, “No signaling and quantum key distribution,” Phys. Rev. Lett. 95, 10503 (2005).

[Crossref]

S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schnabel, “Strong Einstein-Podolsky-Rosen steering with unconditional entangled states,” Phys. Rev. A 87, 022104 (2013).

[Crossref]

V. Scarani, H. Bechmann-Pasquinucci, N. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).

[Crossref]

J. S. Bell, “EPR correlations and EPW distributions,” Ann. N.Y. Acad. Sci. 480, 263–266 (1986).

[Crossref]

A. J. Bennet, D. A. Evans, D. J. Saunders, C. Branciard, E. G. Cavalcanti, H. M. Wiseman, and G. J. Pryde, “Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole,” Phys. Rev. X 2, 031003 (2012).

[Crossref]

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of International Conference on Computers, Systems and Signal Processing, Bangalore, India, 1984.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

F. Furrer, M. Berta, M. Tomamichel, V. B. Scholz, and M. Christandl, “Position-momentum uncertainty relations in the presence of quantum memory,” J. Math. Phys. 55, 122205 (2014).

[Crossref]

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. Scholz, M. Tomamichel, and R. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109, 100502 (2012).

[Crossref]

M. Berta, M. Christandl, R. Colbeck, J. Renes, and R. Renner, “The uncertainty principle in the presence of quantum memory,” Nat. Phys. 6, 659–662 (2010).

[Crossref]

M. Berta, F. Furrer, and V. B. Scholz, “The smooth entropy formalism on von Neumann algebras,” arXiv:1107.5460 (2011).

M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, and A. Zeilinger, “Bell violation using entangled photons without the fair-sampling assumption,” Nature 497, 227–230 (2013).

[Crossref]

I. Białynicki-Birula and J. Mycielski, “Uncertainty relations for information entropy in wave mechanics,” Commun. Math. Phys. 44, 129–132 (1975).

[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

C. Weedbrook, A. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93, 170504 (2004).

[Crossref]

A. J. Bennet, D. A. Evans, D. J. Saunders, C. Branciard, E. G. Cavalcanti, H. M. Wiseman, and G. J. Pryde, “Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole,” Phys. Rev. X 2, 031003 (2012).

[Crossref]

D. H. Smith, G. Gillett, M. P. de Almeida, C. Branciard, A. Fedrizzi, T. J. Weinhold, A. Lita, B. Calkins, T. Gerrits, H. M. Wiseman, S. W. Nam, and A. G. White, “Conclusive quantum steering with superconducting transition-edge sensors,” Nat. Commun. 3, 625 (2012).

[Crossref]

C. Branciard, E. G. Cavalcanti, S. P. Walborn, V. Scarani, and H. M. Wiseman, “One-sided device-independent quantum key distribution: security, feasibility, and the connection with steering,” Phys. Rev. A 85, 010301 (2012).

[Crossref]

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of International Conference on Computers, Systems and Signal Processing, Bangalore, India, 1984.

S. Braunstein and S. Pirandola, “Side-channel-free quantum key distribution,” Phys. Rev. Lett. 108, 130502 (2012).

[Crossref]

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

[Crossref]

F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).

[Crossref]

B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111, 130406 (2013).

[Crossref]

B. Wittmann, S. Ramelow, F. Steinlechner, N. K. Langford, N. Brunner, H. M. Wiseman, R. Ursin, and A. Zeilinger, “Loophole-free Einstein–Podolsky–Rosen experiment via quantum steering,” New J. Phys. 14, 053030 (2012).

[Crossref]

M. Pawłowski and N. Brunner, “Semi-device-independent security of one-way quantum key distribution,” Phys. Rev. A 84, 010302 (2011).

[Crossref]

A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98, 230501 (2007).

[Crossref]

B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111, 130406 (2013).

[Crossref]

M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, and A. Zeilinger, “Bell violation using entangled photons without the fair-sampling assumption,” Nature 497, 227–230 (2013).

[Crossref]

D. H. Smith, G. Gillett, M. P. de Almeida, C. Branciard, A. Fedrizzi, T. J. Weinhold, A. Lita, B. Calkins, T. Gerrits, H. M. Wiseman, S. W. Nam, and A. G. White, “Conclusive quantum steering with superconducting transition-edge sensors,” Nat. Commun. 3, 625 (2012).

[Crossref]

A. J. Bennet, D. A. Evans, D. J. Saunders, C. Branciard, E. G. Cavalcanti, H. M. Wiseman, and G. J. Pryde, “Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole,” Phys. Rev. X 2, 031003 (2012).

[Crossref]

C. Branciard, E. G. Cavalcanti, S. P. Walborn, V. Scarani, and H. M. Wiseman, “One-sided device-independent quantum key distribution: security, feasibility, and the connection with steering,” Phys. Rev. A 85, 010301 (2012).

[Crossref]

J. Fiurášek and N. Cerf, “Gaussian postselection and virtual noiseless amplification in continuous-variable quantum key distribution,” Phys. Rev. A 86, 060302 (2012).

[Crossref]

V. Scarani, H. Bechmann-Pasquinucci, N. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).

[Crossref]

R. Garca-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97, 190503 (2006).

[Crossref]

F. Grosshans, N. J. Cerf, P. Grangier, J. Wenger, and R. Tualle-Brouri, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quantum Inf. Comput. 3, 535–552 (2003).

F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).

[Crossref]

A. Rubenok, J. A. Slater, P. Chan, I. Lucio-Martinez, and W. Tittel, “Real-world two-photon interference and proof-of-principle quantum key distribution immune to detector attacks,” Phys. Rev. Lett. 111, 130501 (2013).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

F. Furrer, M. Berta, M. Tomamichel, V. B. Scholz, and M. Christandl, “Position-momentum uncertainty relations in the presence of quantum memory,” J. Math. Phys. 55, 122205 (2014).

[Crossref]

M. Berta, M. Christandl, R. Colbeck, J. Renes, and R. Renner, “The uncertainty principle in the presence of quantum memory,” Nat. Phys. 6, 659–662 (2010).

[Crossref]

B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111, 130406 (2013).

[Crossref]

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).

[Crossref]

R. Renner and J. Cirac, “de Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography,” Phys. Rev. Lett. 102, 110504 (2009).

[Crossref]

J. Barrett, R. Colbeck, and A. Kent, “Unconditionally secure device-independent quantum key distribution with only two devices,” Phys. Rev. A 86, 062326 (2012).

[Crossref]

M. Berta, M. Christandl, R. Colbeck, J. Renes, and R. Renner, “The uncertainty principle in the presence of quantum memory,” Nat. Phys. 6, 659–662 (2010).

[Crossref]

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).

[Crossref]

S. Wehner, M. Curty, C. Schaffner, and H.-K. Lo, “Implementation of two-party protocols in the noisy-storage model,” Phys. Rev. A 81, 052336 (2010).

[Crossref]

D. H. Smith, G. Gillett, M. P. de Almeida, C. Branciard, A. Fedrizzi, T. J. Weinhold, A. Lita, B. Calkins, T. Gerrits, H. M. Wiseman, S. W. Nam, and A. G. White, “Conclusive quantum steering with superconducting transition-edge sensors,” Nat. Commun. 3, 625 (2012).

[Crossref]

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).

[Crossref]

H. Wiseman, S. Jones, and A. Doherty, “Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox,” Phys. Rev. Lett. 98, 140402 (2007).

[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).

[Crossref]

V. Scarani, H. Bechmann-Pasquinucci, N. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).

[Crossref]

S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schnabel, “Strong Einstein-Podolsky-Rosen steering with unconditional entangled states,” Phys. Rev. A 87, 022104 (2013).

[Crossref]

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).

[Crossref]

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).

[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

A. J. Bennet, D. A. Evans, D. J. Saunders, C. Branciard, E. G. Cavalcanti, H. M. Wiseman, and G. J. Pryde, “Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole,” Phys. Rev. X 2, 031003 (2012).

[Crossref]

D. H. Smith, G. Gillett, M. P. de Almeida, C. Branciard, A. Fedrizzi, T. J. Weinhold, A. Lita, B. Calkins, T. Gerrits, H. M. Wiseman, S. W. Nam, and A. G. White, “Conclusive quantum steering with superconducting transition-edge sensors,” Nat. Commun. 3, 625 (2012).

[Crossref]

A. Ferenczi, “Security proof methods for quantum key distribution protocols,” Ph.D. thesis (University of Waterloo, 2013).

J. Fiurášek and N. Cerf, “Gaussian postselection and virtual noiseless amplification in continuous-variable quantum key distribution,” Phys. Rev. A 86, 060302 (2012).

[Crossref]

R. L. Frank and E. H. Lieb, “Extended quantum conditional entropy and quantum uncertainty inequalities,” Commun. Math. Phys. 323, 487–495 (2014).

[Crossref]

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).

[Crossref]

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. Scholz, M. Tomamichel, and R. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109, 100502 (2012).

[Crossref]

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).

[Crossref]

F. Furrer, M. Berta, M. Tomamichel, V. B. Scholz, and M. Christandl, “Position-momentum uncertainty relations in the presence of quantum memory,” J. Math. Phys. 55, 122205 (2014).

[Crossref]

F. Furrer, “Reverse-reconciliation continuous-variable quantum key distribution based on the uncertainty principle,” Phys. Rev. A 90, 042325 (2014).

[Crossref]

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. Scholz, M. Tomamichel, and R. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109, 100502 (2012).

[Crossref]

M. Berta, F. Furrer, and V. B. Scholz, “The smooth entropy formalism on von Neumann algebras,” arXiv:1107.5460 (2011).

R. Garca-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97, 190503 (2006).

[Crossref]

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).

[Crossref]

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

[Crossref]

M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, and A. Zeilinger, “Bell violation using entangled photons without the fair-sampling assumption,” Nature 497, 227–230 (2013).

[Crossref]

B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111, 130406 (2013).

[Crossref]

D. H. Smith, G. Gillett, M. P. de Almeida, C. Branciard, A. Fedrizzi, T. J. Weinhold, A. Lita, B. Calkins, T. Gerrits, H. M. Wiseman, S. W. Nam, and A. G. White, “Conclusive quantum steering with superconducting transition-edge sensors,” Nat. Commun. 3, 625 (2012).

[Crossref]

D. H. Smith, G. Gillett, M. P. de Almeida, C. Branciard, A. Fedrizzi, T. J. Weinhold, A. Lita, B. Calkins, T. Gerrits, H. M. Wiseman, S. W. Nam, and A. G. White, “Conclusive quantum steering with superconducting transition-edge sensors,” Nat. Commun. 3, 625 (2012).

[Crossref]

B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111, 130406 (2013).

[Crossref]

M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner, “Tight finite-key analysis for quantum cryptography,” Nat. Commun. 3, 634 (2012).

[Crossref]

N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett. 105, 70501 (2010).

[Crossref]

A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98, 230501 (2007).

[Crossref]

M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, and A. Zeilinger, “Bell violation using entangled photons without the fair-sampling assumption,” Nature 497, 227–230 (2013).

[Crossref]

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H.-A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).

[Crossref]

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).

[Crossref]

F. Grosshans, N. J. Cerf, P. Grangier, J. Wenger, and R. Tualle-Brouri, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quantum Inf. Comput. 3, 535–552 (2003).

F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).

[Crossref]

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88, 057902 (2002).

[Crossref]

M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97, 190502 (2006).

[Crossref]

F. Grosshans, N. J. Cerf, P. Grangier, J. Wenger, and R. Tualle-Brouri, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quantum Inf. Comput. 3, 535–552 (2003).

F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).

[Crossref]

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88, 057902 (2002).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).

[Crossref]

E. Hänggi and R. Renner, “Device-independent quantum key distribution with commuting measurements,” arXiv:1009.1833 (2010).

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

J. Barrett, L. Hardy, and A. Kent, “No signaling and quantum key distribution,” Phys. Rev. Lett. 95, 10503 (2005).

[Crossref]

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H.-A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).

[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A 61, 022309 (2000).

[Crossref]

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).

[Crossref]

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

[Crossref]

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H.-A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).

[Crossref]

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

H. Wiseman, S. Jones, and A. Doherty, “Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox,” Phys. Rev. Lett. 98, 140402 (2007).

[Crossref]

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).

[Crossref]

P. Jouguet, S. Kunz-Jacques, and A. Leverrier, “Long-distance continuous-variable quantum key distribution with a Gaussian modulation,” Phys. Rev. A 84, 062317 (2011).

[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

J. Barrett, R. Colbeck, and A. Kent, “Unconditionally secure device-independent quantum key distribution with only two devices,” Phys. Rev. A 86, 062326 (2012).

[Crossref]

J. Barrett, L. Hardy, and A. Kent, “No signaling and quantum key distribution,” Phys. Rev. Lett. 95, 10503 (2005).

[Crossref]

Z. Ou, S. Pereira, and H. Kimble, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables in nondegenerate parametric amplification,” Appl. Phys. B 55, 265–278 (1992).

[Crossref]

M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, and A. Zeilinger, “Bell violation using entangled photons without the fair-sampling assumption,” Nature 497, 227–230 (2013).

[Crossref]

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).

[Crossref]

P. Jouguet, S. Kunz-Jacques, and A. Leverrier, “Long-distance continuous-variable quantum key distribution with a Gaussian modulation,” Phys. Rev. A 84, 062317 (2011).

[Crossref]

B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111, 130406 (2013).

[Crossref]

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H.-A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).

[Crossref]

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).

[Crossref]

N. Walk, T. C. Ralph, T. Symul, and P. K. Lam, “Security of continuous-variable quantum cryptography with Gaussian postselection,” Phys. Rev. A 87, 020303 (2013).

[Crossref]

C. Weedbrook, A. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93, 170504 (2004).

[Crossref]

C. Weedbrook, A. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93, 170504 (2004).

[Crossref]

B. Wittmann, S. Ramelow, F. Steinlechner, N. K. Langford, N. Brunner, H. M. Wiseman, R. Ursin, and A. Zeilinger, “Loophole-free Einstein–Podolsky–Rosen experiment via quantum steering,” New J. Phys. 14, 053030 (2012).

[Crossref]

C. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89, 167901 (2002).

[Crossref]

A. Leverrier, “Composable security proof for continuous-variable quantum key distribution with coherent states,” Phys. Rev. Lett. 114, 070501 (2015).

[Crossref]

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).

[Crossref]

S. Pironio, L. Masanes, A. Leverrier, and A. Acín, “Security of device-independent quantum key distribution in the bounded-quantum-storage model,” Phys. Rev. X 3, 031007 (2013).

[Crossref]

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. Scholz, M. Tomamichel, and R. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109, 100502 (2012).

[Crossref]

P. Jouguet, S. Kunz-Jacques, and A. Leverrier, “Long-distance continuous-variable quantum key distribution with a Gaussian modulation,” Phys. Rev. A 84, 062317 (2011).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

R. L. Frank and E. H. Lieb, “Extended quantum conditional entropy and quantum uncertainty inequalities,” Commun. Math. Phys. 323, 487–495 (2014).

[Crossref]

B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111, 130406 (2013).

[Crossref]

M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner, “Tight finite-key analysis for quantum cryptography,” Nat. Commun. 3, 634 (2012).

[Crossref]

M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, and A. Zeilinger, “Bell violation using entangled photons without the fair-sampling assumption,” Nature 497, 227–230 (2013).

[Crossref]

D. H. Smith, G. Gillett, M. P. de Almeida, C. Branciard, A. Fedrizzi, T. J. Weinhold, A. Lita, B. Calkins, T. Gerrits, H. M. Wiseman, S. W. Nam, and A. G. White, “Conclusive quantum steering with superconducting transition-edge sensors,” Nat. Commun. 3, 625 (2012).

[Crossref]

B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111, 130406 (2013).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

[Crossref]

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).

[Crossref]

S. Wehner, M. Curty, C. Schaffner, and H.-K. Lo, “Implementation of two-party protocols in the noisy-storage model,” Phys. Rev. A 81, 052336 (2010).

[Crossref]

A. Rubenok, J. A. Slater, P. Chan, I. Lucio-Martinez, and W. Tittel, “Real-world two-photon interference and proof-of-principle quantum key distribution immune to detector attacks,” Phys. Rev. Lett. 111, 130501 (2013).

[Crossref]

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).

[Crossref]

T. C. Ralph and A. P. Lund, “Nondeterministic noiseless linear amplification of quantum systems,” in Quantum Communication Measurement and Computing Proceedings of 9th International Conference (2009), pp. 155–160.

V. Scarani, H. Bechmann-Pasquinucci, N. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).

[Crossref]

C. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89, 167901 (2002).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

H. Maassen and J. Uffink, “Generalized entropic uncertainty relations,” Phys. Rev. Lett. 60, 1103–1106 (1988).

[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

S. Pironio, L. Masanes, A. Leverrier, and A. Acín, “Security of device-independent quantum key distribution in the bounded-quantum-storage model,” Phys. Rev. X 3, 031007 (2013).

[Crossref]

L. Masanes, S. Pironio, and A. Acín, “Secure device-independent quantum key distribution with causally independent measurement devices,” Nat. Commun. 2, 238 (2011).

[Crossref]

A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98, 230501 (2007).

[Crossref]

B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111, 130406 (2013).

[Crossref]

M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, and A. Zeilinger, “Bell violation using entangled photons without the fair-sampling assumption,” Nature 497, 227–230 (2013).

[Crossref]

B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111, 130406 (2013).

[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

I. Białynicki-Birula and J. Mycielski, “Uncertainty relations for information entropy in wave mechanics,” Commun. Math. Phys. 44, 129–132 (1975).

[Crossref]

B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111, 130406 (2013).

[Crossref]

M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, and A. Zeilinger, “Bell violation using entangled photons without the fair-sampling assumption,” Nature 497, 227–230 (2013).

[Crossref]

D. H. Smith, G. Gillett, M. P. de Almeida, C. Branciard, A. Fedrizzi, T. J. Weinhold, A. Lita, B. Calkins, T. Gerrits, H. M. Wiseman, S. W. Nam, and A. G. White, “Conclusive quantum steering with superconducting transition-edge sensors,” Nat. Commun. 3, 625 (2012).

[Crossref]

M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97, 190502 (2006).

[Crossref]

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

[Crossref]

Z. Ou, S. Pereira, and H. Kimble, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables in nondegenerate parametric amplification,” Appl. Phys. B 55, 265–278 (1992).

[Crossref]

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

M. Pawłowski and N. Brunner, “Semi-device-independent security of one-way quantum key distribution,” Phys. Rev. A 84, 010302 (2011).

[Crossref]

V. Scarani, H. Bechmann-Pasquinucci, N. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).

[Crossref]

Z. Ou, S. Pereira, and H. Kimble, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables in nondegenerate parametric amplification,” Appl. Phys. B 55, 265–278 (1992).

[Crossref]

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

[Crossref]

S. Braunstein and S. Pirandola, “Side-channel-free quantum key distribution,” Phys. Rev. Lett. 108, 130502 (2012).

[Crossref]

S. Pironio, L. Masanes, A. Leverrier, and A. Acín, “Security of device-independent quantum key distribution in the bounded-quantum-storage model,” Phys. Rev. X 3, 031007 (2013).

[Crossref]

L. Masanes, S. Pironio, and A. Acín, “Secure device-independent quantum key distribution with causally independent measurement devices,” Nat. Commun. 2, 238 (2011).

[Crossref]

N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett. 105, 70501 (2010).

[Crossref]

A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98, 230501 (2007).

[Crossref]

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).

[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

A. J. Bennet, D. A. Evans, D. J. Saunders, C. Branciard, E. G. Cavalcanti, H. M. Wiseman, and G. J. Pryde, “Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole,” Phys. Rev. X 2, 031003 (2012).

[Crossref]

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).

[Crossref]

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).

[Crossref]

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).

[Crossref]

N. Walk, T. C. Ralph, T. Symul, and P. K. Lam, “Security of continuous-variable quantum cryptography with Gaussian postselection,” Phys. Rev. A 87, 020303 (2013).

[Crossref]

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).

[Crossref]

C. Weedbrook, A. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93, 170504 (2004).

[Crossref]

C. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89, 167901 (2002).

[Crossref]

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61, 010303 (1999).

[Crossref]

T. C. Ralph and A. P. Lund, “Nondeterministic noiseless linear amplification of quantum systems,” in Quantum Communication Measurement and Computing Proceedings of 9th International Conference (2009), pp. 155–160.

M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, and A. Zeilinger, “Bell violation using entangled photons without the fair-sampling assumption,” Nature 497, 227–230 (2013).

[Crossref]

B. Wittmann, S. Ramelow, F. Steinlechner, N. K. Langford, N. Brunner, H. M. Wiseman, R. Ursin, and A. Zeilinger, “Loophole-free Einstein–Podolsky–Rosen experiment via quantum steering,” New J. Phys. 14, 053030 (2012).

[Crossref]

M. Reid, “Signifying quantum benchmarks for qubit teleportation and secure quantum communication using Einstein-Podolsky-Rosen steering inequalities,” Phys. Rev. A 88, 062338 (2013).

[Crossref]

M. Reid, “Quantum cryptography with a predetermined key, using continuous-variable Einstein-Podolsky-Rosen correlations,” Phys. Rev. A 62, 062308 (2000).

[Crossref]

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H.-A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).

[Crossref]

M. D. Reid, “Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification,” Phys. Rev. A 40, 913–923 (1989).

[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

M. Berta, M. Christandl, R. Colbeck, J. Renes, and R. Renner, “The uncertainty principle in the presence of quantum memory,” Nat. Phys. 6, 659–662 (2010).

[Crossref]

M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner, “Tight finite-key analysis for quantum cryptography,” Nat. Commun. 3, 634 (2012).

[Crossref]

M. Tomamichel and R. Renner, “Uncertainty relation for smooth entropies,” Phys. Rev. Lett. 106, 110506 (2011).

[Crossref]

M. Berta, M. Christandl, R. Colbeck, J. Renes, and R. Renner, “The uncertainty principle in the presence of quantum memory,” Nat. Phys. 6, 659–662 (2010).

[Crossref]

R. Renner and J. Cirac, “de Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography,” Phys. Rev. Lett. 102, 110504 (2009).

[Crossref]

V. Scarani and R. Renner, “Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way postprocessing,” Phys. Rev. Lett. 100, 200501 (2008).

[Crossref]

E. Hänggi and R. Renner, “Device-independent quantum key distribution with commuting measurements,” arXiv:1009.1833 (2010).

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).

[Crossref]

A. Rubenok, J. A. Slater, P. Chan, I. Lucio-Martinez, and W. Tittel, “Real-world two-photon interference and proof-of-principle quantum key distribution immune to detector attacks,” Phys. Rev. Lett. 111, 130501 (2013).

[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett. 105, 70501 (2010).

[Crossref]

A. J. Bennet, D. A. Evans, D. J. Saunders, C. Branciard, E. G. Cavalcanti, H. M. Wiseman, and G. J. Pryde, “Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole,” Phys. Rev. X 2, 031003 (2012).

[Crossref]

C. Branciard, E. G. Cavalcanti, S. P. Walborn, V. Scarani, and H. M. Wiseman, “One-sided device-independent quantum key distribution: security, feasibility, and the connection with steering,” Phys. Rev. A 85, 010301 (2012).

[Crossref]

V. Scarani, H. Bechmann-Pasquinucci, N. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).

[Crossref]

V. Scarani and R. Renner, “Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way postprocessing,” Phys. Rev. Lett. 100, 200501 (2008).

[Crossref]

A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, “Device-independent security of quantum cryptography against collective attacks,” Phys. Rev. Lett. 98, 230501 (2007).

[Crossref]

C. Schaffner, “Simple protocols for oblivious transfer and secure identification in the noisy-quantum-storage model,” Phys. Rev. A 82, 032308 (2010).

[Crossref]

S. Wehner, M. Curty, C. Schaffner, and H.-K. Lo, “Implementation of two-party protocols in the noisy-storage model,” Phys. Rev. A 81, 052336 (2010).

[Crossref]

S. Wehner, C. Schaffner, and B. Terhal, “Cryptography from noisy storage,” Phys. Rev. Lett. 100, 220502 (2008).

[Crossref]

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).

[Crossref]

S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schnabel, “Strong Einstein-Podolsky-Rosen steering with unconditional entangled states,” Phys. Rev. A 87, 022104 (2013).

[Crossref]

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. Scholz, M. Tomamichel, and R. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109, 100502 (2012).

[Crossref]

F. Furrer, M. Berta, M. Tomamichel, V. B. Scholz, and M. Christandl, “Position-momentum uncertainty relations in the presence of quantum memory,” J. Math. Phys. 55, 122205 (2014).

[Crossref]

M. Berta, F. Furrer, and V. B. Scholz, “The smooth entropy formalism on von Neumann algebras,” arXiv:1107.5460 (2011).

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111, 130406 (2013).

[Crossref]

C. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89, 167901 (2002).

[Crossref]

A. Rubenok, J. A. Slater, P. Chan, I. Lucio-Martinez, and W. Tittel, “Real-world two-photon interference and proof-of-principle quantum key distribution immune to detector attacks,” Phys. Rev. Lett. 111, 130501 (2013).

[Crossref]

D. H. Smith, G. Gillett, M. P. de Almeida, C. Branciard, A. Fedrizzi, T. J. Weinhold, A. Lita, B. Calkins, T. Gerrits, H. M. Wiseman, S. W. Nam, and A. G. White, “Conclusive quantum steering with superconducting transition-edge sensors,” Nat. Commun. 3, 625 (2012).

[Crossref]

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

[Crossref]

B. Wittmann, S. Ramelow, F. Steinlechner, N. K. Langford, N. Brunner, H. M. Wiseman, R. Ursin, and A. Zeilinger, “Loophole-free Einstein–Podolsky–Rosen experiment via quantum steering,” New J. Phys. 14, 053030 (2012).

[Crossref]

S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schnabel, “Strong Einstein-Podolsky-Rosen steering with unconditional entangled states,” Phys. Rev. A 87, 022104 (2013).

[Crossref]

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).

[Crossref]

N. Walk, T. C. Ralph, T. Symul, and P. K. Lam, “Security of continuous-variable quantum cryptography with Gaussian postselection,” Phys. Rev. A 87, 020303 (2013).

[Crossref]

C. Weedbrook, A. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93, 170504 (2004).

[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H.-A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).

[Crossref]

S. Wehner, C. Schaffner, and B. Terhal, “Cryptography from noisy storage,” Phys. Rev. Lett. 100, 220502 (2008).

[Crossref]

A. Rubenok, J. A. Slater, P. Chan, I. Lucio-Martinez, and W. Tittel, “Real-world two-photon interference and proof-of-principle quantum key distribution immune to detector attacks,” Phys. Rev. Lett. 111, 130501 (2013).

[Crossref]

F. Furrer, M. Berta, M. Tomamichel, V. B. Scholz, and M. Christandl, “Position-momentum uncertainty relations in the presence of quantum memory,” J. Math. Phys. 55, 122205 (2014).

[Crossref]

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. Scholz, M. Tomamichel, and R. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109, 100502 (2012).

[Crossref]

M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner, “Tight finite-key analysis for quantum cryptography,” Nat. Commun. 3, 634 (2012).

[Crossref]

M. Tomamichel and R. Renner, “Uncertainty relation for smooth entropies,” Phys. Rev. Lett. 106, 110506 (2011).

[Crossref]

F. Grosshans, N. J. Cerf, P. Grangier, J. Wenger, and R. Tualle-Brouri, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quantum Inf. Comput. 3, 535–552 (2003).

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

H. Maassen and J. Uffink, “Generalized entropic uncertainty relations,” Phys. Rev. Lett. 60, 1103–1106 (1988).

[Crossref]

M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, and A. Zeilinger, “Bell violation using entangled photons without the fair-sampling assumption,” Nature 497, 227–230 (2013).

[Crossref]

B. Wittmann, S. Ramelow, F. Steinlechner, N. K. Langford, N. Brunner, H. M. Wiseman, R. Ursin, and A. Zeilinger, “Loophole-free Einstein–Podolsky–Rosen experiment via quantum steering,” New J. Phys. 14, 053030 (2012).

[Crossref]

U. Vazirani and T. Vidick, “Fully device-independent quantum key distribution,” Phys. Rev. Lett. 113, 140501 (2014).

[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

U. Vazirani and T. Vidick, “Fully device-independent quantum key distribution,” Phys. Rev. Lett. 113, 140501 (2014).

[Crossref]

C. Branciard, E. G. Cavalcanti, S. P. Walborn, V. Scarani, and H. M. Wiseman, “One-sided device-independent quantum key distribution: security, feasibility, and the connection with steering,” Phys. Rev. A 85, 010301 (2012).

[Crossref]

H. M. Chrzanowski, N. Walk, S. M. Assad, J. Janousek, S. Hosseini, T. C. Ralph, T. Symul, and P. K. Lam, “Measurement-based noiseless linear amplification for quantum communication,” Nat. Photonics 8, 333–338 (2014).

[Crossref]

N. Walk, T. C. Ralph, T. Symul, and P. K. Lam, “Security of continuous-variable quantum cryptography with Gaussian postselection,” Phys. Rev. A 87, 020303 (2013).

[Crossref]

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H.-A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9, 397–402 (2015).

[Crossref]

C. Weedbrook, A. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93, 170504 (2004).

[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).

[Crossref]

S. Wehner, M. Curty, C. Schaffner, and H.-K. Lo, “Implementation of two-party protocols in the noisy-storage model,” Phys. Rev. A 81, 052336 (2010).

[Crossref]

S. Wehner, C. Schaffner, and B. Terhal, “Cryptography from noisy storage,” Phys. Rev. Lett. 100, 220502 (2008).

[Crossref]

D. H. Smith, G. Gillett, M. P. de Almeida, C. Branciard, A. Fedrizzi, T. J. Weinhold, A. Lita, B. Calkins, T. Gerrits, H. M. Wiseman, S. W. Nam, and A. G. White, “Conclusive quantum steering with superconducting transition-edge sensors,” Nat. Commun. 3, 625 (2012).

[Crossref]

F. Grosshans, N. J. Cerf, P. Grangier, J. Wenger, and R. Tualle-Brouri, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quantum Inf. Comput. 3, 535–552 (2003).

F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using Gaussian-modulated coherent states,” Nature 421, 238–241 (2003).

[Crossref]

F. Furrer, T. Franz, M. Berta, A. Leverrier, V. Scholz, M. Tomamichel, and R. Werner, “Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks,” Phys. Rev. Lett. 109, 100502 (2012).

[Crossref]

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6, 8795 (2015).

[Crossref]

D. H. Smith, G. Gillett, M. P. de Almeida, C. Branciard, A. Fedrizzi, T. J. Weinhold, A. Lita, B. Calkins, T. Gerrits, H. M. Wiseman, S. W. Nam, and A. G. White, “Conclusive quantum steering with superconducting transition-edge sensors,” Nat. Commun. 3, 625 (2012).

[Crossref]

H. Wiseman, S. Jones, and A. Doherty, “Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox,” Phys. Rev. Lett. 98, 140402 (2007).

[Crossref]

C. Branciard, E. G. Cavalcanti, S. P. Walborn, V. Scarani, and H. M. Wiseman, “One-sided device-independent quantum key distribution: security, feasibility, and the connection with steering,” Phys. Rev. A 85, 010301 (2012).

[Crossref]

D. H. Smith, G. Gillett, M. P. de Almeida, C. Branciard, A. Fedrizzi, T. J. Weinhold, A. Lita, B. Calkins, T. Gerrits, H. M. Wiseman, S. W. Nam, and A. G. White, “Conclusive quantum steering with superconducting transition-edge sensors,” Nat. Commun. 3, 625 (2012).

[Crossref]

B. Wittmann, S. Ramelow, F. Steinlechner, N. K. Langford, N. Brunner, H. M. Wiseman, R. Ursin, and A. Zeilinger, “Loophole-free Einstein–Podolsky–Rosen experiment via quantum steering,” New J. Phys. 14, 053030 (2012).

[Crossref]

A. J. Bennet, D. A. Evans, D. J. Saunders, C. Branciard, E. G. Cavalcanti, H. M. Wiseman, and G. J. Pryde, “Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole,” Phys. Rev. X 2, 031003 (2012).

[Crossref]

M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, and A. Zeilinger, “Bell violation using entangled photons without the fair-sampling assumption,” Nature 497, 227–230 (2013).

[Crossref]

B. Wittmann, S. Ramelow, F. Steinlechner, N. K. Langford, N. Brunner, H. M. Wiseman, R. Ursin, and A. Zeilinger, “Loophole-free Einstein–Podolsky–Rosen experiment via quantum steering,” New J. Phys. 14, 053030 (2012).

[Crossref]

G. Y. Xiang, T. C. Ralph, A. P. Lund, N. Walk, and G. J. Pryde, “Heralded noiseless linear amplification and distillation of entanglement,” Nat. Photonics 4, 316–319 (2010).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, and A. Zeilinger, “Bell violation using entangled photons without the fair-sampling assumption,” Nature 497, 227–230 (2013).

[Crossref]

B. Wittmann, S. Ramelow, F. Steinlechner, N. K. Langford, N. Brunner, H. M. Wiseman, R. Ursin, and A. Zeilinger, “Loophole-free Einstein–Podolsky–Rosen experiment via quantum steering,” New J. Phys. 14, 053030 (2012).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111, 130406 (2013).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).

[Crossref]