Abstract

Nonlocal correlations, a longstanding foundational topic in quantum information, have recently found application as a resource for cryptographic tasks where not all devices are trusted, for example, in settings with a highly secure central hub, such as a bank or government department, and less secure satellite stations, which are inherently more vulnerable to hardware “hacking” attacks. The asymmetric phenomena of Einstein–Podolsky–Rosen (EPR) steering plays a key role in one-sided device-independent (1sDI) quantum key distribution (QKD) protocols. In the context of continuous-variable (CV) QKD schemes utilizing Gaussian states and measurements, we identify all protocols that can be 1sDI and their maximum loss tolerance. Surprisingly, this includes a protocol that uses only coherent states. We also establish a direct link between the relevant EPR steering inequality and the secret key rate, further strengthening the relationship between these asymmetric notions of nonlocality and device independence. We experimentally implement both entanglement-based and coherent-state protocols, and measure the correlations necessary for 1sDI key distribution up to an applied loss equivalent to 7.5 and 3.5 km of optical fiber transmission, respectively. We also engage in detailed modeling to understand the limits of our current experiment and the potential for further improvements. The new protocols we uncover apply the cheap and efficient hardware of CV-QKD systems in a significantly more secure setting.

© 2016 Optical Society of America

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2015 (5)

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]

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. 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]

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

2014 (6)

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]

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

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

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

2013 (8)

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]

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]

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]

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]

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]

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]

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]

2012 (10)

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

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

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]

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]

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

2011 (4)

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

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

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

2010 (5)

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]

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]

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]

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

2009 (2)

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. 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]

2008 (2)

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

2007 (2)

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]

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

2006 (2)

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]

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

2005 (1)

J. Barrett, L. Hardy, and A. Kent, “No signaling and quantum key distribution,” Phys. Rev. Lett. 95, 10503 (2005).
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2004 (1)

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).
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2003 (2)

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).
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2002 (2)

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88, 057902 (2002).
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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).
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2000 (2)

M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A 61, 022309 (2000).
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M. Reid, “Quantum cryptography with a predetermined key, using continuous-variable Einstein-Podolsky-Rosen correlations,” Phys. Rev. A 62, 062308 (2000).
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1999 (1)

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61, 010303 (1999).
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1992 (1)

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).
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1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
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1989 (1)

M. D. Reid, “Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification,” Phys. Rev. A 40, 913–923 (1989).
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1988 (1)

H. Maassen and J. Uffink, “Generalized entropic uncertainty relations,” Phys. Rev. Lett. 60, 1103–1106 (1988).
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1986 (1)

J. S. Bell, “EPR correlations and EPW distributions,” Ann. N.Y. Acad. Sci. 480, 263–266 (1986).
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1975 (1)

I. Białynicki-Birula and J. Mycielski, “Uncertainty relations for information entropy in wave mechanics,” Commun. Math. Phys. 44, 129–132 (1975).
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1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
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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).
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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).
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L. Masanes, S. Pironio, and A. Acín, “Secure device-independent quantum key distribution with causally independent measurement devices,” Nat. Commun. 2, 238 (2011).
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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).
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M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. 97, 190502 (2006).
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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).
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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).
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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).
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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).
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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).
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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).
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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).
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J. Barrett, R. Colbeck, and A. Kent, “Unconditionally secure device-independent quantum key distribution with only two devices,” Phys. Rev. A 86, 062326 (2012).
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J. Barrett, L. Hardy, and A. Kent, “No signaling and quantum key distribution,” Phys. Rev. Lett. 95, 10503 (2005).
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S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schnabel, “Strong Einstein-Podolsky-Rosen steering with unconditional entangled states,” Phys. Rev. A 87, 022104 (2013).
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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).
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J. S. Bell, “EPR correlations and EPW distributions,” Ann. N.Y. Acad. Sci. 480, 263–266 (1986).
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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).
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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).
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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).
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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).
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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).
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M. Berta, F. Furrer, and V. B. Scholz, “The smooth entropy formalism on von Neumann algebras,” arXiv:1107.5460 (2011).

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

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).
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Branciard, C.

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).
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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).
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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).
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Brassard, G.

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.

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

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).
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Brouri, R.

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).
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Brunner, N.

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

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).
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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).
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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).
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Cavalcanti, E. G.

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).
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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).
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Cerf, N.

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

R. Garca-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97, 190503 (2006).
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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).
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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).
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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).
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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).
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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).
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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).
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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).
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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).
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J. Barrett, R. Colbeck, and A. Kent, “Unconditionally secure device-independent quantum key distribution with only two devices,” Phys. Rev. A 86, 062326 (2012).
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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).
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H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).
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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).
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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).
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Duhme, J.

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).
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Dušek, M.

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).
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Eberle, T.

S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schnabel, “Strong Einstein-Podolsky-Rosen steering with unconditional entangled states,” Phys. Rev. A 87, 022104 (2013).
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A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
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A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
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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).
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Evans, D. A.

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

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

Garca-Patrón, R.

R. Garca-Patrón and N. J. Cerf, “Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97, 190503 (2006).
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Supplementary Material (1)

NameDescription
» Supplement 1: PDF (968 KB)      Additional proofs and modelling.

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Figures (5)

Fig. 1.
Fig. 1.

Conceptual picture of a 1sDI-CV-QKD protocol. From the perspective of Alice (Bob) the local devices are known and allow a secret key to be extracted from a direct (reverse) reconciliation protocol, even though the other party exists only as an unknown red (blue) box.

Fig. 2.
Fig. 2.

Secure regions for 1sDI-CV-QKD protocols for a Gaussian channel parameterized by a transmission T and excess noise ξ . DR protocols are plotted in blue when Alice homodynes (or equivalently sends squeezed states) and purple when Alice heterodynes (or equivalently sends coherent states). RR schemes are plotted in red when Bob homodynes and orange when Bob heterodynes. For each protocol, secure communication is possible for all channels above the corresponding line. Inset: summary of 1sDI-CV-QKD protocols where subscript A (B) indicates independence of Alice’s (Bob’s) devices.

Fig. 3.
Fig. 3.

Schematic diagram of all the experimentally realized 1sDI protocols. Alice and Bob can choose between homodyne and heterodyne measurements, using a source that generates either EPR or coherent states. Direct (reverse) reconciliation protocols are demonstrated using right (left) pointing arrows. The table summarizes each performed protocol and the experimentally achieved results. The same color scheme as Fig. 2 is used here to show the different performed protocols.

Fig. 4.
Fig. 4.

Schematic diagram of all the experimental setups. (a)(i) EPR source: OPA1 and OPA2 are two similar optical parametric amplifiers (OPAs), which produced amplitude-squeezed beams. A 1064 nm Nd:YAG laser was used to seed both OPAs. They both generated 6.5    dB of squeezing and 10.7 dB of anti-squeezing. PZT is a piezo-electric crystal and BS is a 50 50 beam splitter. Two amplitude squeezed beams were mixed on a beam splitter with their relative phase locked in quadrature to produce an EPR state. (a)(ii) Optical components used to simulate the lossy channel, which consisted of a half-wave plate and a polarizing beam splitter (PBS). In (b)–(d), one part of the entangled state is sent to Alice locally and the other through a lossy channel to Bob. Here “Hom” refers to alternating homodyne measurements, and “Het” to a heterodyne measurement. The measurement configurations for Alice and Bob are (b) Homodyne (Alice)—Homodyne (Bob), (c) Heterodyne (Alice)—Homodyne (Bob), and (d) Homodyne (Alice)—Heterodyne (Bob). (e) P&M experiment: AM and PM are electro-optic modulators (EOMs) driven by function generators (FG), which, in turn, provided a Gaussian distributed displacement of the vacuum state in amplitude and phase quadratures. The resulting coherent states were then sent to Bob through a lossy channel where he performed a homodyne measurement. Details of the experimental setups are presented in Supplement 1.

Fig. 5.
Fig. 5.

Key rates versus distance for (a) DR and RR protocols with EB source and homodyne–homodyne detection and (b) P&M coherent state DR scheme (protocols 1, 2, and 5 in the table in Fig. 3). Theoretical curves, including imperfect reconciliation efficiency were evaluated from the expressions given in Supplement 1, part 3 using models described in Supplement 1, part 4 and part 5, which took into account the finite reconciliation efficiency β , source and locking imperfection, and optical losses. The experimental data points are superposed on the plot, with error bars (1 standard deviation) estimated from error propagation of uncertainties. (c) Example experimental data points from the EB DR protocol. Phase-space plots show the correlations between the quadratures, P A and P B and X A and X B , measured by Alice and Bob. Using their statistics, the conditional variances are calculated and used to estimate the EPR steering parameters. The circle on the right illustrates the comparison of the measured value of the EPR steering (purple), the necessary condition for obtaining a positive key rate (dashed), and the upper bound for EPR steerability (green). Panels (d) and (e) illustrate circles corresponding to each plotted data point in (a) and (b), showing the connection between the measured values of EPR steering and the generation of positive key rates.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

K I ( X A : X B ) χ ( X B : E ) ,
S ( X B | E ) = H ( X B ) + d x B p ( x B ) S ( ρ E x B ) S ( E ) ,
K H ( X B ) + d x B p ( x B ) S ( ρ E x B ) S ( E ) H ( X B | X A ) = S ( X B | E ) H ( X B | X A ) .
S ( X A | E ) + S ( P A | B ) log 2 π .
K log 4 π H ( X A | X B ) S ( P B | A ) log 4 π H ( X A | X B ) H ( P A | P B ) ,
K log ( 2 e V X B | X A V P B | P A ) .
K log ( 2 e E ) .
K G ( ) log ( 1 E ( ) ) .

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