Abstract

We present a high-fidelity quantum teleportation experiment over a high-loss free-space channel between two laboratories. We teleported six states of three mutually unbiased bases and obtained an average state fidelity of 0.82(1), well beyond the classical limit of 2/3. With the obtained data, we tomographically reconstructed the process matrices of quantum teleportation. The free-space channel attenuation of 31 dB corresponds to the estimated attenuation regime for a down-link from a low-earth-orbit satellite to a ground station. We also discussed various important technical issues for future experiments, including the dark counts of single-photon detectors, coincidence-window width etc. Our experiment tested the limit of performing quantum teleportation with state-of-the-art resources. It is an important step towards future satellite-based quantum teleportation and paves the way for establishing a worldwide quantum communication network.

© 2012 OSA

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2011 (1)

Y.-S. Kim, Y.-C. Jeong, S. Sauge, V. Makarov, and Y.-H. Kim “Ultra-low noise single-photon detector based on Si avalanche photodiode,” Rev. Sci. Instrum. 82, 093110 (2011).
[Crossref] [PubMed]

2010 (4)

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photon. 4, 376–381 (2010).
[Crossref]

T. Scheidl, R. Ursin, J. Kofler, S. Ramelow, X.-S. Ma, T. Herbst, L. Ratschbacher, A. Fedrizzi, N. K. Langford, T. Jennewein, and A. Zeilinger “Violation of local realism with freedom of choice,” Proc. Natl. Acad. Sci. USA 107, 19709–19713 (2010).
[Crossref]

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature 464, 45–53 (2010).
[Crossref] [PubMed]

M. Stipčević, H. Skenderović, and D. Gracin “Characterization of a novel avalanche photodiode for single photon detection in VIS-NIR range,” Opt. Express. 18, 17448–17459 (2010).
[Crossref]

2009 (2)

A. Fedrizzi, R. Ursin, T. Herbst, M. Nespoli, R. Prevedel, T. Scheidl, F. Tiefenbacher, T. Jennewein, and A. Zeilinger, “High-fidelity transmission of entanglement over a high-loss free-space channel,” Nat. Phys. 5, 389–392 (2009).
[Crossref]

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11085002 (2009).
[Crossref]

2008 (1)

P. Villoresi, T. Jennewein, F. Tamburini, M. Aspelmeyer, C. Bonato, R. Ursin, C. Pernechele, V. Luceri, G. Bianco, A. Zeilinger, and C. Barbieri, “Experimental verification of the feasibility of a quantum channel between space and Earth,” New J. Phys. 10, 033038 (2008).
[Crossref]

2007 (3)

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Free-space distribution of entanglement and single photons over 144 km,” Nat. Phys. 3, 481–486 (2007).
[Crossref]

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692–695 (2007).
[Crossref]

2005 (2)

K. Resch, M. Lindenthal, B. Blauensteiner, H. R. Böhm, A. Fedrizzi, C. Kurtsiefer, A. Poppe, T. Schmitt-Manderbach, M. Taraba, R. Ursin, P. Walther, H. Weier, H. Weinfurter, and A. Zeilinger, “Distributing entanglement and single photons through an intra-city free-space quantum channel,” Opt. Express 13, 202–209 (2005)
[Crossref] [PubMed]

C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over a noisy ground atmosphere of 13 km: towards satellite-based global quantum communication,” Phys. Rev. Lett. 94, 150501 (2005).
[Crossref] [PubMed]

2004 (1)

R. Ursin, T. Jennewein, M. Aspelmeyer, R. Kaltenbaek, M. Lindenthal, P. Walther, and A. Zeilinger, “Quantum teleportation across the Danube,” Nature 430, 849 (2004).
[Crossref] [PubMed]

2003 (3)

I. Marcikic, H. De Riedmatten, W. Tittel, H. Zbinden, and N. Gisin, “Long distance teleportation of qubits at telecommunication wavelengths,” Nature 421, 509–513 (2003).
[Crossref] [PubMed]

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. Leeb, and A. Zeilinger “Long-distance quantum communication with entangled photons using satellites,” IEEE J. Sel. Top. Quantum Electron. 9, 1541–1551 (2003).
[Crossref]

M. Aspelmeyer, H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, “Long-distance free-space distribution of quantum entanglement,” Science 301, 621–623 (2003).
[Crossref] [PubMed]

2002 (2)

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4, 43.1–43.14 (2002).
[Crossref]

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, “Quantum cryptography: a step towards global key distribution,” Nature 419, 450 (2002).
[Crossref] [PubMed]

2001 (4)

L. M. Duan, M. D. Lukin, J. I Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[Crossref] [PubMed]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref] [PubMed]

J. Calsamiglia and Norbert Lütkenhaus, “Maximum efficiency of a linear-optical Bell-state analyzer,” Appl. Phys. B 72, 67–71 (2001).
[Crossref]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White “Measurement of qubits,” Phys. Rev. A,  64, 052312 (2001).
[Crossref]

1999 (2)

A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, “Nonmaximally entangled states: Production, characterization, and utilization,” Phys. Rev. Lett. 83, 3103–3107 (1999).
[Crossref]

D. Gottesmann and I. L. Chuang, “Quantum teleportation is a universal computational primitive,” Nature 402, 390–393 (1999).
[Crossref]

1998 (3)

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[Crossref]

S. Bose, V. Vedral, and P. L. Knight, “Multiparticle generalization of entanglement swapping,” Phys. Rev. A 57, 822–829 (1998).
[Crossref]

H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[Crossref]

1997 (1)

D. Bouwmeester, J. W. Pan, K. Mattle, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

1994 (1)

S. Popescu, “Bell’s inequalities versus teleportation: What is nonlocality?” Phys. Rev. Lett. 72, 797–799 (1994).
[Crossref] [PubMed]

1993 (2)

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

M. Žukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “‘Event-ready-detectors’ Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
[Crossref] [PubMed]

1992 (1)

B. Yurke and D. Stoler, “Bell’s-inequality experiments using independent-particle sources,” Phys. Rev. A 46, 2229–2234 (1992).
[Crossref] [PubMed]

1982 (1)

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802–803 (1982).
[Crossref]

Aspelmeyer, M.

P. Villoresi, T. Jennewein, F. Tamburini, M. Aspelmeyer, C. Bonato, R. Ursin, C. Pernechele, V. Luceri, G. Bianco, A. Zeilinger, and C. Barbieri, “Experimental verification of the feasibility of a quantum channel between space and Earth,” New J. Phys. 10, 033038 (2008).
[Crossref]

R. Ursin, T. Jennewein, M. Aspelmeyer, R. Kaltenbaek, M. Lindenthal, P. Walther, and A. Zeilinger, “Quantum teleportation across the Danube,” Nature 430, 849 (2004).
[Crossref] [PubMed]

M. Aspelmeyer, H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, “Long-distance free-space distribution of quantum entanglement,” Science 301, 621–623 (2003).
[Crossref] [PubMed]

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. Leeb, and A. Zeilinger “Long-distance quantum communication with entangled photons using satellites,” IEEE J. Sel. Top. Quantum Electron. 9, 1541–1551 (2003).
[Crossref]

Bao, X.-H.

C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over a noisy ground atmosphere of 13 km: towards satellite-based global quantum communication,” Phys. Rev. Lett. 94, 150501 (2005).
[Crossref] [PubMed]

Barbieri, C.

P. Villoresi, T. Jennewein, F. Tamburini, M. Aspelmeyer, C. Bonato, R. Ursin, C. Pernechele, V. Luceri, G. Bianco, A. Zeilinger, and C. Barbieri, “Experimental verification of the feasibility of a quantum channel between space and Earth,” New J. Phys. 10, 033038 (2008).
[Crossref]

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Free-space distribution of entanglement and single photons over 144 km,” Nat. Phys. 3, 481–486 (2007).
[Crossref]

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Beveratos, A.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692–695 (2007).
[Crossref]

Bianco, G.

P. Villoresi, T. Jennewein, F. Tamburini, M. Aspelmeyer, C. Bonato, R. Ursin, C. Pernechele, V. Luceri, G. Bianco, A. Zeilinger, and C. Barbieri, “Experimental verification of the feasibility of a quantum channel between space and Earth,” New J. Phys. 10, 033038 (2008).
[Crossref]

Blauensteiner, B.

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Free-space distribution of entanglement and single photons over 144 km,” Nat. Phys. 3, 481–486 (2007).
[Crossref]

K. Resch, M. Lindenthal, B. Blauensteiner, H. R. Böhm, A. Fedrizzi, C. Kurtsiefer, A. Poppe, T. Schmitt-Manderbach, M. Taraba, R. Ursin, P. Walther, H. Weier, H. Weinfurter, and A. Zeilinger, “Distributing entanglement and single photons through an intra-city free-space quantum channel,” Opt. Express 13, 202–209 (2005)
[Crossref] [PubMed]

Böhm, H. R.

K. Resch, M. Lindenthal, B. Blauensteiner, H. R. Böhm, A. Fedrizzi, C. Kurtsiefer, A. Poppe, T. Schmitt-Manderbach, M. Taraba, R. Ursin, P. Walther, H. Weier, H. Weinfurter, and A. Zeilinger, “Distributing entanglement and single photons through an intra-city free-space quantum channel,” Opt. Express 13, 202–209 (2005)
[Crossref] [PubMed]

M. Aspelmeyer, H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, “Long-distance free-space distribution of quantum entanglement,” Science 301, 621–623 (2003).
[Crossref] [PubMed]

Bonato, C.

P. Villoresi, T. Jennewein, F. Tamburini, M. Aspelmeyer, C. Bonato, R. Ursin, C. Pernechele, V. Luceri, G. Bianco, A. Zeilinger, and C. Barbieri, “Experimental verification of the feasibility of a quantum channel between space and Earth,” New J. Phys. 10, 033038 (2008).
[Crossref]

Boschi, D.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[Crossref]

Bose, S.

S. Bose, V. Vedral, and P. L. Knight, “Multiparticle generalization of entanglement swapping,” Phys. Rev. A 57, 822–829 (1998).
[Crossref]

Bouwmeester, D.

D. Bouwmeester, J. W. Pan, K. Mattle, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Branca, S.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[Crossref]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Briegel, H. J.

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R. Ursin, T. Jennewein, M. Aspelmeyer, R. Kaltenbaek, M. Lindenthal, P. Walther, and A. Zeilinger, “Quantum teleportation across the Danube,” Nature 430, 849 (2004).
[Crossref] [PubMed]

M. Aspelmeyer, H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, “Long-distance free-space distribution of quantum entanglement,” Science 301, 621–623 (2003).
[Crossref] [PubMed]

Wang, S.-K.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photon. 4, 376–381 (2010).
[Crossref]

Weier, H.

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Free-space distribution of entanglement and single photons over 144 km,” Nat. Phys. 3, 481–486 (2007).
[Crossref]

K. Resch, M. Lindenthal, B. Blauensteiner, H. R. Böhm, A. Fedrizzi, C. Kurtsiefer, A. Poppe, T. Schmitt-Manderbach, M. Taraba, R. Ursin, P. Walther, H. Weier, H. Weinfurter, and A. Zeilinger, “Distributing entanglement and single photons through an intra-city free-space quantum channel,” Opt. Express 13, 202–209 (2005)
[Crossref] [PubMed]

Weinfurter, H.

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Free-space distribution of entanglement and single photons over 144 km,” Nat. Phys. 3, 481–486 (2007).
[Crossref]

K. Resch, M. Lindenthal, B. Blauensteiner, H. R. Böhm, A. Fedrizzi, C. Kurtsiefer, A. Poppe, T. Schmitt-Manderbach, M. Taraba, R. Ursin, P. Walther, H. Weier, H. Weinfurter, and A. Zeilinger, “Distributing entanglement and single photons through an intra-city free-space quantum channel,” Opt. Express 13, 202–209 (2005)
[Crossref] [PubMed]

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, “Quantum cryptography: a step towards global key distribution,” Nature 419, 450 (2002).
[Crossref] [PubMed]

D. Bouwmeester, J. W. Pan, K. Mattle, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

White, A. G.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White “Measurement of qubits,” Phys. Rev. A,  64, 052312 (2001).
[Crossref]

A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, “Nonmaximally entangled states: Production, characterization, and utilization,” Phys. Rev. Lett. 83, 3103–3107 (1999).
[Crossref]

Wootters, W. K.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802–803 (1982).
[Crossref]

Xu, X.-F.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photon. 4, 376–381 (2010).
[Crossref]

Yang, B.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photon. 4, 376–381 (2010).
[Crossref]

C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over a noisy ground atmosphere of 13 km: towards satellite-based global quantum communication,” Phys. Rev. Lett. 94, 150501 (2005).
[Crossref] [PubMed]

Yang, D.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photon. 4, 376–381 (2010).
[Crossref]

Yang, J.

C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over a noisy ground atmosphere of 13 km: towards satellite-based global quantum communication,” Phys. Rev. Lett. 94, 150501 (2005).
[Crossref] [PubMed]

Yang, T.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photon. 4, 376–381 (2010).
[Crossref]

C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over a noisy ground atmosphere of 13 km: towards satellite-based global quantum communication,” Phys. Rev. Lett. 94, 150501 (2005).
[Crossref] [PubMed]

Yi, Z.-H.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photon. 4, 376–381 (2010).
[Crossref]

Yin, H.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photon. 4, 376–381 (2010).
[Crossref]

Yin, J.

C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over a noisy ground atmosphere of 13 km: towards satellite-based global quantum communication,” Phys. Rev. Lett. 94, 150501 (2005).
[Crossref] [PubMed]

Yurke, B.

B. Yurke and D. Stoler, “Bell’s-inequality experiments using independent-particle sources,” Phys. Rev. A 46, 2229–2234 (1992).
[Crossref] [PubMed]

Zarda, P.

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, “Quantum cryptography: a step towards global key distribution,” Nature 419, 450 (2002).
[Crossref] [PubMed]

Zbinden, H.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692–695 (2007).
[Crossref]

I. Marcikic, H. De Riedmatten, W. Tittel, H. Zbinden, and N. Gisin, “Long distance teleportation of qubits at telecommunication wavelengths,” Nature 421, 509–513 (2003).
[Crossref] [PubMed]

Zeilinger, A.

T. Scheidl, R. Ursin, J. Kofler, S. Ramelow, X.-S. Ma, T. Herbst, L. Ratschbacher, A. Fedrizzi, N. K. Langford, T. Jennewein, and A. Zeilinger “Violation of local realism with freedom of choice,” Proc. Natl. Acad. Sci. USA 107, 19709–19713 (2010).
[Crossref]

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11085002 (2009).
[Crossref]

A. Fedrizzi, R. Ursin, T. Herbst, M. Nespoli, R. Prevedel, T. Scheidl, F. Tiefenbacher, T. Jennewein, and A. Zeilinger, “High-fidelity transmission of entanglement over a high-loss free-space channel,” Nat. Phys. 5, 389–392 (2009).
[Crossref]

P. Villoresi, T. Jennewein, F. Tamburini, M. Aspelmeyer, C. Bonato, R. Ursin, C. Pernechele, V. Luceri, G. Bianco, A. Zeilinger, and C. Barbieri, “Experimental verification of the feasibility of a quantum channel between space and Earth,” New J. Phys. 10, 033038 (2008).
[Crossref]

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Free-space distribution of entanglement and single photons over 144 km,” Nat. Phys. 3, 481–486 (2007).
[Crossref]

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref] [PubMed]

K. Resch, M. Lindenthal, B. Blauensteiner, H. R. Böhm, A. Fedrizzi, C. Kurtsiefer, A. Poppe, T. Schmitt-Manderbach, M. Taraba, R. Ursin, P. Walther, H. Weier, H. Weinfurter, and A. Zeilinger, “Distributing entanglement and single photons through an intra-city free-space quantum channel,” Opt. Express 13, 202–209 (2005)
[Crossref] [PubMed]

R. Ursin, T. Jennewein, M. Aspelmeyer, R. Kaltenbaek, M. Lindenthal, P. Walther, and A. Zeilinger, “Quantum teleportation across the Danube,” Nature 430, 849 (2004).
[Crossref] [PubMed]

M. Aspelmeyer, H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, “Long-distance free-space distribution of quantum entanglement,” Science 301, 621–623 (2003).
[Crossref] [PubMed]

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. Leeb, and A. Zeilinger “Long-distance quantum communication with entangled photons using satellites,” IEEE J. Sel. Top. Quantum Electron. 9, 1541–1551 (2003).
[Crossref]

D. Bouwmeester, J. W. Pan, K. Mattle, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

M. Žukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “‘Event-ready-detectors’ Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
[Crossref] [PubMed]

Zhang, J.

C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over a noisy ground atmosphere of 13 km: towards satellite-based global quantum communication,” Phys. Rev. Lett. 94, 150501 (2005).
[Crossref] [PubMed]

Zhang, Q.

C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over a noisy ground atmosphere of 13 km: towards satellite-based global quantum communication,” Phys. Rev. Lett. 94, 150501 (2005).
[Crossref] [PubMed]

Zhou, F.

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photon. 4, 376–381 (2010).
[Crossref]

Zoller, P.

L. M. Duan, M. D. Lukin, J. I Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[Crossref] [PubMed]

H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[Crossref]

Žukowski, M.

M. Žukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “‘Event-ready-detectors’ Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
[Crossref] [PubMed]

Zurek, W. H.

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802–803 (1982).
[Crossref]

Appl. Phys. B (1)

J. Calsamiglia and Norbert Lütkenhaus, “Maximum efficiency of a linear-optical Bell-state analyzer,” Appl. Phys. B 72, 67–71 (2001).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

M. Aspelmeyer, T. Jennewein, M. Pfennigbauer, W. Leeb, and A. Zeilinger “Long-distance quantum communication with entangled photons using satellites,” IEEE J. Sel. Top. Quantum Electron. 9, 1541–1551 (2003).
[Crossref]

Nat. Photon. (1)

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photon. 4, 376–381 (2010).
[Crossref]

Nat. Phys. (3)

A. Fedrizzi, R. Ursin, T. Herbst, M. Nespoli, R. Prevedel, T. Scheidl, F. Tiefenbacher, T. Jennewein, and A. Zeilinger, “High-fidelity transmission of entanglement over a high-loss free-space channel,” Nat. Phys. 5, 389–392 (2009).
[Crossref]

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692–695 (2007).
[Crossref]

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Free-space distribution of entanglement and single photons over 144 km,” Nat. Phys. 3, 481–486 (2007).
[Crossref]

Nature (9)

I. Marcikic, H. De Riedmatten, W. Tittel, H. Zbinden, and N. Gisin, “Long distance teleportation of qubits at telecommunication wavelengths,” Nature 421, 509–513 (2003).
[Crossref] [PubMed]

R. Ursin, T. Jennewein, M. Aspelmeyer, R. Kaltenbaek, M. Lindenthal, P. Walther, and A. Zeilinger, “Quantum teleportation across the Danube,” Nature 430, 849 (2004).
[Crossref] [PubMed]

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, “Quantum cryptography: a step towards global key distribution,” Nature 419, 450 (2002).
[Crossref] [PubMed]

D. Gottesmann and I. L. Chuang, “Quantum teleportation is a universal computational primitive,” Nature 402, 390–393 (1999).
[Crossref]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
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T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature 464, 45–53 (2010).
[Crossref] [PubMed]

D. Bouwmeester, J. W. Pan, K. Mattle, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

L. M. Duan, M. D. Lukin, J. I Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[Crossref] [PubMed]

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802–803 (1982).
[Crossref]

New J. Phys. (3)

T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X.-S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys. 11085002 (2009).
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R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4, 43.1–43.14 (2002).
[Crossref]

P. Villoresi, T. Jennewein, F. Tamburini, M. Aspelmeyer, C. Bonato, R. Ursin, C. Pernechele, V. Luceri, G. Bianco, A. Zeilinger, and C. Barbieri, “Experimental verification of the feasibility of a quantum channel between space and Earth,” New J. Phys. 10, 033038 (2008).
[Crossref]

Opt. Express (1)

Opt. Express. (1)

M. Stipčević, H. Skenderović, and D. Gracin “Characterization of a novel avalanche photodiode for single photon detection in VIS-NIR range,” Opt. Express. 18, 17448–17459 (2010).
[Crossref]

Phys. Rev. A (3)

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White “Measurement of qubits,” Phys. Rev. A,  64, 052312 (2001).
[Crossref]

S. Bose, V. Vedral, and P. L. Knight, “Multiparticle generalization of entanglement swapping,” Phys. Rev. A 57, 822–829 (1998).
[Crossref]

B. Yurke and D. Stoler, “Bell’s-inequality experiments using independent-particle sources,” Phys. Rev. A 46, 2229–2234 (1992).
[Crossref] [PubMed]

Phys. Rev. Lett. (9)

M. Žukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “‘Event-ready-detectors’ Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
[Crossref] [PubMed]

H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[Crossref]

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[Crossref]

C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over a noisy ground atmosphere of 13 km: towards satellite-based global quantum communication,” Phys. Rev. Lett. 94, 150501 (2005).
[Crossref] [PubMed]

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
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S. Popescu, “Bell’s inequalities versus teleportation: What is nonlocality?” Phys. Rev. Lett. 72, 797–799 (1994).
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C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, “Nonmaximally entangled states: Production, characterization, and utilization,” Phys. Rev. Lett. 83, 3103–3107 (1999).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

T. Scheidl, R. Ursin, J. Kofler, S. Ramelow, X.-S. Ma, T. Herbst, L. Ratschbacher, A. Fedrizzi, N. K. Langford, T. Jennewein, and A. Zeilinger “Violation of local realism with freedom of choice,” Proc. Natl. Acad. Sci. USA 107, 19709–19713 (2010).
[Crossref]

Rev. Sci. Instrum. (1)

Y.-S. Kim, Y.-C. Jeong, S. Sauge, V. Makarov, and Y.-H. Kim “Ultra-low noise single-photon detector based on Si avalanche photodiode,” Rev. Sci. Instrum. 82, 093110 (2011).
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Science (1)

M. Aspelmeyer, H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, “Long-distance free-space distribution of quantum entanglement,” Science 301, 621–623 (2003).
[Crossref] [PubMed]

Other (1)

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000), pp. 377, 393.

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Figures (5)

Fig. 1
Fig. 1

The setup for quantum teleportation over a high-loss channel. We up-convert near-infrared femtosecond pulses (central wavelength of 808 nm) emitted from a mode-locked Ti:Sapphire laser to blue pulses (central wavelength of 404 nm) via a β-barium borate crystal (BBO0). Polarization-entangled photon pairs, photons 1 and 2, are produced by using photon emissions of a non-collinear type-II spontaneous parametric down conversion from BBO1 and sent to Alice and Bob. Photon 2 is delayed with a 50 m single-mode fiber and then sent to Bob. The input photon of teleportation, photon 3, is generated from BBO2 via a collinear heralded single-photon source. Alice performs a Bell-state measurement (BSM) on photons 1 and 3 via fiber beam splitter (FBS) and can unambiguously identify the results of singlet (|Ψ13) or triplet (|Ψ+13). These BSM results are then encoded in a 1064 nm laser via an encoder and sent to Bob. We use a 532 nm laser and a charge-coupled device (CCD) camera to simulate the tracking and pointing system, which will be required in an experiment between satellites and ground stations. The beams of photon 2, of the 1064 nm laser and of the 532 nm laser are multiplexed to a common optical path by means of various dichroic mirrors at Alice’s side and propagate along the hallway connecting two separate labs and through keyholes of of both doors. On Bob’s side, we demultiplex the three beams and perform feed-forward operations with a photodetector (PD), a decoder and an electro-optical modulator (EOM). The 3 nm interference filters (IF) are employed to eliminate the spectral distinguishability of single photons. The combination of a quarter-wave plate (QWP), a half-wave plate (HWP), a polarization beam splitter (PBS) and avalanche photodiodes (APD, D1-D6) is used to measure the polarization state of single photons. Various neutral density filters (NDF) are used to vary the attenuation of the link. Polarization controllers (PC) are used to compensate the unwanted polarization rotation induced by fibers. See text for details.

Fig. 2
Fig. 2

State fidelity results for the six unbiased-basis states teleported from Alice to Bob over a high-loss (−31 dB) free-space channel. The observed fidelities, f, of the teleported quantum states are: |H〉 with fidelity f = 0.87(1), |V〉 with f = 0.83(1), |P〉 = |H〉 + |V〉 with f = 0.90(1), |P〉 = |H〉 − |V〉 with f = 0.74(1), |R〉 = |H〉 + i|V〉 with f = 0.81(1), |L〉 = |H〉 − i|V〉 with f = 0.80(1). All fidelities significantly exceed the average classical limit of 2/3. The data shown comprise a total of 9891 four-fold coincidence counts in about 50 hours summed over all input states. Error bars are given by Poissonian statistics.

Fig. 3
Fig. 3

(A) The real part of the reconstructed quantum process matrix, Re(χlk), with l, k = 0, 1, 2, and 3 with feed-forward operation. The process matrix of quantum state teleportation is reconstructed from the state tomography of the six mutually unbiased bases states teleported between Alice and Bob. The operators σi are the identity (i = 0) and the x-, y-, and z-Pauli matrices (i = 1, 2, 3). As intended, the dominant component of χlk is the contribution of the identity operation, yielding an overall process fidelity fprocess = tr(χidealχ) = 0.77(1). The plot in (B) shows how the input states lying on the surface of the initial Bloch sphere (meshed surface) are transformed by our teleportation protocol, with the output states lying on the solid blue surface. (C) The real part of the reconstructed quantum process matrix, Re(χlk), with l, k = 0, 1, 2, 3 without feed-forward operation. The quantum process fidelity fprocess = tr(χidealχ) = 0.24(2). The resultant low fidelity is due to the lack of feed-forward operation. This can be also visualized in (D), where the pure input states (meshed surface) are transformed into a mixture (solid blue surface).

Fig. 4
Fig. 4

Teleportation visibility and count rate depending on the link attenuation. The measurements were completed on a setup in a single room and without feed-forward, but otherwise the same as the final experiment. The red squares and the blue circles are the experimentally obtained visibilities and teleportation rate (4-fold coincidence count rate), respectively. The red and blue curves are the predictions of our model. Note that the tele-portation rate becomes steady above 50 dB. This is because the dominant contribution to the teleportation rate in this attenuation regime is a four-fold coincidence arising from a three-fold coincidence at Alice’s side and a dark count at Bob’s side. The error bars are calculated based on a Poissonian distribution.

Fig. 5
Fig. 5

(A) Teleportation visibility vs coincidence-window width. We measure the teleportation visibility with a time-tagging unit and vary the coincidence-window widthin data post processing from 1 ns to 29 ns. The visibility and the numbers of standard deviation (B) violating the classic bound (black straight line in A) of teleportation in general reduces as we increase the coincidence-window width. An obvious drop in both visibility and number of the standard deviation is pointed out. It is due to the increased accidental coincidence counts between consecutive laser pulses, separated by 12.5 ns. This set of data is measured under 31 dB, in 2 hours.

Equations (3)

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| Ψ 12 = 1 2 ( | H 1 | V 2 | V 1 | H 2 ) ,
| ϕ 3 = α | H + β | V ,
SNR = η n 1 τ .

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