Abstract

Entanglement is an essential resource in current experimental implementations for quantum information processing. We review a class of experiments exploiting photonic entanglement, ranging from one-way quantum computing over quantum communication complexity to long-distance quantum communication. We then propose a set of feasible experiments, that will exploit the advantages of photonic entanglement for quantum information processing.

© 2007 Optical Society of America

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2006

A.-N. Zhang, C.-Y. Lu, X.-Q. Zhou, Y.-A. Chen, Z. Zhao, T. Yang, and J.-W. Pan, "Experimental construction of optical multiqubit cluster states from Bell states," Phys. Rev. A 73, 022330 (2006).
[CrossRef]

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, "Experimental quantum cryptography with qutrits," New J. Phys. 8, 75 (2006).
[CrossRef]

R. Kaltenbaek, B. Blauensteiner, M. Zukowski, M. Aspelmeyer, and A. Zeilinger, "Experimental interference of independent photons," Phys. Rev. Lett. 96, 240502 (2006).
[CrossRef] [PubMed]

2005

P. Trojek, C. Schmid, M. Bourennane, C. Brukner, M. Zukowski, and H. Weinfurter, "Experimental quantum communication complexity," Phys. Rev. A 72, 050305(R) (2005).
[CrossRef]

K. Resch, M. Lindenthal, B. Blauensteiner, H. 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 13km: towards satellite-based global quantum communication," Phys. Rev. Lett. 94, 150501 (2005).
[CrossRef] [PubMed]

N. K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, A. Gilchrist, J. L. O'Brien, G. J. Pryde, and A. G. White, "Demonstration of a simple entangling optical gate and its use in Bell-state analysis," Phys. Rev. Lett. 95, 210504 (2005).
[CrossRef] [PubMed]

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, "Linear optics controlled-phase gate made simple," Phys. Rev. Lett. 95, 210505 (2005).
[CrossRef] [PubMed]

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, "Demonstration of an optical quantum controlled-NOT gate without path interference," Phys. Rev. Lett. 95, 210506 (2005).
[CrossRef] [PubMed]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).
[CrossRef] [PubMed]

N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Gühne, R. Ursin, and H. Weinfurter, "Experimental analysis of a four-qubit photon cluster state," Phys. Rev. Lett. 95, 210502 (2005).
[CrossRef] [PubMed]

2004

M. A. Nielsen, "Optical quantum computation using cluster states," Phys. Rev. Lett. 93, 040503 (2004).
[CrossRef] [PubMed]

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

M. Riebe, H. Häffner, C. F. Roos, W. Hänsel, J. Benhelm, G. P. T. Lancaster, T. W. Körber, C. Becher, F. Schmidt-Kaler, D. F. V. James, and R. Blatt, "Deterministic quantum teleportation with atoms," Nature 429, 734-737 (2004).
[CrossRef] [PubMed]

M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, "Quantum teleportation with atomic qubits," Nature 429, 737-739 (2004).
[CrossRef] [PubMed]

C. Brukner, M. Zukowski, J.-W. Pan, and A. Zeilinger, "Bell's equalities and quantum communication complexity," Phys. Rev. Lett. 92, 127901 (2004).
[CrossRef] [PubMed]

2003

C. Brukner, T. Paterek, and M. Zukowski, "Quantum communication complexity protocols based on higher-dimensional entangled systems," Int. J. Quantum Inf. 1, 519-525 (2003).
[CrossRef]

J.-W. Pan, S. Gasparoni, R. Ursin, G. Weihs, and A. Zeilinger, "Experimental entanglement purification," Nature 423, 417-422 (2003).
[CrossRef] [PubMed]

M. Aspelmeyer, H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbae, 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. R. Leeb, and A. Zeilinger, "Long-distance quantum communication with entangled photons using satellites," IEEE J. Sel. Top. Quantum Electron. 9, 1541-1551 (2003).
[CrossRef]

2002

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, "Practical free-space quantum key distribution over 10km in daylight and at night," New J. Phys. 4, 43 (2002).
[CrossRef]

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, "A step towards global key distribution," Nature 419, 450-450 (2002).
[CrossRef] [PubMed]

J. E. Nordholt, R. Hughes, G. L. Morgan, C. G. Peterson, and C. C. Wipf, "Present and future free-space quantum key distribution," in Free-Space Laser Communication Technologies XIV, Proc. SPIE 4635, 116-126 (2002).
[CrossRef]

J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, "Ground to satellite secure key exchange using quantum cryptography," New J. Phys. 4, 82 (2002).
[CrossRef]

T. Jennewein, G. Weihs, J.-W. Pan, and A. Zeilinger, "Experimental nonlocality proof of quantum teleportation and entanglement + swapping," Phys. Rev. Lett. 88, 017903 (2002).
[CrossRef] [PubMed]

E. F. Galvao, "Feasible quantum communication complexity protocol," Phys. Rev. A 65, 012318 (2002).
[CrossRef]

C. Brukner, M. Zukowski, and A. Zeilinger, "Quantum communication complexity protocol with two entangled qutrits," Phys. Rev. Lett. 89, 197901 (2002).
[CrossRef] [PubMed]

S. Giacomini, F. Sciarrino, E. Lombardi, and F. D. Martini, "Active teleportation of a quantum bit," Phys. Rev. A 66, 030302(R) (2002).
[CrossRef]

T. B. Pittman, B. C. Jacobs, and J. D. Franson, "Demonstration of feed-forward control for linear optics quantum computation," Phys. Rev. A 66, 052305 (2002).
[CrossRef]

2001

R. Raussendorf and H. J. Briegel, "A one-way quantum computer," Phys. Rev. Lett. 86, 5188-5191 (2001).
[CrossRef] [PubMed]

L. M. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, M. H. Sherwood, and I. L. Chuang, "Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance," Nature 414, 883-887 (2001).
[CrossRef]

J. Rarity, P. Tapster, and P. Gorman, "Secure free-space key exchange to 1.9km and beyond," J. Mod. Opt. 48, 1887-1901 (2001).
[CrossRef]

2000

T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, "Quantum cryptography with entangled photons," Phys. Rev. Lett. 84, 4729-4732 (2000).
[CrossRef] [PubMed]

D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, "Entangled state quantum cryptography: eavesdropping on the Ekert protocol," Phys. Rev. Lett. 84, 4733-4736 (2000).
[CrossRef] [PubMed]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, "Quantum cryptography using entangled photons in energy-time Bell states," Phys. Rev. Lett. 84, 4737-4740 (2000).
[CrossRef] [PubMed]

E. Knill, R. Laflamme, and G. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2000).
[CrossRef]

1998

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, "Violation of Bell's inequality under strict Einstein locality conditions," Phys. Rev. Lett. 81, 5039-5043 (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

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurte, and A. Zeilinger, "Experimental quantum teleportation," Nature 390, 575-579 (1997).
[CrossRef]

R. Cleve and H. Buhrman, "Substituting quantum entanglement for communication," Phys. Rev. A 56, 1201-1204 (1997).
[CrossRef]

1996

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, "Dense coding in experimental quantum communication," Phys. Rev. Lett. 76, 4656-4659 (1996).
[CrossRef] [PubMed]

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, "Purification of noisy entanglement and faithful teleportation via noise channels," Phys. Rev. Lett. 76, 722-725 (1996).
[CrossRef] [PubMed]

B. Jacobs and J. Franson, "Quantum cryptography in free space," Opt. Lett. 21, 1854-1856 (1996)
[CrossRef] [PubMed]

1995

M. Zukowski, A. Zeilinger, and H. Weinfurter, "Entangling photons radiated by independent pulsed sources," Ann. N.Y. Acad. Sci. 755, 91-102 (1995).
[CrossRef]

1993

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).
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R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Oemer, M. Fuerst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, "Free-space distribution of entanglement and single photons over 144km," arxiv.org e-print archive, quant-ph/0607182, July 27, 2006, http://arxiv.org/abs/quant-ph/0607182.

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Strictly speaking, in communication complexity problems of Ref. each party i receives two one-bit inputs (xi,yi), and their goal is to compute a function of the form F(x1,y1,...,xn,yn)=y1∙···∙yn∙f(x1,...,xn). The values of the function f and the yi are ±1. Each party is allowed to broadcast only one bit of information (denoted as ei). For the present analysis, the existence of inputs yi is not of importance and is ommitted here. See Ref. for details.

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Figures (4)

Fig. 1
Fig. 1

Circuit diagram showing the principle idea of error correction via feed forward for one-way quantum computing.

Fig. 2
Fig. 2

Dotted volume indicates the region where the visibility V, detection efficiency η, and the number of partners n allow for a multiparty quantum communication complexity protocol, which is more efficient than any classical one for the same task. The volume corresponds to that given by inequality (7).

Fig. 3
Fig. 3

(Left) Setup demonstrating the photon manipulation by a spatial light modulator (SLM) (Ref. [46]). The photon pairs produced by downconversion in a β-barium borate (BBO crystal; L, focusing lens) are entangled in their orbital angular momentum, represented by the Laguerre–Gaussian mode functions. The mode index corresponds to the orbital angular momentum of each photon. The transformation between different modes is performed by passing the photons through phase diffraction gratings containing a phase singularity, which is generated by the SLM. Analyzer holograms in different modes behind beamsplitters (BS) are used to confirm the mode index. (Right) Demonstrating the transformation of the photon by the computer-calculated hologram on the SLM. The coincidence between the detectors D 0 A and D 1 B is shown. Due to the initial correlation between the photons, there are little coincidence counts, unless the SLM performs a 1 transformation. This clearly demonstrates that we are able to manipulate the orbital angular momentum of the entangled photon by means of the computer-generated hologram.

Fig. 4
Fig. 4

Quantum communication links realized as uplinks from ground to space. Entangled photons or single photons are generated on the ground and sent toward one or more space-based receivers. If only one receiver is available, link (a) will allow single quantum communication. If this were a geostationary Earth orbit (GEO) satellite, several ground stations could see the very same receiver, for successive quantum key exchanges [link (d)]. If a second receiver were available, e.g., also in GEO [link (b)] or in low-Earth orbit (LEO) [link (c)], also the study of fundamental aspects of quantum entanglement over large distances may be accomplished.

Tables (1)

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Table 1 Compensation for Two Pauli Errors on Qubit 3

Equations (4)

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ψ o u t = σ x s 2 H R z ( ( 1 ) s 1 β ) σ x s 1 H R z ( α ) ψ i n = σ x s 2 σ x s 1 R x ( ( 1 ) s 1 β ) R z ( α ) ψ i n ,
x 1 , , x n = 0 1 g ( x 1 , , x n ) E ( x 1 , , x n ) B ( n ) .
P class = 1 2 ( 1 + 1 2 n 1 ) ,
η n V + ( 1 η ) n P class + ( 1 η n V ( 1 η ) n ) 1 2 > P class .

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