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Quantum Entanglement and its Applications


Affiliations
1 Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
 

Quantum correlation, such as entanglement, is one of the important ingredients in most of the known quantum communication schemes. In this article, we first introduce the concept of entangled states and then discuss the communication protocols without security, both in a two-party and in a multiple-party domain.

Keywords

Entanglement, Quantum Correlations, Quantum Communication Protocols, Quantum Dense Coding, Quantum Teleportation.
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  • Nielsen, M. A. and Chuang, I., Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000.

  • Bennett, C. H. and Brassard, G., Quantum cryptography: public key distribution and coin tossing. Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, 1984, p. 175.

  • Ekert, A. K., Quantum cryptography based on Bells theorem.Phys. Rev. Lett., 1991, 67, 661.

  • Gisin, N., Ribordy, G., Tittel, W. and Zbinden, H., Quantum cryptography.Rev. Mod. Phys., 2002, 74, 145.

  • Jennewein, T., Simon, C., Weihs, G., Weinfurter, H. and Zeilinger, A., Quantum cryptography with entangled photons. Phys. Rev.Lett., 2000, 84, 4729.

  • Bennett, C. H. and Wiesner, S. J., Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys.Rev. Lett., 1992, 69, 2881.

  • Mattle, K., Weinfurter, H., Kwiat, P. G. and Zeilinger, A., Dense coding in experimental quantum communication. Phys. Rev. Lett., 1996, 76, 4656.

  • Bennett, C. H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A. and Wootters, W. K., Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett., 1993, 70, 1895.

  • Bouwmeester, D., Pan, J. W., Mattle, K., Eibl, M., Weinfurter, H., and Zeilinger, A., Experimental quantum teleportation. Nature, 1997, 390, 575.

  • Shor, P. W., Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. Proceedings of the 35th Annual Symposium on Foundations of Computer Science (ed. Goldwasser, S.), IEEE Computer Society Press, 1994, 124134.

  • Pan, J. W., Chen, Z. B., Lu, C.-Y., Weinfurter, H., Zeilinger, A. and Zukowski, M., Multiphoton entanglement and interferometry. Rev. Mod. Phys., 2012, 84, 777.

  • Leibfried, D., Blatt, R., Monroe, C. and Wineland, D., Quantum dynamics of single trapped ions. Rev. Mod. Phys., 2003, 75, 281.

  • Hafner, H., Roose, C. F. and Blatt, R., Quantum computing with trapped ions. Phys. Rep., 2008, 469, 155.

  • Raimond, J. M., Brune, M. and Haroche, S., Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys., 2001, 73, 565.

  • Mandel, O., Greiner, M., Widera, A., Rom, T., Hänsch, T. W. and Bloch, I., Controlled collisions for multi-particle entanglement of optically trapped atoms. Nature, 2003, 425, 937.

  • Horodecki, R., Horodecki, P., Horodecki, M. and Horodecki, K., Quantum entanglement. Rev. Mod. Phys., 2009, 81, 865.

  • Monz, T. et al., 14-qubit entanglement: creation and coherence. Phys. Rev. Lett., 2011, 106, 130506.

  • Wang, X.-L. et al., Experimental ten-photon entanglement. Phys. Rev. Lett., 2016, 117, 210502.

  • Barends, R. et al., Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature, 2014, 508, 500503.

  • Steane, A. M., Quantum computing. Rept. Prog. Phys., 1998, 61, 117.

  • Steane, A. M. and Lucas, D. M., Quantum computing with trapped ions, atoms and light, 2000, arXiv:quant-ph/0004053.

  • Cirac, J. I. and Zoller, P., A scalable quantum computer with ions in an array of microtraps. Nature, 2010, 404, 579.

  • Sen (De), A. and Sen, U., Quantum advantage in communication networks. Phys. News, 2010, 40, 17–32; arXiv:1105.2412 (quantph)).

  • Werner, R. F., Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A, 1989, 40, 4277.

  • Dür, W., Vidal, G. and Cirac, J. I., Three qubits can be entangled in two inequivalent ways. Phys. Rev. A, 2000, 62, 062314.

  • Greenberger, D. M., Horne, M. A. and Zeilinger, A., In Bells Theorem, Quantum Theory, and Conceptions of the Universe (ed.

  • Kafatos, M.), Kluwer Academic, Dordrecht, The Netherlands, 1989.

  • Zeilinger, A., Horne, M. A. and Greenberger, D. M., In Proceedings of Squeezed States and Quantum Uncertainty (eds Han, D. et al.), NASA Conf. Publ., 1992, vol. 3135, p. 73.

  • Blasone, M., DellAnno, F., DeSiena, S. and Illuminati, F., Hierarchies of geometric entanglement. Phys. Rev. A, 2008, 77, 062304.

  • An arbitrary two-dimensional quantum state is called a qubit (quantum bit).

  • Walter, M., Gross, D. and Eisert, J., Multi-partite entanglement, arXiv: 1612:02437.

  • Gühne, O. and Toth, G., Entanglement detection. Phys. Rep., 2009, 474, 1.

  • DAriano, G. M., Vasilyev, M. and Kumar, P., Self-homodyne tomography of a twin-beam state. Phys. Rev. A, 1998, 58, 636.

  • White, A. G., James, D. F. V., Eberhard, P. H. and Kwiat, P. G., Nonmaximally entangled states: production, characterization and utilization. Phys. Rev. Lett., 1999, 83, 3103.

  • Peres, A., Separability criterion for density matrices. Phys. Rev. Lett., 1996, 77, 1413.

  • Horodecki, M., Horodecki, P. and Horodecki, R., Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A, 1996, 223, 1.

  • The von Neumann entropy of an arbitrary state,  is defined as S(σ) = –trσ log2σ.

  • Cerf, N. and Adami, C., Negative entropy and information in quantum mechanics. Phys. Rev. Lett., 1997, 79, 5194.

  • Horodecki, R., Horodecki, P. and Horodecki, M., Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A, 1996, 210, 377.

  • Horodecki, R. and Horodecki, M., Information-theoretic aspects of inseparability of mixed states. Phys. Rev. A, 1996, 54, 1838.

  • Nielsen, M. A. and Kempe, J., Separable states are more disordered globally than locally. Phys. Rev. Lett., 2001, 86, 5184.

  • Gühne, O., Hyllus, P., Gittsovich, O. and Eisert, J., Covariance matrices and the separability problem. Phys. Rev. Lett., 2007, 99, 130504.

  • Gittsovich, O., Gühne, O., Hyllus, P. and Eisert, J., Unifying several separability conditions using the covariance matrix criterion. Phys. Rev. A, 2008, 78, 052319.

  • Lewenstein, M., Kraus, B., Cirac, J. I. and Horodecki, P., Optimization of entanglement witnesses. Phys. Rev. A, 2000, 62, 052310.

  • Bruβ, D., Cirac, J. I., Horodecki, P., Hulpke, F., Kraus, B., Lewenstein, M. and Sanpera, A., Reflections upon separability and distillability. J. Mod. Opt., 2002, 49, 1399.

  • Terhal, B. M., Bell inequalities and the separability criterion. Phys. Lett. A, 2000, 271, 319.

  • Bennett, C. H., Bernstein, H. J., Popescu, S. and Schumacher, B., Concentrating partial entanglement by local operations. Phys. Rev. A, 1996, 53, 2046.

  • Modi, K., Brodutch, A., Cable, H., Paterek, T. and Vedral, V., The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys., 2012, 84, 1655.

  • Horodecki, M., Horodecki, P., Horodecki, R., Oppenheim, J., Sen (De), A., Sen, U. and Synak-Radtke, B., Local versus nonlocal information in quantum-information theory: formalism and phenomena. Phys. Rev. A, 2005, 71, 062307.

  • Bennett, C. H., DiVincenzo, D. P., Smolin, J. and Wootters, W. K., Mixed-state entanglement and quantum error correction. Phys. Rev. A, 1996, 54, 3824.

  • Wootters, W. K., Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett., 1998, 80, 2245.

  • Lewenstein, M., Sanpera, A., Ahufinger, V., Damski, B., Sen (De), A. and Sen, U., Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond. Adv. Phys., 2007, 56, 243.

  • Amico, L., Fazio, R., Osterloh, A. and Vedral, V., Entanglement in many-body systems. Rev. Mod. Phys., 2008, 80, 517.

  • Vidal, G. and Werner, R. F., Computable measure of entanglement. Phys. Rev. A, 2002, 65, 032314.

  • Vedral, V., Plenio, M. B., Rippin, M. A. and Knight, P. L., Quantifying entanglement. Phys. Rev. Lett., 1997, 78, 2275.

  • Bennett, C. H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J. A. and Wootters, W. K., Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett., 1996, 76, 722.

  • Horodecki, M., Horodecki, P. and Horodecki, R., Limits for entanglement measures. Phys. Rev. Lett., 2000, 84, 2014.

  • Sen (De), A. and Sen, U., Channel capacities versus entanglement measures in multiparty quantum states. Phys. Rev. A, 2010, 81, 012308.

  • Biswas, A., Prabhu, R., Sen (De), A. and Sen, U., Genuine multipartite entanglement trends in gapless-gapped transitions of quantum spin systems. Phys. Rev. A, 2014, 90, 032301.

  • Barnum, H. and Linden, N., Monotones and invariants for multiparticle quantum states. J. Phys. A, 2001, 34, 6787.

  • Wei, T.-C. and Goldbart, P. M., Geometric measure of entanglement and applications to bipartite and multipartite quantum states. Phys. Rev. A, 2003, 68, 042307.

  • Das, T., Roy, S. S., Bagchi, S., Misra, A., Sen (De), A. and Sen, U., Generalized geometric measure of entanglement for multiparty mixed states. Phys. Rev. A, 2016, 94, 022336.

  • Coffman, V., Kundu, J. and Wootters, W. K., Distributed entanglement. Phys. Rev. A, 2000, 61, 052306.

  • Dhar, H. S., Pal, A. K., Rakshit, D., Sen (De), A. and Sen, U., Monogamy of quantum correlations – a review. arXiv: 1610.01069.

  • The smallest unit in a classical computer which can take a binary value {0, 1}, is called a bit (binary digit). Computation in a classical computer has been performed by using bits.

  • Bose, S., Plenio, M. B. and Vedral, V., Mixed state dense coding and its relation to entanglement measures. J. Mod. Opt., 2000, 47, 291.

  • Hiroshima, T., Optimal dense coding with mixed state entanglement. J. Phys. A: Math. Gen., 2001, 34, 6907.

  • Bruß, D., D’Ariano, G. M., Lewenstein, M., Macchiavello, C., Sen (De), A. and Sen, U., Distributed quantum dense coding. Phys. Rev. Lett., 2004, 93, 210501.

  • Bruß, D., Lewenstein, M., Sen (De), A., Sen, U., DAriano, G. M. and Macchiavello, C., Dense coding with multipartite quantum states. Int. J. Quantum Inf., 2006, 4, 415.

  • Gordon, J. P., In Proceedings of the International School Phys. Enrico Fermi, Course XXXI (ed. Miles, P. A.), Academic Press, NY 1964, p. 156.

  • Levitin, L. B., In Proceedings of the VI National Conference Inf. Theory, Tashkent, 1969, p. 111.

  • Holevo, A. S., Probl. Pereda. Inf., 1973, 9, 3; Probl. Inf. Transm. 1973, 9, 110.

  • Yuen, H. P. and Ozawa, M., Ultimate information carrying limit of quantum systems. Phys. Rev. Lett., 1993, 70, 363.

  • Yuen, H. P., In Quantum Communication, Computing, and Measurement (eds Hirota, O. et al.), Plenum, NY, 1997.

  • Badziag, P., Horodecki, M., Sen (De), A. and Sen, U., Locally accessible information: how much can the parties gain by cooperating? Phys. Rev. Lett., 2003, 91, 117901.

  • Horodecki, M., Oppenheim, J., Sen (De), A. and Sen, U., Distillation protocols: output entanglement and local mutual information. Phys. Rev. Lett., 2004, 93, 170503.

  • Shadman, Z., Kampermann, H., Macchiavello, C. and Bruß, D., Optimal super dense coding over noisy quantum channels. New J.Phys., 2010, 12, 073042.

  • Das, T., Prabhu, R., Sen (De), A. and Sen, U., Multipartite dense coding versus quantum correlation: noise inverts relative capability of information transfer. Phys. Rev. A, 2014, 90, 022319.

  • Das, T., Prabhu, R., Sen (De), A. and Sen, U., Distributed quantum dense coding with two receivers in noisy environments. Phys. Rev. A, 2015, 92, 052330.

  • Prabhu, R., Pati, A. K., Sen (De), A. and Sen, U., Exclusion principle for quantum dense coding. Phys. Rev. A, 2013, 87, 052319.

  • Nepal, R., Prabhu, R., Sen (De), A. and Sen, U., Maximallydensecodingcapable quantum states. Phys. Rev. A, 2013, 87, 032336.

  • Wootters, W. K. and Zurek, W. H., A single quantum cannot be cloned. Nature, 1982, 299, 802.

  • Horodecki, P., Horodecki, M. and Horodecki, R., General teleportation channel, singlet fraction and quasi-distillation. Phys. Rev. A, 1999, 60, 1888.

  • Verstraete, F. and Verschelde, H., Fidelity of mixed states of two qubits. Phys. Rev. A, 2002, 66, 022307.

  • Acin, A., Bru, D., Lewenstein, M. and Sanpera, A., Classification of mixed three-qubit states. Phys. Rev. Lett., 2000, 87, 040401.


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  • Quantum Entanglement and its Applications

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Authors

Aditi Sen
Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India

Abstract


Quantum correlation, such as entanglement, is one of the important ingredients in most of the known quantum communication schemes. In this article, we first introduce the concept of entangled states and then discuss the communication protocols without security, both in a two-party and in a multiple-party domain.

Keywords


Entanglement, Quantum Correlations, Quantum Communication Protocols, Quantum Dense Coding, Quantum Teleportation.

References





DOI: https://doi.org/10.18520/cs%2Fv112%2Fi07%2F1361-1368