Abstract
In this article we present milestone developments in the theory and application of quantum information from historical perspectives. The domain of quantum information is very promising to develop quantum computer, quantum communication and varieties of other applications of quantum technologies. We also give the light on experimental manifestations of major theoretical developments. In addition, we present important no-go theorems frequently used in quantum information along with ideas of their respective mathematical proofs.
The publication has been prepared with the support of the “RUDN University Program 5–100”.
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References
Shannon, C.E.: A Mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423, 623–656 (1948)
Bishnoi, B.: Quantum-computation and applications. arXiv:2006.02799 (2020)
Landauer, R.: Information is physical. Phys. Today 44, 23–29 (1991)
Landauer, R.: Information is a physical entity. Physica A 263, 63–67 (1999)
Oldofredi, A.: No-go theorems and the foundations of quantum physics. J. Gen. Philos. Sci. 49(3), 355–370 (2018). https://doi.org/10.1007/s10838-018-9404-5
Luo, M.-X., Li, H.-R., Lai, H., Wang, X.: Unified quantum no-go theorems and transforming of quantum pure states in a restricted set. Quantum Inf. Process. 16(12), 1–32 (2017). https://doi.org/10.1007/s11128-017-1754-0
Bennett, C.H.: Logical reversibility of computation. IBM J. Res. Dev. 17(6), 525–532 (1973)
Toffoli, T.: Reversible computing, Tech. Memo MIT/LCS/TM-151, MIT Lab for Computer Science (1980)
Holevo, A.S.: Bounds for the quantity of information transmitted by a quantum communication channel. Probl. Inf. Transm. 9(3), 177–183 (1973)
Ingarden, R.S.: Quantum information theory. Rept. Math. Phys. 10, 43–72 (1976)
Manin, Y.I.: Vychislimoe i nevychislimoe. Sov. Radio, Moskva (1980). (in Russian)
Feynman, R.P.: Simulating physics with computers. Int. J. Theoret. Phys. 21(6), 467–478 (1982)
Park, L.: The concept of transition in quantum mechanics. Found. Phys. 1, 23–33 (1970). https://doi.org/10.1007/BF00708652
Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature 299, 802–803 (1982)
Dieks, D.: Communication by EPR devices. Phys. Lett. A. 92, 271–272 (1982)
Benioff, P.: Quantum mechanical Hamiltonian models of Turing machines. J. Stat. Phys. 29(3), 515–546 (1982). https://doi.org/10.1007/BF01342185
Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. 10th Anniversary edition. Cambridge University Press, Cambridge (2010)
Bennet, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, December pp. 175–179 (1984)
Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991)
Deutsch, D., Jozsa, R.: Rapid solutions of problems by quantum computation. Proc. R. Soc. London 439, 553–558 (1992)
Shor, P.W.: Polynomial time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)
Shor., P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493–R2496 (1995)
Rivest, R., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21, 120–126 (1978)
Steane, A.M.: Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793–797 (1996)
Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Anual ACM Symposium on the Theory of Computing, Philadelphia, Pensylvania, pp. 212–219 (1996)
Bennett, C.H., et al.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993)
Bouwmeester, D., et al.: Experimental quantum teleportation. Nature 390, 575–579 (1997)
Gershenfeld, N.F., et al.: Bulk spin-resonance quantum computation. Science 275, 350–356 (1997)
Jones, J.A., Mosca, M.: Implementation of a quantum algorithm to solve Deutsch’s problem on a nuclear magnetic resonance quantum computer. J. Chem. Phys. 109, 1648 (1998)
Chuang, I.L., Gershenfeld, N., Kubinec, M.: Experimental implementation of fast quantum searching. Phys. Rev. Lett. 80, 3408–3411 (1998)
Pati, A.K., Braunstein, S.L.: Impossibility of deleting an unknown quantum state. Nature 404, 164–165 (2000)
Vandersypen, L.M.K., et al.: Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883–887 (2001)
Knill, E., Laflamme, L., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001)
Pittman, T.B., et al.: Experimental controlled-NOT logic gate for single photons in the coincidence basis. Phys. Rev. A 68, 032316 (2003)
O’Brien, J.L., Branning, D., et al.: Demonstration of an all-optical quantum controlled-NOT gate. Nature 426, 264–267 (2003)
Elliott, C.: The DARPA quantum network. arXiv:quant-ph/0412029v1 (2004)
Brennen, G., Giacobino, E., Simon, C.: Focus on Quantum Memory. New J. Phys. 17, 050201 (2015)
Kimble, H.: The quantum internet. Nature 453, 1023–1030 (2008)
Chaneliere, T., et al.: Storage and retrieval of single photons transmitted between remote quantum memories. Nature 438, 833–836 (2005)
Murao, M., et al.: Quantum telecloning and multiparticle entanglement. Phys. Rev. A 59, 156–161 (1999)
Koike, S., et al.: Demonstration of quantum telecloning of optical coherent states. Phys. Rev. Lett. 96, 060504 (2006)
Pirandola, S., et al.: Macroscopic entanglement by entanglement swapping. Phys. Rev. Lett. 97, 150403 (2006)
Brennecke, F., et al.: Cavity QED with a Bose Einstein condensate. Nature 450, 268–271 (2007)
Lanyon, B.P., et al.: Manipulating biphotonic qutrits. Phys. Rev. Lett. 100, 060504 (2008)
Chen, J., et al.: Demonstration of a quantum controlled-NOT gate in the telecommunications band. Phys. Rev. Lett. 100, 133603 (2008)
Mariantoni, M., et al.: Implementing the quantum von Neumann architecture with superconducting circuits. Science 334, 61–65 (2011)
Pfaff, W., et al.: Unconditional quantum teleportation between distant solid-state quantum bits. Science 345, 532–535 (2014)
Dattani, N.S., Bryans, N.: Quantum factorization of 56153 with only 4 qubits. arXiv:1411.6758 (2014)
Zhong, M., et al.: Optically addressable nuclear spins in a solid with a six-hour coherence time. Nature 517, 177–180 (2015)
Gibney, E.: D-Wave upgrade: how scientists are using the world’s most controversial quantum computer. Nature 541, 447–448 (2017)
Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)
Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 30, 598–601 (2009)
Sharma, K.K., Awasthi, S.K., Pandey, S.N.: Entanglement sudden death and birth in qubit-qutrit systems under Dzyaloshinskii-Moriya interaction. Quantum Inf. Process. 12, 3437–3447 (2013). https://doi.org/10.1007/s11128-013-0607-8
Sharma, K.K., Pandey, S.N.: Entanglement Dynamics in two parameter qubit-qutrit states under Dzyaloshinskii-Moriya interaction. Quantum Inf. Process. 13, 2017–2038 (2014). https://doi.org/10.1007/s11128-014-0794-y
Sharma, K.K., Pandey, S.N.: Influence of Dzyaloshinshkii-Moriya interaction on quantum correlations in two qubit Werner states and MEMS. Quantum Inf. Process. 14, 1361–1375 (2015). https://doi.org/10.1007/s11128-015-0928-x
Sharma, K.K., Pandey, S.N.: Dzyaloshinshkii-Moriya interaction as an agent to free the bound entangled states. Quantum. Info. Process. 15, 1539 (2016)
Sharma, K.K., Pandey, S.N.: Dynamics of entanglement in two parameter qubit-qutrit states with x-component of DM interaction. Commun. Theor. Phys. 65, 278–284 (2016)
Sharma, K.K., Pandey, S.N.: Robustness of Greenberger-Horne-Zeilinger and W states against Dzyaloshinskii-Moriya interaction. Quantum Inf. Process 15, 4995–5009 (2016)
Sharma, K.K., Gerdt, V.P.: Entanglement sudden death and birth effects in two qubits maximally entangled mixed states under quantum channels. Int. J. Theoret. Phys. 59, 403–414 (2020). https://doi.org/10.1007/s10773-019-04332-z
Horodecki, R., et al.: Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009)
Acin, A., et al.: The quantum technologies roadmap: a European community view. New J. Phys. 20, 080201 (2018)
Pathak, A.: Elements of Quantum Computation and Quantum Communication. Taylor & Francis Group, Boca Raton (2013)
Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61, 052306 (2000)
Terhal, B.M.: Is entanglement monogamous? IBM J. Res. Dev. 48, 71–78 (2004)
Koashi, M., Winter, A.: Monogamy of quantum entanglement and other correlations. Phys. Rev. A 69, 022309 (2004)
Osborne, T.J., Verstraete, F.: General Monogamy inequality for bipartite qubit entanglement. Phys. Rev. Lett. 96, 220503 (2006)
Barnum, H., et al.: Noncommuting mixed states cannot be broadcast. Phys. Rev. 76, 2818–2821 (1996)
D’Ariano, G.M., Macchiavello, C., Perinotti, P.: Superbroadcasting of mixed states. Phys. Rev. Lett. 95, 060503 (2005)
Lindblad, G.: A general no-cloning theorem. Lett. Math. Phys. 47, 189–196 (1999)
Barnum, H., et al.: Generalized no-broadcasting theorem. Phys. Rev. Lett. 99, 240501 (2007)
Kalev, A., Hen, I.: No-broadcasting theorem and its classical counterpart. Phys. Rev. Lett. 100, 210502 (2008)
Piani, M., Horodecki, P., Horodecki, R.: No-local-broadcasting theorem for multipartite quantum correlations. Phys. Rev. Lett. 100, 090502 (2008)
Daffertshofer, A., Plastino, A.R., Plastino, A.: Classical no-cloning theorem. Phys. Rev. Lett. 88, 210601 (2002)
Gruska, J., Imai, H.: Power, puzzles and properties of entanglement. In: Margenstern, M., Rogozhin, Y. (eds.) MCU 2001. LNCS, vol. 2055, pp. 25–68. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45132-3_3
Popescu, S., Rohrlich, D.: Causality and nonlocality as axioms for quantum mechanics. In: Hunter, G., Jeffers, S., Vigier, J.P. (eds.) Causality and Locality in Modern Physics. Fundamental Theories of Physics (An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application), vol. 97, pp. 383–390. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0990-3_45
Peres, A., Terno, D.R.: Quantum information and relativity theory. Rev. Mod. Phys. 76, 93–123 (2004)
Benenti, G., Casatti, G., Strini, G.: Principles of Quantum Computation and Information. Vol. I: Basic Concepts. World Scientific, Singapore (2004)
Braunstein, S.L., Pati, A.K.: Quantum information cannot be completely hidden in correlations: implications for black hole information paradox. Phys. Rev. Lett. 98, 080502 (2007)
Pani, S.J., Pati, A.K.: Experimental test of the quantum no-hiding theorem. Phys. Rev. Lett. 106, 080401 (2011)
Nielsen, M.A., Chuang, I.L.: Programmable quantum gate arrays. Phys. Rev. Lett. 79, 321–324 (1997)
Kubicki, A.M., Palazuelos, C., Peréz-Garcia, D.: Resource quantification for the no-programing theorem. Phys. Rev. Lett. 122, 080505 (2019)
Diamanti, E. et al.: Practical challenges in quantum key distribution. npj Quantum Inf. 2, 16025 (2016). https://doi.org/10.1038/npjqi.2016.25
Bedington, R., Arrazola, J.M., Ling, A.: Progress in satellite quantum key distribution. npj Quantum Inf. 3, 30 (2017)
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Sharma, K.K., Gerdt, V.P., Gerdt, P.V. (2020). Milestone Developments in Quantum Information and No-Go Theorems. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks. DCCN 2020. Lecture Notes in Computer Science(), vol 12563. Springer, Cham. https://doi.org/10.1007/978-3-030-66471-8_39
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