Abstract
This paper explores the role of a priori knowledge in the optimization of quantum information processing by investigating optimum unambiguous discrimination problems for both the qubit and qutrit states. In general, a priori knowledge in optimum unambiguous discrimination problems can be classed into two types: a priori knowledge of discriminated states themselves and a priori probabilities of preparing the states. It is clarified that whether a priori probabilities of preparing discriminated states are available or not, what type of discriminators one should design just depends on what kind of the classical knowledge of discriminated states. This is in contrast to the observation that choosing the parameters of discriminators not only relies on the a priori knowledge of discriminated states, but also depends on a priori probabilities of preparing the states. Two types of a priori knowledge can be utilized to improve optimum performance but play the different roles in the optimization from the view point of decision theory.
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Nielsen M.A., Chuang I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Bennett C.H., Brassard G., Crepeau C., Jozsa R., Peres A., Wootters W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70(13), 1895–1898 (1993)
Bouwmeester D., Pan J.W., Mattle K., Eibl M., Weinfurter H., Zeilinger A.: Experimental quantum teleportation. Nature 390, 575–579 (1997)
Mattle K., Weinfurter H., Kwiat P.G., Zeilinger A.: Dense coding in experimental quantum communication. Phys. Rev. Lett. 76, 4656–4659 (1996)
Ekert A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991)
Bennett C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68, 3121–3124 (1992)
Deutsch D., Ekert A.K., Jozsa R. et al.: Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys. Rev. Lett. 77, 2818–2821 (1996)
Feymann R.P.: Quantum theory, the church turing principle and the universal quantum computer. Int. J. Theor. Phys. 21, 6–7 (1982)
Shor, P.W.: Algorithms for quantum computation discretelog and factoring. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 124–134. Santa Fe, New Mexico (1994)
Sleator T., Weinfurter H.: Realizable universal quantum logic gates. Phys. Rev. Lett. 74, 4087–4090 (1995)
Desurvire E.: Classical and Quantum Information Theory: Introduction for the Telecom Scientist. Cambridge University Press, Cambridge (2009)
Nielsen M.A., Chuang I.L.: Programmable quantum gate arrays. Phys. Rev. Lett. 79, 321–324 (1997)
Vidal G., Masanes L., Cirac J.I.: Storing quantum dynamics in quantum states: a stochastic programmable gate. Phys. Rev. Lett. 88, 047905 (2002)
Hillery M., Ziman M., Buzek V.: Implementation of quantum maps by programmable quantum processors. Phys. Rev. A 66, 042302 (2002)
Paz J.P., Roncaglia A.: Quantum gate arrays can be programmed to evaluate the expectation value of any operator. Phys. Rev. A 68, 052316 (2003)
Bergou J.A., Hillery M.: Universal programmable quantum state discriminator that is optimal for unambiguously distinguishing between unknown States. Phys. Rev. Lett. 94, 160501 (2005)
Hayashi A., Horibe M., Hashimoto T.: Unambiguous pure-state identification without classical knowledge. Phys. Rev. A 73, 012328 (2006)
Hayashi A., Horibe M., Hashimoto T.: Quantum pure-state identification. Phys. Rev. A 72, 052306 (2005)
Zhang C., Ying M., Qiao B.: Optimal distinction between two non-orthogonal quantum states. Phys. Rev. A 74, 042308 (2006)
Bergou J.A., Buzek V., Feldman E., Herzog U., Hillery M.: Programmable quantum-state discriminators with simple programs. Phys. Rev. A 73, 062334 (2006)
Berger J.O.: Statistical decision theory and Bayesian analysis. Springer, Berlin (1985)
Helstrom C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976)
Ivanovic I.D.: How to differentiate between non-orthogonal states. Phys. Lett. A 123, 257–259 (1987)
Dieks D.: Overlap and distinguishability of quantum states. Phys. Lett. A 126, 303–306 (1988)
Peres A.: How to differentiate between non-orthogonal states. Phys. Lett. A 128, 19–19 (1988)
Bergou, J.A., Herzog, U., Hillery, M.: Discrimination of quantum states. In: Quantum State Estimation, ser. Lecture Notes in Physics, vol. 649, Springer, Berlin, Heidelberg (2004)
Zhang M., Zhou Z.T., Dai H.Y., Hu D.: On impact of a priori classical knowledge of discriminated states on the optimal unambiguous discrimination. Quantum Inf. Comput. 8(10), 0951–0964 (2008)
D’Ariano G.M., Sacchi M.F., Kahn J.: Minimax quantum-state discrimination. Phys. Rev. A 72, 032310 (2005)
Jaeger G., Shimony A.: Optimal distinction between two non-orthogonal quantum states. Phys. Lett. A 197, 83–87 (1995)
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Zhang, M., Lin, M., Schirmer, S.G. et al. On the role of a priori knowledge in the optimization of quantum information processing. Quantum Inf Process 11, 639–673 (2012). https://doi.org/10.1007/s11128-011-0278-2
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DOI: https://doi.org/10.1007/s11128-011-0278-2