Optimum unambiguous identification of d unknown pure qudit states
Ulrike Herzog, Janos A. Bergou
备注：
A reference has been included and a sign error has been corrected that propagated and affected the final result and is unfortunately also present in the printed journal version
发表信息：
Phys. Rev. A 78, 032320 (2008), Erratum: Phys. Rev. A 78, 069902 (2008)
We address the problem of unambiguously identifying the state of a probe qudit with the state of one of d reference qudits. The reference states are assumed pure and linearly independent but we have no knowledge of them. The state of the probe qudit is assumed to coincide equally likely with either one of the d unknown reference states. We derive the optimum measurement strategy that maximizes the success probability of unambiguous identification and find that the optimum strategy is a generalized measurement. We give both the measurement operators and the optimum success probability explicitly. Technically, the problem we solve amounts to the optimum unambiguous discrimination of d known mixed quantum states.
We consider the unambiguous discrimination between two unknown qudit states in $n$-dimensional ($n\geqslant2$) Hilbert space. By equivalence of unknown pure states to known mixed states and with the Jordan-basis method, we demonstrate that the optimal success probability of the discrimination between two unknown states is independent of the dimension $n$. We also give a scheme for a physical implementation of the programmable state discriminator that unambiguously discriminate between two unknown states with optimal probability of success.
Experimental demonstration of optimal measurement for unambiguously discriminating asymmetric qudit states
Center for Quantum Technology, Korea Institute of Science and Technology (KIST)（韩国科学技术院量子技术中心）；Division of Quantum Information, KIST School, University of Science and Technology（韩中科技大学KIST学院量子信息系）；Department of Applied Physics, Kyung Hee University（庆熙大学应用物理系）
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