We address a problem of identifying a given pure state with one of two reference pure states, when no classical knowledge on the reference states is given, but a certain number of copies of them are available. We assume the input state is guaranteed to be either one of the two reference states. This problem, which we call quantum pure state identification, is a natural generalization of the standard state discrimination problem. The two reference states are assumed to be independently distributed in a unitary invariant way in the whole state space. We give a complete solution for the averaged maximal success probability of this problem for an arbitrary number of copies of the reference states in general dimension. It is explicitly shown that the obtained mean identification probability approaches the mean discrimination probability as the number of the reference copies goes to infinity.

The mass shift of charmonium near the critical temperature of the deconfining transition is investigated by a c-c potential model through the change of the string tension. On the basis of the results, detection of the shift by lepton-pair production is discussed by the use of the hydrodynamical model of ultrarelativistic nucleus-nucleus collisions. It is shown that the mass shift is detectable if the critical temperature is not lower than 300 MeV. PACS numbers: 12.38.Mh, 12.40.Ee, 12.40.Qq, 25.70.Np Although there has been increasing support for the existence of deconfinement and/or chiral restoring transitions at finite temperature or high density in theoretical 1 and numerical 2 investigations, the possibility of detection of these transitions and the new phases is not yet clear. 3 On this problem, the hadronic mass shift related to the restoration of chiral symmetry has been discussed recently. 4,5 Despite the uniqueness of the phenomenon, detectability of the effect in actual collisions is still uncertain. In this Letter, we present some results for the mass shift of charmonium and the change of its leptonic width with variation of string tension, which is expected to be temperature dependent. Recent works in Monte Carlo simulation 6 " 8 and model investigation 9 ' 10 suggest critical behavior of the string tension near the deconfining transition. Further, we discuss detection of the mass shift by leptonpair production in heavy-ion collisions based on hydrodynamical development. 11 " 13 We see that the effect could be detectable if the deconfining temperature is not lower than 300 MeV.The computation of the mass shift adopted here is based on the c-c potential modelwhere the first term is the gluon-exchange Coulombic term given by Buchmuller and Tye, 14 i.e., with A = 250 MeV and b Q -9 (three flavors).Since we consider the string tension k at finite temperature, our present interest is to solve for c-c states under variation of k. Generally speaking, the Coulombic term might also be temperature dependent. Here we restrict ourselves to variation of the string tension, because the long-range part, kr, would primarily show a finite-temperature effect below the critical temperature. The mass of the charm quark in the potential model may also be temperature dependent. In the case of heavy quarks, this would be a minor effect and is omitted in the present calculation. We shall comment further on this in later discussions.Calculations are made by a variational method with variation of the string tension. In the calculation of the leptonic width, the reliability of the value of the variational wave function at the origin is rather poor. So we adopt the values from the sum rule for the potential, i.e., l^(0)| 2 =(/^/27r)

We study how to unambiguously identify a given quantum pure state with one of the two reference pure states when no classical knowledge on the reference states is given but a certain number of copies of each reference quantum state are presented. By unambiguous identification, we mean that we are not allowed to make a mistake but our measurement can produce an inconclusive result. Assuming the two reference states are independently distributed over the whole pure state space in a unitary invariant way, we determine the optimal mean success probability for an arbitrary number of copies of the reference states and a general dimension of the state space. It is explicitly shown that the obtained optimal mean success probability asymptotically approaches that of the unambiguous discrimination as the number of the copies of the reference states increases

In quantum teleportation, neither Alice nor Bob acquires any classical knowledge on teleported states. The teleportation protocol is said to be oblivious to both parties. In remote state preparation (RSP) it is assumed that Alice is given complete classical knowledge on the state that is to be prepared by Bob. Recently, Leung and Shor [8] showed that the same amount of classical information as that in teleportation needs to be transmitted in any exact and deterministic RSP protocol that is oblivious to Bob. We study similar RSP protocols, but not necessarily oblivious to Bob. First it is shown that Bob's quantum operation can be safely assumed to be a unitary transformation. We then derive an equation that is a necessary and sufficient condition for such a protocol to exist. By studying this equation, we show that one qubit RSP requires 2 cbits of classical communication, which is the same amount as in teleportation, even if the protocol is not assumed oblivious to Bob. For higher dimensions, it is still open whether the amount of classical communication can be reduced by abandoning oblivious conditions.

We investigate a state discrimination problem which interpolates minimum-error and unambiguous discrimination by introducing a margin for the probability of error. We closely analyze discrimination of two pure states with general occurrence probabilities. The optimal measurements are classified into three types. One of the three types of measurement is optimal depending on parameters (occurrence probabilities and error margin). We determine the three domains in the parameter space and the optimal discrimination success probability in each domain in a fully analytic form. It is also shown that when the states to be discriminated are multipartite, the optimal success probability can be attained by local operations and classical communication. For discrimination of two mixed states, an upper bound of the optimal success probability is obtained.

The quantum color coding scheme proposed by Korff and Kempe ͓e-print quant-ph/0405086͔ is easily extended so that the color coding quantum system is allowed to be entangled with an extra auxiliary quantum system. It is shown that in the extended scheme we need only ϳ2 ͱ N quantum colors to order N objects in large N limit, whereas ϳN / e quantum colors are required in the original nonextended version. The maximum success probability has asymptotics expressed by the Tracy-Widom distribution of the largest eigenvalue of a random Gaussian unitary ensemble ͑GUE͒ matrix.

There are two common settings in a quantum-state discrimination problem. One is minimum-error discrimination where a wrong guess (error) is allowed and the discrimination success probability is maximized. The other is unambiguous discrimination where errors are not allowed but the inconclusive result "I don't know" is possible. We investigate discrimination problem with a finite margin imposed on the error probability. The two common settings correspond to the error margins 1 and 0. For arbitrary error margin, we determine the optimal discrimination probability for two pure states with equal occurrence probabilities. We also consider the case where the states to be discriminated are multipartite, and show that the optimal discrimination probability can be achieved by local operations and classical communication.Comment: 7 pages, 1 figure, typos corrected, references and an appendix added, to appear in Phys. Rev. A 7

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