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Chinese Physics B

Implementation of unambiguous comparison for unknown pure quantum states with cavity-assisted interaction

Liu‐Yong Cheng, Hong‐Fu Wang, Shou Zhang, Kyu-Hwang Yeon

Published May 1, 2013• 3 citations
Publisher

Abstract

We propose two effective schemes for local and remote unknown atomic state comparisons with a cavity-assisted single photon input—output process without any initial entanglement or auxiliary resource. The unambiguous state discrimination is considered using the state comparison process as the basic module. All the implementation schemes here just involve common quantum logic gates and the single qubit measurement. The analysis shows that our schemes are feasible under the current experimental conditions.

DOI
10.1088/1674-1056/22/5/050306

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We propose two effective schemes for local and remote unknown atomic state comparisons with a cavity-assisted single photon input—output process without any initial entanglement or auxiliary resource. The unambiguous state discrimination is considered using the state comparison process as the basic module. All the implementation schemes here just involve common quantum logic gates and the single qubit measurement. The analysis shows that our schemes are feasible under the current experimental conditions.
In this paper, we propose an experimental scheme for unambiguous quantum state comparison assisted by linear optical manipulations, twin-photons produced from parametric down-conversion, and postselection from the coincidence measurement. In this scheme the preparation of the general two mixed qubit states with arbitrary prior probabilities and the realization of the optimal POVMs for unambiguous quantum state comparison are presented. This proposal is feasible by current experimental technology, and may be used in single-qubit quantum flngerprinting.
Quantum theory of unambiguous measurements In the present paper I formulate a framework that accommodates many unambiguous discrimination problems. I show that the prior information about any type of constituent (state, channel, or observable) allows us to reformulate the discrimination among finite number of alternatives as the discrimination among finite number of average constituents. Using this framework I solve several unambiguous tasks. I present a solution to optimal unambiguous comparison of two ensembles of unknown quantum states. I consider two cases: 1) The two unknown states are arbitrary pure states of qudits. 2) Alternatively, they are coherent states of single-mode optical fields. For this case I propose simple and optimal experimental setup composed of beam-splitters and a photodetector. As a second tasks I consider an unambiguous identification (UI) of coherent states. In this task identical quantum systems are prepared in coherent states and labeled as unknown and reference states, respectively. The promise is that one reference state is the same as the unknown state and the task is to find out unambiguously which one it is. The particular choice of the reference states is unknown to us, and only the probability distribution describing this choice is known. In a general case when multiple copies of unknown and reference states are available I propose a scheme consisting of beamsplitters and photodetectors that is optimal within linear optics. UI can be considered as a search in a quantum database, whose elements are the reference states and the query is represented by the unknown state. This perspective motivated me to show that reference states can be recovered after the measurement and might be used (with reduced success rate) in subsequent UI. Moreover, I analyze the influence of noise in preparation of coherent states on the performance of the proposed setup. Another problem I address is the unambiguous comparison of a pair of unknown qudit unitary channels. I characterize all solutions and identify the optimal ones. I prove that in optimal experiments for comparison of unitary channels the entanglement is necessary. The last task I studied is the unambiguous comparison of unknown non-degenerate projective measurements. I distinguish between measurement devices with apriori labeled and unlabeled outcomes. In both cases only the difference of the measurements can be concluded unambiguously. For the labeled case I derive the optimal strategy if each unknown measurement is used only once. However, if the apparatuses are not labeled, then each measurement device must be used (at least) twice. In particular, for qubit measurement apparatuses with unlabeled outcomes I derive the optimal test state in the two-shots scenario.
We propose a feasible scheme for implementing probabilistic teleportation of an unknown atomic state. In this scheme, atom 1 is initially in an arbitrary state, atoms 2 and 3 are prepared in a partially entangled pure state. After receiving the result of Bell-state measurement performed by Alice on atoms 1 ant 2, Bob lets atoms 2 and auxiliary atom A simultaneously interact with a single-mode vacuum cavity. Only controlling the interact time, we can reconstruct the initial state of atom 1 on the atom 3, i.e. double of square of mode of smaller coefficient of superposition state serving as quantum channel. Moreover, our scheme is insensitive to cavity decay, because atoms are interacting with a large detuning vacuum cavity field.