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arXiv:1105.3339

Experimental Optimum Maximum-Confidence Discrimination and Optimum Unambiguous Discrimination of Two Mixed Single-Photon States

Gesine A. Steudle, Sebastian Knauer, Ulrike Herzog, E. Stock, Vladimir Anatolievich Haisler, D. Bimberg, Oliver J. Benson

Published May 17, 2011• 0 citations
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Abstract

We present an experimental implementation of optimum measurements for quantum state discrimination. Optimum maximum-confidence discrimination and optimum unambiguous discrimination of two mixed single-photon polarization states were performed. For the latter the states of rank two in a four-dimensional Hilbert space are prepared using both path and polarization encoding. Linear optics and single photons from a true single-photon source based on a semiconductor quantum dot are utilized.

DOI
10.48550/arxiv.1105.3339

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We present an experimental implementation of optimum measurements for quantum state discrimination. Optimum maximum-confidence discrimination and optimum unambiguous discrimination of two mixed single-photon polarization states were performed. For the latter the states of rank two in a four-dimensional Hilbert space are prepared using both path and polarization encoding. Linear optics and single photons from a true single-photon source based on a semiconductor quantum dot are utilized.
Measurement schemes for discriminating two given mixed states of a quantum system have been optimized with respect to various criteria. In many cases the optimum measurements are generalized ones, characterized by detection operators that are not projectors. Here we focus on two generalized measurements. The first refers to the discrimination of two mixed qubit states with maximum confidence at a minimum probability of inconclusive results, and the second to the optimum unambiguous discrimination of two mixed states that are connected by a special similarity transformation. For both measurements we consider linear-optical implementations using single-photon polarization states.
We present the first experimental demonstration of the maximum confidence measurement strategy for quantum state discrimination. Applying this strategy to an arbitrary set of states assigns to each input state a measurement outcome which, when realized, gives the highest possible confidence that the state was indeed present. The theoretically optimal measurement for discriminating between three equiprobable symmetric qubit states is implemented in a polarization-based free-space interferometer. The maximum confidence in the measurement result is 2/3. This is the first explicit demonstration that an improvement in the confidence over the optimal minimum error measurement is possible for linearly dependent states.
We study an optimized measurement which discriminates NNN mixed quantum states occurring with given prior probabilities. The measurement yields the maximum achievable confidence for each of the NNN conclusive outcomes, thereby keeping the overall probability of inconclusive outcomes as small as possible. It corresponds to optimum unambiguous discrimination when for each outcome the confidence is equal to unity. Necessary and sufficient optimality conditions are derived and general properties of the optimum measurement are obtained. The results are applied to the optimized maximum-confidence discrimination of NNN equiprobable symmetric mixed states. Analytical solutions are presented for a number of examples, including the discrimination of NNN symmetric pure states spanning a ddd-dimensional Hilbert space ($d\ensuremath{\leqslant}N$) and the discrimination of NNN symmetric mixed qubit states.
In this paper, we present a linear optical scheme for optimal unambiguous discrimination among nonorthogonal quantum states in terms of the multiple-rail and polarization representation of a single photon. In our scheme, discriminated quantum states are expressed by using the spatial degree of freedom of a single photon while the polarization degree of freedom of the single photon is used to act as an auxiliary qubit. The optical components used in our scheme are only passive linear optical elements such as polarizing beam splitters, wave plates, polarizers, single photon detectors, and single photon source.