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arXiv:quant-ph/0105139 · Fortschritte der Physik

Discrimination between Non-orthogonal Two-photon Polarization States

Ulrike Herzog

Published Oct 1, 2001• 6 citations
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Abstract

It is shown that generalized measurements, required for optimally discriminating between non-orthogonal joint polarization states of two indistinguishable photons, can be realized with the help of polarization-dependent two-photon absorption and by means of sum-frequency generation. Optimization schemes are investigated with respect to minimizing the error probability in inferring the states, as well as with respect to maximizing the probability of success for unambiguous discrimination. Moreover, an implementation of error-minimizing discrimination between N symmetric single-photon states is studied. The latter can be used to extract information from the inconclusive results occurring in unambiguous discrimination between three symmetric two-photon polarization states.

DOI
10.1002/1521-3978(200110)49:10/11<981::aid-prop981>3.0.co;2-f

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It is shown that generalized measurements, required for optimally discriminating between non-orthogonal joint polarization states of two indistinguishable photons, can be realized with the help of polarization-dependent two-photon absorption and by means of sum-frequency generation. Optimization schemes are investigated with respect to minimizing the error probability in inferring the states, as well as with respect to maximizing the probability of success for unambiguous discrimination. Moreover, an implementation of error-minimizing discrimination between N symmetric single-photon states is studied. The latter can be used to extract information from the inconclusive results occurring in unambiguous discrimination between three symmetric two-photon polarization states.
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Quantum mechanics allows for the realization of optimized measurements based on photon counting for the discrimination of nonorthogonal coherent states able to surpass the conventional limits of detection, such as the homodyne and heterodyne limits. Such measurements have a large potential for increasing sensitivities and information transfer in communications and for information processing. In this talk I will describe our current work in the problem of generalized measurements for coherent state discrimination. We implement an optimal inconclusive measurement for binary coherent states [1], a non-projective measurement that allows for achieving the lowest probability of error for a given rate of inconclusive results. This measurement encompasses standard measurement paradigms for state discrimination, specifically minimum error and unambiguous discrimination, and allows to transition between them in an optimal way. [1] M. T. DiMario, F. E. Becerra, Npj Quantum Inf. 8 (1), 1-8.
Abstract Quantum state discrimination is a central problem in quantum measurement theory, with applications spanning from quantum communication to computation. Typical measurement paradigms for state discrimination involve a minimum probability of error or unambiguous discrimination with a minimum probability of inconclusive results. Alternatively, an optimal inconclusive measurement, a non-projective measurement, achieves minimal error for a given inconclusive probability. This more general measurement encompasses the standard measurement paradigms for state discrimination and provides a much more powerful tool for quantum information and communication. Here, we experimentally demonstrate the optimal inconclusive measurement for the discrimination of binary coherent states using linear optics and single-photon detection. Our demonstration uses coherent displacement operations based on interference, single-photon detection, and fast feedback to prepare the optimal feedback policy for the optimal non-projective quantum measurement with high fidelity. This generalized measurement allows us to transition among standard measurement paradigms in an optimal way from minimum error to unambiguous measurements for binary coherent states. As a particular case, we use this general measurement to implement the optimal minimum error measurement for phase-coherent states, which is the optimal modulation for communications under the average power constraint. Moreover, we propose a hybrid measurement that leverages the binary optimal inconclusive measurement in conjunction with sequential, unambiguous state elimination to realize higher dimensional inconclusive measurements of coherent states.