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Discrimination between nonorthogonal two-photon polarization states

Ulrike Herzog

Published Jan 1, 2001• 8 citations
OpenAlex

Abstract

It is shown that generalized measurements, required for optimally discriminating between nonorthogonal 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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Discrimination between Non-orthogonal Two-photon Polarization States

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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.

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It is shown that generalized measurements, required for optimally discriminating between nonorthogonal 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.
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.
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 propose an experimental setup for discriminating four linearly independent nonorthogonal symmetric quantum states. The setup is based on linear optics only and can be configured to implement both optimal unambiguous state discrimination [Chefles and Barnett, Phys. Lett. A 250, 223 (1998)] and minimum error discrimination. In both cases, the setup is characterized by an optimal success probability. The experimental setup can be generalized to the case of discrimination among NNN linearly nonorthogonal symmetric quantum states. We also study the discrimination between two incoherent superpositions of symmetric states. In this case, the setup also achieves an optimal success probability in the case of unambiguous discrimination as well as minimum error discrimination.
Quantum mechanics forbids deterministic discrimination among nonorthogonal states. Nonetheless, the capability to distinguish nonorthogonal states unambiguously is an important primitive in quantum information processing. In this work, we experimentally implement generalized measurements in an optical system and demonstrate the first optimal unambiguous discrimination between three nonorthogonal states, with a success rate of 55%, to be compared with the 25% maximum achievable using projective measurements. Furthermore, we present the first realization of unambiguous discrimination between a pure state and a nonorthogonal mixed state.
It is known that unambiguous discrimination among nonorthogonal but linearly independent quantum states is possible with a certain probability of success. Here, we consider a variant of that problem. Instead of discriminating among all of the different states, we shall only discriminate between two subsets of them. In particular, for the case of three nonorthogonal states, ${|{\ensuremath{\psi}}_{1}〉,|{\ensuremath{\psi}}_{2}〉,|{\ensuremath{\psi}}_{3}〉},$ we show that the optimal strategy to distinguish $|{\ensuremath{\psi}}_{1}〉$ from the set ${|{\ensuremath{\psi}}_{2}〉,|{\ensuremath{\psi}}_{3}〉}$ has a higher success rate than if we wish to discriminate among all three states. Somewhat surprisingly, for unambiguous discrimination the subsets need not be linearly independent. A fully analytical solution is presented, and we also show how to construct generalized interferometers (multiport) which provide an optical implementation of the optimal strategy.
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.