Reinforcement Learning with Neural Networks for Quantum Multiple Hypothesis Testing

Brandsen, Sarah; Stubbs, Kevin D.; Pfister, Henry D.

doi:10.1109/isit44484.2020.9174150

“…Already the minimum extension of three symmetric states is a highly non-trivial case. For minimum error the direct application of local measurements with Bayesian updating for two copies of the states does not give the optimal global performance [46,45]. As far as we are aware, there is no proof that this is the case for more general one-way local protocols.…”

Section: Discussionmentioning

confidence: 97%

“…One can nevertheless carry out a numerical study. It has been recently shown numerically that local measurements supplemented with the Bayesian updating rule do not yield the optimal global success probability in the minimum error approach already in the case of three symmetric states [45] (see also [46] for an analysis with symmetric coherent states). However, it remains an open question whether this feature also holds for zero-error protocols, which we discuss next.…”

Section: Two-state Minimum Error Discriminationmentioning

confidence: 99%

Online identification of symmetric pure states

Sentís,

Martínez-Vargas,

Muñoz-Tapia

2021

Preprint

0

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We consider online strategies for discriminating between symmetric pure states with zero error when n copies of the states are provided. Optimized online strategies involve local, possibly adaptive measurements on each copy and are optimal at each step, which makes them robust in front of particle losses or an abrupt termination of the discrimination process. We first review previous results on binary minimum and zero error discrimination with local measurements that achieve the maximum success probability set by optimizing over global measurements, highlighting their online features. We then extend these results to the case of zero error identification of three symmetric states with constant overlap. We provide optimal online schemes that attain global performance for any n if the state overlaps are positive, and for odd n if overlaps have a negative value. For arbitrary complex overlaps, we show compelling evidence that online schemes fail to reach optimal global performance. The online schemes that we describe only require to store the last outcome obtained in a classical memory, and adaptiveness of the measurements reduce to at most two changes, regardless of the value of n.

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“…Already the minimum extension of three symmetric states is a highly non-trivial case. For minimum error the direct application of local measurements with Bayesian updating for two copies of the states does not give the optimal global performance [46,47]. As far as we are aware, there is no proof that this is the case for more general one-way local protocols.…”

Section: Discussionmentioning

confidence: 97%

“…One can nevertheless carry out a numerical study. It has been recently shown numerically that local measurements supplemented with the Bayesian updating rule do not yield the optimal global success probability in the minimum error approach already in the case of three symmetric states [46] (see also [47] for an analysis with symmetric coherent states). However, it remains an open question whether this feature also holds for zero-error protocols, which we discuss next.…”

Section: Two-state Minimum Error Discriminationmentioning

confidence: 99%

Online identification of symmetric pure states

Sentís

¹

,

Martínez-Vargas

²

,

Muñoz-Tapia

³

2022

Quantum

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We consider online strategies for discriminating between symmetric pure states with zero error when n copies of the states are provided. Optimized online strategies involve local, possibly adaptive measurements on each copy and are optimal at each step, which makes them robust in front of particle losses or an abrupt termination of the discrimination process. We first review previous results on binary minimum and zero error discrimination with local measurements that achieve the maximum success probability set by optimizing over global measurements, highlighting their online features. We then extend these results to the case of zero error identification of three symmetric states with constant overlap. We provide optimal online schemes that attain global performance for any n if the state overlaps are positive, and for odd n if overlaps have a negative value. For arbitrary complex overlaps, we show compelling evidence that online schemes fail to reach optimal global performance. The online schemes that we describe only require to store the last outcome obtained in a classical memory, and adaptiveness of the measurements reduce to at most two changes, regardless of the value of n.

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“…Equivalently, we had to distinguish between two sequences of constant-amplitude coherent pulses, which is a special case of sequences of pure states. This general class of problems was considered in, e.g., [24]- [26], with an emphasis on optimal strategies that apply "local" measurements to the individual states. Specifically, Theorem 2 of [25] directly generalizes the properties of the Dolinar receiver to such sequences of states.…”

Section: Concave Casementioning

confidence: 99%

Optimal Discrimination Between Two Pure States and Dolinar-Type Coherent-State Detection

Katz,

Samorodnitsky,

Kochman

2024

IEEE Trans. Inform. Theory

0

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We consider the problem of discrimination between two pure quantum states. It is well known that the optimal measurement under both the error-probability and log-loss criteria is a projection, while under an "erasure-distortion" criterion it is a three-outcome positive operator-valued measure (POVM). These results were derived separately.We present a unified approach which finds the optimal measurement under any distortion measure that satisfies a convexity relation with respect to the Bhattacharyya distance. Namely, whenever the measure is relatively convex (resp. concave), the measurement is the projection (resp. three-outcome POVM) above. The three above-mentioned results are obtained as special cases of this simple derivation. As for further measures for which our result applies, we prove that Renyi entropies of order 1 and above (resp. 1/2 and below) are relatively convex (resp. concave). A special setting of great practical interest, is the discrimination between two coherent-light waveforms. In a remarkable work by Dolinar it was shown that a simple detector consisting of a photon counter and a feedback-controlled local oscillator obtains the quantum-optimal error probability. Later it was shown that the same detector (with the same local signal) is also optimal in the log-loss sense. By applying a similar convexity approach, we obtain in a unified manner the optimal signal for a variety of criteria.

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Reinforcement Learning with Neural Networks for Quantum Multiple Hypothesis Testing

Cited by 4 publications

References 21 publications

Online identification of symmetric pure states

Online identification of symmetric pure states

Online identification of symmetric pure states

Optimal Discrimination Between Two Pure States and Dolinar-Type Coherent-State Detection

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