Quantum process discrimination with restricted strategies

Nakahira, Kenji

doi:10.48550/arxiv.2104.09038

Cited by 1 publication

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“…For examples of such restricted problems, the reader can refer to Ref. [64]. We will extend this work to a broad class of optimization criteria.…”

Section: Restricted Testersmentioning

confidence: 99%

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Generalized quantum process discrimination problems

Nakahira,

Kato

2021

Preprint

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We study a broad class of quantum process discrimination problems that can handle many optimization strategies such as the Bayes, Neyman-Pearson, and unambiguous strategies, where each process can consist of multiple time steps and can have an internal memory. Given a collection of candidate processes, our task is to find a discrimination strategy, which may be adaptive and/or entanglement-assisted, that maximizes a given objective function subject to given constraints. Our problem can be formulated as a convex problem. Its Lagrange dual problem with no duality gap and necessary and sufficient conditions for an optimal solution are derived. We also show that if a problem has a certain symmetry and at least one optimal solution exists, then there also exists an optimal solution with the same type of symmetry. A minimax strategy for a process discrimination problem is also discussed. As applications of our results, we provide some problems in which an adaptive strategy is not necessary for optimal discrimination. We also present an example of single-shot channel discrimination for which an analytical solution can be obtained.

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“…For examples of such restricted problems, the reader can refer to Ref. [64]. We will extend this work to a broad class of optimization criteria.…”

Section: Restricted Testersmentioning

confidence: 99%

“…Very recently, a general formulation of restricted problems of finding minimum-error testers has been discussed in Ref. [64]. For examples of such restricted problems, the reader can refer to Ref.…”

Section: Restricted Testersmentioning

confidence: 99%