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arXiv:2510.15506 · New Journal of Physics

Adaptive quantum channel discrimination using methods of quantum metrology

Stanisław Sieniawski, Rafał Demkowicz-Dobrzański

Published Jan 28, 2026• 1 citation
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Abstract

Abstract We present an efficient tensor-network based algorithm for finding the optimal adaptive quantum channel discrimination strategies inspired by recently developed numerical methods in quantum metrology to find the optimal adaptive channel estimation protocols. We examine the connection between channel discrimination and estimation problems, highlighting in particular an appealing structural similarity between models that admit Heisenberg scaling estimation performance, and models that admit perfect channel discrimination in finite–number of channel uses.

DOI
10.1088/1367-2630/ae3edd

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We investigate the performance of parallel and adaptive quantum channel discrimination strategies for a finite number of channel uses. It has recently been shown that, in the asymmetric setting with asymptotically vanishing type I error probability, adaptive strategies are asymptotically not more powerful than parallel ones. We extend this result to the non-asymptotic regime with finitely many channel uses, by explicitly constructing a parallel strategy for any given adaptive strategy, and bounding the difference in their performances, measured in terms of the decay rate of the type II error probability per channel use. We further show that all parallel strategies can be optimized over in time polynomial in the number of channel uses, and hence our result can also be used to obtain a poly-time-computable asymptotically tight upper bound on the performance of general adaptive strategies.
We investigate the performance of parallel and adaptive quantum channel discrimination strategies for a finite number of channel uses. It has recently been shown that, in the asymmetric setting with asymptotically vanishing type I error probability, adaptive strategies are asymptotically not more powerful than parallel ones. We extend this result to the non-asymptotic regime with finitely many channel uses, by explicitly constructing a parallel strategy for any given adaptive strategy, and bounding the difference in their performances, measured in terms of the decay rate of the type II error probability per channel use. We further show that all parallel strategies can be optimized over in time polynomial in the number of channel uses, and hence our result can also be used to obtain a poly-time-computable asymptotically tight upper bound on the performance of general adaptive strategies.
We consider the problem of estimating a classical parameter encoded in a quantum channel, assuming the most general strategy allowed by quantum mechanics. This strategy is based on the exploitation of an unlimited amount of pre-shared entanglement plus the use of adaptive probings, where the input of the channel is interactively updated during the protocol. We show that, for the wide class of teleportation-stretchable channels in finite dimension, including all Pauli channels and erasure channels, the quantum Fisher information cannot exceed an ultimate bound given by the Choi matrix of the encoding channel. We also extend our methods and results to quantum channel discrimination, finding a corresponding ultimate bound for the minimum error probability. Thus, our findings establish the ultimate precision limits that are achievable in quantum metrology and quantum discrimination for the most basic models of discrete-variable quantum channels.