Characterising memory in quantum channel discrimination via constrained separability problems

Ties-Albrecht Ohst; Shijun Zhang; Hai Chau Nguyen; Martin Plávala; Marco Túlio Quintino

doi:10.22331/q-2026-01-28-1988

Characterising memory in quantum channel discrimination via constrained separability problems

Ties-Albrecht Ohst¹, Shijun Zhang², Hai Chau Nguyen¹, Martin Plávala^1,3, and Marco Túlio Quintino²

¹Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Siegen 57068, Germany
²Sorbonne Université, CNRS, LIP6, F-75005 Paris, France
³Institut für Theoretische Physik, Leibniz Universität Hannover, Hannover, Germany

Published:	2026-01-28, volume 10, page 1988
Editor:	Thomas Elliott
Eprint:	arXiv:2411.08110v2
Doi:	https://doi.org/10.22331/q-2026-01-28-1988
Citation:	Quantum 10, 1988 (2026).

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Abstract

Quantum memories are a crucial precondition in many protocols for processing quantum information. A fundamental problem that illustrates this statement is given by the task of channel discrimination, in which an unknown channel drawn from a known random ensemble should be determined by applying it for a single time. In this paper, we characterise the quality of channel discrimination protocols when the quantum memory, quantified by the auxiliary dimension, is limited. This is achieved by formulating the problem in terms of separable quantum states with additional affine constraints that all of their factors in each separable decomposition obey. We discuss the computation of upper and lower bounds to the solutions of such problems which allow for new insights into the role of memory in channel discrimination. In addition to the single-copy scenario, this methodological insight allows to systematically characterise quantum and classical memories in adaptive channel discrimination protocols. Especially, our methods enabled us to identify channel discrimination scenarios where classical or quantum memory is required, and to identify the hierarchical and non-hierarchical relationships within adaptive channel discrimination protocols.

Featured image: Any causally ordered quantum channel discrimination protocol acting on two uses of a channel $\mathcal{C}$ can be characterised by a state preparation $\rho$, an intermediate quantum instrument $\mathcal{K}_j$, and a final quantum measurement $M^{i\mid j}$, whose setting may depend on the intermediate outcome. While the quantum memory used in the protocol is quantified by the dimensionality of the state and the final measurement, the corresponding classical memory is encoded in the number of outcomes of the intermediate instrument.

Popular summary

Quantum technologies often rely on storing information encoded in quantum states in so-called quantum memories, but in practice such quantum memories are always limited. In particular, it is challenging to build memories that coherently store quantum states in a high dimension. A key question is how these limitations affect what quantum protocols can achieve. We address this question using the fundamental task of channel discrimination, where one must identify an unknown physical process from a known set using only a single or limited number of applications.

We develop a general framework to quantify how well channel discrimination can be performed when the available memory — classical or quantum — has restricted size. Our approach leads to practical computational methods that provide rigorous bounds on the best achievable performance under these constraints.

By applying these tools to both single- and multi-step scenarios, including adaptive strategies, we identify situations where the presence of quantum memory is essential and clarify how the coherent transfer of quantum information enables improved discrimination. Overall, our results provide a systematic way to understand the role of memory resources in quantum information processing.

► BibTeX data

@article{Ohst2026characterising,
  doi = {10.22331/q-2026-01-28-1988},
  url = {https://doi.org/10.22331/q-2026-01-28-1988},
  title = {Characterising memory in quantum channel discrimination via constrained separability problems},
  author = {Ohst, Ties-Albrecht and Zhang, Shijun and Nguyen, Hai Chau and Pl{\'{a}}vala, Martin and Quintino, Marco T{\'{u}}lio},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {1988},
  month = jan,
  year = {2026}
}

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