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arXiv:2511.10758 · Physical Review A

Certifying the dimensionality of any quantum channel with minimal assumptions

Saheli Mukherjee, Bivas Mallick, Pratik Ghosal

quant-phSubmitted Nov 13, 2025• Announced Nov 17, 2025• 1 citation
v1 · Nov 13, 2025v2 · Dec 23, 2025v3 · Jul 20, 2026
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Abstract

High-dimensional entanglement offers significant advantages over low-dimensional ones in various information-processing tasks. However, to harness these advantages, it is crucial that the quantum channels used to store or transmit the subsystems of an entangled system not only preserve entanglement but also maintain its dimensionality above a certain threshold. The maximum entanglement dimension that a channel can preserve is referred to as its effective dimensionality, since the channel cannot be used to transmit information of dimension greater than that in a single use. In this work, we present a method to certify whether a quantum channel can preserve entanglement dimension above a given threshold. Unlike existing approaches, our method is faithful -- it can be applied to any channel, and avoids common assumptions such as reliable preparation of entangled states, auxiliary side channels, or perfect measurement devices. Moreover, the method can be extended to faithfully certify other classes of non-resource-breaking channels, such as non-NPT-breaking channels. Finally, we discuss possible experimental realizations of our certification scheme through explicit examples.

Journal reference
Phys. Rev. A 114, 012445 (2026)
DOI
10.1103/xry9-j4g6
Comments
8 pages, 3 figures; Comments are welcome

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Quantum memories are key ingredients for future quantum networks. Developing methods for their certification is therefore an important, yet challenging, problem. In this work, we present a general framework for certifying quantum memories and quantifying their performance in an operational and efficient manner, taking advantage of developments in the theory of quantum channels. We start by giving a pedagogical introduction to these concepts and tools and illustrate their natural application to quantum memories. Specifically, we quantify the fidelity of a quantum memory via the notion of average channel fidelity, which can be estimated precisely in an experiment via a finite set of probe states forming a so-called 222-design. We then present a number of witnessing techniques for certifying this quantity, and show that it gives access to other important properties of the channel, such as its dimensionality and its capacity to transmit quantum information. We consider mostly a simple prepare-and-measure scenario, but discuss also the case of an entanglement-based setup, as well as a semi-device-independent approach. Finally, we apply these methods to a solid-state quantum memory experiment, certifying an average channel fidelity of 98.6%. Our certification methods can be readily applied to other quantum devices, such as fibers, transducers and gates.