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Entropy

Quantum Capacity of Continuously Observed Ion Channels

Paulina Trybek, Jerzy Dajka

Published May 15, 2026• 0 citations
Publisher

Abstract

A quantum model describing ion channels from an information-theoretic perspective is considered. The information χ-capacity of an ion channel, treated as an information channel whose properties are modified by continuous quantum measurements, is investigated. The behavior of the χ-capacity is analyzed as a function of the measurement parameters, in particular the type of measured observable, the measurement duration, and the measurement strength. It is shown that the information χ-capacity exhibits qualitatively different behaviors depending on the measurement conditions, including regimes of rapid decay as well as regimes where it remains finite for long observation times. These results indicate that, within the considered model, continuous observation may significantly influence the information-theoretic properties of the effective ion-channel dynamics.

DOI
10.3390/e28050555

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A quantum model describing ion channels from an information-theoretic perspective is considered. The information χ-capacity of an ion channel, treated as an information channel whose properties are modified by continuous quantum measurements, is investigated. The behavior of the χ-capacity is analyzed as a function of the measurement parameters, in particular the type of measured observable, the measurement duration, and the measurement strength. It is shown that the information χ-capacity exhibits qualitatively different behaviors depending on the measurement conditions, including regimes of rapid decay as well as regimes where it remains finite for long observation times. These results indicate that, within the considered model, continuous observation may significantly influence the information-theoretic properties of the effective ion-channel dynamics.
In this paper we consider the classical capacities of quantum-classical channels corresponding to measurement of observables. Special attention is paid to the case of continuous observables. We give formulas for unassisted and entanglement-assisted classical capacities C and C ea and consider some explicitly solvable cases, which give simple examples of entanglement-breaking channels with C < C ea. We also elaborate on the ensemble-observable duality to show that C ea for the measurement channel is related to the χ-quantity for the dual ensemble in the same way as C is related to the accessible information. This provides both accessible information and the χ-quantity for quantum ensembles dual to our examples.
A coding theorem for entanglement-assisted communication via an infinite-dimensional quantum channel with linear constraints is extended to a natural degree of generality. Relations between the entanglement-assisted classical capacity and χ-capacity of constrained channels are obtained, and conditions for their coincidence are given. Sufficient conditions for continuity of the entanglement-assisted classical capacity as a function of a channel are obtained. Some applications of the obtained results to analysis of Gaussian channels are considered. A general (continuous) version of the fundamental relation between coherent information and the measure of privacy of classical information transmission via an infinite-dimensional quantum channel is proved.
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We study the relation between the unassisted and entanglement-assisted classical capacities C and C ea of entanglement-breaking channels. We argue that the gain of entanglement assistance C ea / C > 1 generically for measurement channels with unsharp observables; in particular for the measurements with pure posterior states the information loss in the entanglement-assisted protocol is zero, resulting in an arbitrarily large gain for very noisy or weak signal channels. This is illustrated by examples of continuous observables corresponding to state tomography in finite dimensions and heterodyne measurement. In contrast, state preparations are characterized by the property of having no gain of entanglement assistance, C ea / C = 1.