Efficiently computable bounds on the energy-constrained quantum reading capacity

2026-10-06

AI Summary

This study investigates computable bounds on the reading capacity of finite-dimensional quantum channels under energy constraints. It proposes an input-dependent chain rule based on the Belavkin–Staszewski relative entropy to construct a tight converse upper bound, and develops bilinear semidefinite approximations with alternating optimization algorithms to efficiently compute achievable rate lower bounds. The primary contributions include establishing computable upper and lower bounds on the capacity under adaptive protocols, and proving that, in the absence of energy constraints, non-adaptive protocols suffice to achieve the capacity limit for joint classical-quantum channels. These results provide both a rigorous theoretical characterization and practical computational tools for quantum channel reading.

Abstract

In quantum reading, classical messages are encoded in sequences of quantum channels and recovered by probing the channels and processing their outputs. We study the reading capacity of a finite family of finite-dimensional channels under an average constraint on the probing energy, allowing arbitrary adaptive operations between channel uses. Using an input-dependent chain rule for the Belavkin-Staszewski relative entropy, we derive a converse bound expressed as an optimization involving channel Choi operators and the operator relative entropy. This formulation admits semidefinite approximations and reduces, without an energy constraint, to a channel information radius. To obtain achievable rates, we construct bilinear semidefinite lower approximations to a standard non-adaptive reading bound. Alternating optimization produces feasible probe states and encoding distributions, whose Holevo information gives a directly evaluable achievable rate. For jointly classical-quantum channels, we derive a separate converse based on the Umegaki relative entropy. Without an energy constraint, this converse matches a non-adaptive achievable rate, recovering a recent result of Pascual Abraldes and Winter: non-adaptive protocols suffice to achieve the unconstrained reading capacity of jointly classical-quantum channels.

Problem

• quantum reading capacity
• energy constraint
• converse bound
• achievable rate
• adaptive protocols

Innovation

• quantum reading capacity
• Belavkin-Staszewski relative entropy
• semidefinite programming
• alternating optimization
• jointly classical-quantum channels