Quantum channel reading capacity bounded with efficient computable methods
Efficiently computable bounds on the energy-constrained quantum reading capacity
Information Theory
Summary
Quantum reading is about decoding messages hidden in quantum channels by sending probes and examining outputs. This paper provides new mathematical ways to estimate limits on how well one can read these messages when there is a limit on the energy used for probing. The authors develop methods that can be computed efficiently and apply to different types of quantum channels. They also identify scenarios where simpler, non-adaptive strategies are just as good as more complex ones for reading information.
What this means in practice
- •For quantum communication engineers: Design energy-efficient protocols to read data encoded in quantum channels using provably tight capacity bounds.
- •For quantum hardware developers: Set practical limits on information retrieval capabilities given energy constraints in quantum device operations.
Authors
Vishal Singh, Zixin Huang, Mark M. Wilde
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.