Quantum

Efficiently computable bounds on the energy-constrained quantum reading capacity

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Briefings

This research presents new bounds for the energy-constrained quantum reading capacity of finite-dimensional channels. Using an input-dependent chain rule for the Belavkin-Staszewski relative entropy, the authors derive a converse bound involving channel Choi operators and operator relative entropy. For achievable rates, they construct bilinear semidefinite lower approximations to a standard non-adaptive reading bound, enabling feasible probe states and encoding distributions. The study also derives a separate converse for jointly classical-quantum channels based on the Umegaki relative entropy, which matches a non-adaptive achievable rate for unconstrained scenarios.

Key points

• The study derives a converse bound for the energy-constrained quantum reading capacity using an input-dependent chain rule for the Belavkin-Staszewski relative entropy, expressed as an optimization involving channel Choi operators and operator relative entropy.
• Achievable rates are obtained via bilinear semidefinite lower approximations to a standard non-adaptive reading bound, producing feasible probe states and encoding distributions whose Holevo information yields a directly evaluable rate.

Context and limitations

The results apply to finite-dimensional channels under an average constraint on probing energy with arbitrary adaptive operations. Converse bounds are expressed in terms of Choi operators and relative entropy, while achievable rates rely on semidefinite approximations. The study covers jointly classical-quantum channels but does not provide bounds for other channel types or energy constraints.

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