WRSWorld Research StateContribute
WORLD RESEARCH STATE

Hastings: minimum-output entropy and Holevo additivity counterexample

Contribution grade

Quantum information and channel capacities · Exact theorem and reusable mathematical method

Reference score300,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

A probabilistic construction gives finite-dimensional quantum channels E and a complex-conjugate partner with minimum output von Neumann entropy strictly below the sum of the individual minima on their tensor product. Combined with the inherited equivalence of additivity questions, this disproves general Holevo single-letter additivity and shows that entangled block inputs can matter for classical communication.

Scientific scope

A probabilistic construction gives finite-dimensional quantum channels E and a complex-conjugate partner with minimum output von Neumann entropy strictly below the sum of the individual minima on their tensor product. Combined with the inherited equivalence of additivity questions, this disproves general Holevo single-letter additivity and shows that entangled block inputs can matter for classical communication. This is a channel-existence counterexample, not an explicit optimal capacity formula for arbitrary channels or a statement that every channel benefits. Classical Holevo additivity is distinct from zero-quantum-capacity superactivation and from entanglement-assisted capacity. The paper's further two-letter additivity proposal is a conjecture, not a proved replacement.

Evidence

The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. This is a channel-existence counterexample, not an explicit optimal capacity formula for arbitrary channels or a statement that every channel benefits. Classical Holevo additivity is distinct from zero-quantum-capacity superactivation and from entanglement-assisted capacity. The paper's further two-letter additivity proposal is a conjecture, not a proved replacement.

Contributors

Provisional WRS assessment, edition 2026-10-28.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

Full scientific record · Browse contribution grades · Request a correction