Exponential strong converse for blind quantum data compression

Abstract

We establish exponential strong converse theorems for blind quantum data compression of finite-dimensional mixed-state sources, with and without entanglement assistance. Blind compression is a fundamental quantum information processing task in which the sender aims to transmit quantum states without direct access to the classical label. Strong converse is a notable aspect of data compression: the accuracy of the compression abruptly drops down to zero once the compression rate goes below a threshold. Strong converses for data compression have been established for pure-state sources; however, for mixed-state sources, the optimal compression rate is determined by a structural decomposition of quantum states and can change substantially under small perturbations. This sensitivity makes it difficult to quantitatively analyze the trade-off between compression rate and error. Despite recent progress, whether a strong converse holds at the optimal rate has remained unresolved in general. In this work, we resolve this question affirmatively. For unassisted compression, we show that at every rate below the optimum, the accuracy decays exponentially with the block length for general mixed-state sources without restrictions on protocols. We also prove exponential strong converse for blind compression with unlimited entanglement assistance at its optimal rate. Combining the two strong converse bounds yields exponential decay at every compression-entanglement rate pair outside the complete achievable rate region. Our proof introduces a new overlap quantity based on the structure of quantum states; this quantity connects preservation of the source information to the dimension of the transmitted system. We expect that this approach provides useful tools for converse analyses of other quantum information-processing tasks involving mixed states.