For classical-quantum states, the conditional entropy can change by at most epsilon log2(d_B-1) + h2(epsilon) under a trace-distance perturbation epsilon, and this bound cannot be improved.
Advanced Alicki-Fannes-Winter method for energy-constrained quantum systems and its use
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abstract
We describe an universal method for quantitative continuity analysis of entropic characteristics of energy-constrained quantum systems and channels. It gives asymptotically tight continuity bounds for basic characteristics of quantum systems of wide class (including multi-mode quantum oscillators) and channels between such systems under the energy constraint. The main application of the proposed method is the advanced version of the uniform finite-dimensional approximation theorem for basic capacities of energy-constrained quantum channels.
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Optimal uniform continuity bound for conditional entropy of classical--quantum states
For classical-quantum states, the conditional entropy can change by at most epsilon log2(d_B-1) + h2(epsilon) under a trace-distance perturbation epsilon, and this bound cannot be improved.