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Constructive counterexamples to the additivity of the minimum output Rényi entropy of quantum channels for all \(p > 2\). (English) Zbl 1201.81026

Summary: We present a constructive example of the violation of the additivity of minimum output Rényi entropy for each \(p > 2\). The example is provided by an antisymmetric subspace of a suitable dimension. We discuss the possibility of extension of the result to go beyond \(p > 2\) and obtain additivity for \(p = 0\) for a class of entanglement breaking channels.

MSC:

81P45 Quantum information, communication, networks (quantum-theoretic aspects)
94A40 Channel models (including quantum) in information and communication theory
94A17 Measures of information, entropy
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