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Transformations on density operators that leave the Holevo bound invariant. (English) Zbl 1302.81048
Summary: For a given probability distribution \(\lambda_1,\dots,\lambda_m\) we determine the structure of all such maps defined on a dense subset of density operators which leave the Holevo bound invariant i.e. which satisfy \[ S\left(\sum\limits_{k=1}^m \lambda_k \phi(\rho_k)\right)-\sum\limits_{k=1}^m \lambda_k S\left(\phi (\rho_k)\right)= S\left(\sum\limits_{k=1}^m \lambda_k \rho_k\right)-\sum_{k=1}^m \lambda_k S(\rho_k) \] for all possible collections \(\rho_1,\dots,\rho_m\) of density operators.

MSC:
81P15 Quantum measurement theory, state operations, state preparations
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
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