Passive States Optimize the Output of Bosonic Gaussian Quantum Channels


An ordering between the quantum states emerging from one-mode gauge-covariant bosonic Gaussian channel is proved. Specifically, we have a tendency to show that among the set of input density matrices with the same given spectrum, the element passive with respect to the Fock basis (i.e., diagonal with decreasing eigenvalues) produces an output, which majorizes all the other outputs emerging from the same set. When applied to pure input states, our finding includes as a special case the result of Mari et al., Nat. Comm. five, 3826 (2014) that implies that the output associated to the vacuum majorizes the others.

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