The passive states of a quantum system minimize the average energy among all the states with a given spectrum. We prove that passive states are the optimal inputs of single-jump lossy quantum channels. These channels arise from a weak interaction of the quantum system of interest with a large Markovian bath in its ground state, such that the interaction Hamiltonian couples only consecutive energy eigenstates of the system. We prove that the output generated by any input state ρ majorizes the output generated by the passive input state ρ0 with the same spectrum of ρ. Then, the output generated by ρ can be obtained applying a random unitary operation to the output generated by ρ0. This is an extension of De Palma [IEEE Trans. Inf. Theory 62, 2895 (2016)], where the same result is proved for one-mode bosonic Gaussian channels. We also prove that for finite temperature this optimality property can fail already in a two-level system, where the best input is a coherent superposition of the two energy eigenstates.

Passive states as optimal inputs for single-jump lossy quantum channels

De Palma, G.
;
Mari, A.;LLOYD, SETH;Giovannetti, V.
2016

Abstract

The passive states of a quantum system minimize the average energy among all the states with a given spectrum. We prove that passive states are the optimal inputs of single-jump lossy quantum channels. These channels arise from a weak interaction of the quantum system of interest with a large Markovian bath in its ground state, such that the interaction Hamiltonian couples only consecutive energy eigenstates of the system. We prove that the output generated by any input state ρ majorizes the output generated by the passive input state ρ0 with the same spectrum of ρ. Then, the output generated by ρ can be obtained applying a random unitary operation to the output generated by ρ0. This is an extension of De Palma [IEEE Trans. Inf. Theory 62, 2895 (2016)], where the same result is proved for one-mode bosonic Gaussian channels. We also prove that for finite temperature this optimality property can fail already in a two-level system, where the best input is a coherent superposition of the two energy eigenstates.
Settore MAT/07 - Fisica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/68986
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