Passive states as optimal inputs for single-jump lossy quantum channels
Name
PhysRevA.93.062328.pdf
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150.98 KB
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Author(s)
De Palma, Giacomo
Mari, Andrea
Lloyd, Seth
Giovannetti, Vittorio
Date Issued
June 2016
Journal
Physical Review A
Publisher
American Physical Society
Citation
De Palma, Giacomo et al. “Passive States as Optimal Inputs for Single-Jump Lossy Quantum Channels.” Physical Review A 93.6 (2016): n. pag. © 2016 American Physical Society
Version
Final published version
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 ρ[subscript 0] 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 ρ[superscript 0]. This is an extension of De Palma et al. [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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Research Laboratory of Electronics
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.93.062328
