Recovery Map for Fermionic Gaussian Channels
arXiv:1811.04956 · doi:10.1063/1.5093326
Abstract
A recovery map effectively cancels the action of a quantum operation to a partial or full extent. We study the Petz recovery map in the case where the quantum channel and input states are fermionic and Gaussian. Gaussian states are convenient because they are totally determined by their covariance matrix and because they form a closed set under so-called Gaussian channels. Using a Grassmann representation of fermionic Gaussian maps, we show that the Petz recovery map is also Gaussian and determine it explicitly in terms of the covariance matrix of the reference state and the data of the channel. As a by-product, we obtain a formula for the fidelity between two fermionic Gaussian states. We also discuss subtleties arising from the singularities of the involved matrices.
arXiv comment13 pages and 11 pages of appendices. Updated references and footnotes in v2. Updated for a new paragraph of twisted recovery map and change of format in v3
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