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arXiv · 1403.0863

Phase-space representation of completely positive quantum operation: Two-mode squeezed vacuum and thermal states

Sumiyoshi Abe·Yasuyuki Matsuo
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Abstract

Completely positive quantum operations are frequently discussed in the contexts of statistical mechanics and quantum information. They are customarily given by maps forming positive operator-values measures. To intuitively understand physical meanings of such abstract operations, the method of phase-space representations is examined. This method enables one to grasp the operations in terms of the classical statistical notions. As an example of physical importance, here, the phase-space representation of the completely positive quantum operation arising from the single-mode subdynamics of the two-mode squeezed vacuum state, which maps from the vacuum state at vanishing temperature to mixed states with perfect decoherence including the thermal state, is studied. It is found in the $P$ representation that remarkably this operation is invertible, implying that coherence lost by the quantum operation can be recovered.

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cond-mat.stat-mechphysics.opticsquant-ph

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Sumiyoshi Abe, Yasuyuki Matsuo. 2014-03-04. Phase-space representation of completely positive quantum operation: Two-mode squeezed vacuum and thermal states. https://doi.org/10.1103/physreve.91.012126

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