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Updated: Apr 17, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Phase-space representation of completely positive quantum operation: invertible subdynamics of two-mode squeezed
Sumiyoshi Abe1, Yasuyuki Matsuo2
1Department of Physical Engineering, Mie University, Mie 514-8507, Japan and Institute of Physics, Kazan Federal University, Kazan 420008, Russia.
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 the 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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