Reversibility of a quantum channel: general conditions and their applications to Bosonic linear channels

Abstract

The method of complementary channel for analysis of reversibility (sufficiency) of a quantum channel with respect to families of input states (pure states for the most part) are considered and applied to Bosonic linear (quasi-free) channels, in particular, to Bosonic Gaussian channels. The obtained reversibility conditions for Bosonic linear channels have clear physical interpretation and their sufficiency is also shown by explicit construction of reversing channels. The method of complementary channel gives possibility to prove necessity of these conditions and to describe all reversed families of pure states in the Schrodinger representation. Some applications in quantum information theory are considered. Conditions for existence of discrete classical-quantum subchannels and of completely depolarizing subchannels of a Bosonic linear channel are obtained in the Appendix.

26 pages, journal version, several criteria for reversibility with respect to orthogonal families of mixed states have been added, relations to the zero-error capacities of a channel have been mentioned (Remark 4)

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Cited by in corpus (8)

• Preservation of a quantum Renyi relative entropy implies existence of a recovery map
• On superactivation of zero-error capacities and reversibility of a quantum channel
• All phase-space linear bosonic channels are approximately Gaussian dilatable
• Recoverability of quantum channels via hypothesis testing
• Covariant quantum combinatorics with applications to zero-error communication
• Lower semicontinuity of the entropic disturbance and its applications in quantum information theory
• On singular Bosonic linear channels
• Quantum detailed balance via elementary transitions