2013/02/27 by M. E. Shirokov, Shirokov, M. E.
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #math-ph #math.MP #math.OA #quant-ph
paper · pdf · doi:10.48550/arxiv.1302.6879
9 pages, any comments and references are welcome
arxiv created 2013/02/27 · openalex publication_date 2013/02/27 · arxiv updated 2013/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Properties of Bosonic linear (quasi-free) channels, in particular, Bosonic Gaussian channels with two types of degeneracy are considered. The first type of degeneracy can be interpreted as existence of noise-free canonical variables (for Gaussian channels it means that detα=0). It is shown that this degeneracy implies existence of (infinitely many) "direct sum decompositions" of Bosonic linear channel, which clarifies reversibility properties of this channel (described in arXiv:1212.2354) and provides explicit construction of reversing channels. The second type of degeneracy consists in rank deficiency of the operator describing transformations of canonical variables. It is shown that this degeneracy implies existence of (infinitely many) decompositions of input space into direct sum of orthogonal subspaces such that the restriction of Bosonic linear channel to each of these subspaces is a discrete classical-quantum channel.