2012/06/30 by Wojciech Roga, Zbigniew Puchała, Łukasz Rudnicki +1 · 23 citations
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physreva.87.032308
published in Physical Review A 87(3) (American Physical Society) · 10 pages, 4 figures
openalex publication_date 2013/03/07 · arxiv created 2013/05/24 · arxiv updated 2013/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Spectral properties of an arbitrary matrix can be characterized by the entropy of its rescaled singular values. Any quantum operation can be described by the associated dynamical matrix or by the corresponding superoperator. The entropy of the dynamical matrix describes the degree of decoherence introduced by the map, while the entropy of the superoperator characterizes the a priori knowledge of the receiver of the outcome of a quantum channel \ensuremathΦ. We prove that for any map acting on an N-dimensional quantum system the sum of both entropies is not smaller than lnN. For any bistochastic map this lower bound reads 2lnN. We investigate also the corresponding R'enyi entropies, providing an upper bound for their sum, and analyze the entanglement of the bi-partite quantum state associated with the channel.