2009/05/31 by Piotr Gawron, Zbigniew Puchała, Jarosław Adam Miszczak +2 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #math.OA #quant-ph
paper · pdf · doi:10.1063/1.3496901
published as J. Math. Phys. 51, 102204 (2010) · 39 pages, 7 figures, Original preprint "Local numerical range: a versatile tool in the theory of quantum information" was broadened and split into two papers: "Restricted numerical range: a versatile tool in the theory of quantum information", and "Product numerical range in a space with tensor product structure"
arxiv created 2010/08/20 · openalex publication_date 2010/10/01 · arxiv updated 2010/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Numerical range of a Hermitian operator X is defined as the set of all possible expectation values of this observable among a normalized quantum state. We analyze a modification of this definition in which the expectation value is taken among a certain subset of the set of all quantum states. One considers for instance the set of real states, the set of product states, separable states, or the set of maximally entangled states. We show exemplary applications of these algebraic tools in the theory of quantum information: analysis of k-positive maps and entanglement witnesses, as well as study of the minimal output entropy of a quantum channel. Product numerical range of a unitary operator is used to solve the problem of local distinguishability of a family of two unitary gates.