Impossibility of local state transformation via hypercontractivity
type: Item
instance of: scholarly article
title: Impossibility of local state transformation via hypercontractivity
zbMATH Open document ID: 1304.81034
author: Payam Delgosha
author: Salman Beigi
published in: Communications in Mathematical Physics
publication date: 2014-10-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/1307.2747
review text: Can a target bipartite quantum state \(\sigma_{A'B'}\) be obtained by applying local operations to (arbitrarily many) \(n\) copies of a given bipartite state \(\rho_{AB}\)? Necessary conditions for a positive answer are given in terms of hypercontractivity properties of superoperators related to duly ``normalized'' states \(\tilde{\rho}^{\otimes n}\) and \(\tilde{\sigma}\) via Choi-Jamiolkowski correspondence. The superoperators are endowed with norms and completely bounded norms, with respect to the scales of Schatten spaces, to analyze the arising hypercontractivity ribbons. The latter notion was known in the classical case, as well as maximal correlation, and both are generalized to the noncommutative quantum setting to provide measures of bipartite correlation. Illustrative examples are also given.
Mathematics Subject Classification ID: 81P40
Mathematics Subject Classification ID: 94A40
Mathematics Subject Classification ID: 47A30
zbMATH DE Number: 6353812
zbMATH Keywords: bipartite quantum state
zbMATH Keywords: Choi-Jamiolkowski isomorphism
zbMATH Keywords: maximal correlation
zbMATH Keywords: hypercontractivity ribbons
zbMATH Keywords: operators between Schatten classes
zbMATH Keywords: completely bounded norms
zbMATH Keywords: quantum channel
reviewed by: Andrey V. Bulinski
MaRDI profile type: Publication
OpenAlex ID: W2054460121
arXiv ID: 1307.2747
cites work: New version of the probabilistic generalization of the large sieve
cites work: On measures of dependence
cites work: A new quantum data processing inequality
cites work: Q5759902
cites work: On Sequences of Pairs of Dependent Random Variables
cites work: Spreading of sets in product spaces and hypercontraction of the Markov operator
cites work: Sandwiched Rényi divergence satisfies data processing inequality
cites work: Q2706552
cites work: Modulus of continuity of the matrix absolute value
cites work: Q3522509
cites work: A note on the \(p \rightarrow q\) norms of 2-positive maps
cites work: Multiplicativity of completely bounded \(p\)-norms implies a new additivity result
cites work: Q4215796
cites work: Comparing gaussian and Rademacher cotype for operators on the space of continuous functions
cites work: Q4544834
cites work: Q4112938
cites work: Positive definite matrices
cites work: Q4110023
cites work: Hypercontractivity in noncommutative \(L_1\) spaces
cites work: Quantum logarithmic Sobolev inequalities and rapid mixing
cites work: Hypercontractivity for semigroups of unital qubit channels
cites work: On reverse hypercontractivity
cites work: Channel capacities via \( p\)-summing norms
cites work: Q4066072
cites work: Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Rényi relative entropy
cites work: On quantum Rényi entropies: A new generalization and some properties
DOI: 10.1007/S00220-014-2105-Y
description: scientific article; zbMATH DE number 6353812