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A quantum version of Wielandt's inequality

By Mikel Sanz, David Pérez García, Juan I. Cirac and Michael Wolf

Abstract

In this paper, Wielandt's inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found. Using this bound, dichotomy theorems for the zero--error capacity of quantum channels and for the Matrix Product State (MPS) dimension of ground states of frustration-free Hamiltonians are derived. The obtained inequalities also imply new bounds on the required interaction-range of Hamiltonians with unique MPS ground state

Topics: Física matemática, Teoría de los quanta
Publisher: IEEE
Year: 2010
DOI identifier: 10.1109/TIT.2010.2054552
OAI identifier: oai:www.ucm.es:12162
Provided by: EPrints Complutense

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