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A quantum version of Wielandt's inequality

Sanz, Mikel and Pérez García, David and Cirac, Juan I. and Wolf, Michael (2010) A quantum version of Wielandt's inequality. (Submitted)

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Official URL: http://arxiv.org/abs/0909.5347

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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.


Item Type:Article
Additional Information:

last revised 28 May 2010

Uncontrolled Keywords:Teoría cuántica, Física matemática, Quantum Physics, Mathematical Physics, Terms—classical channels, Information rates, Quantum channels, Spin systems, Strongly correlated electrons, Wielandt’s inequality
Subjects:Sciences > Physics > Mathematical physics
Sciences > Physics > Quantum theory
ID Code:12162
Deposited On:03 Feb 2011 09:33
Last Modified:06 Feb 2014 09:18

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