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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. IEEE Transactions on Information Theory, 56 (9). ISSN 4668-4673 (Submitted)


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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
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:03 Dec 2014 11:13

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