A Quantum Version of Wielandt's Inequality

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 ca...

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Veröffentlicht in:	IEEE transactions on information theory 2010-09, Vol.56 (9), p.4668-4673
Hauptverfasser:	Sanz, M, Pérez-García, David, Wolf, M M, Cirac, J I
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied sciences Channel capacity Classical channels Electrons Exact sciences and technology Information rates Information systems Information theory Information, signal and communications theory Linear matrix inequalities Mathematical models Memoryless systems Probability distribution quantum channels Quantum mechanics spin systems Stationary state Stochastic processes strongly correlated electrons Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Theorems Transmission and modulation (techniques and equipments) Upper bound Wielandt's inequality
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Beschreibung
Zusammenfassung:	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.
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2010.2054552