Typical support and Sanov large deviations of correlated states
Igor Bjelakovic, Jean-Dominique Deuschel, Tyll Krüger, Ruedi Seiler, Rainer Siegmund-Schultze, and Arleta Szkola
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Submission date: 29. Mar. 2007
published in: Communications in mathematical physics, 279 (2008) 2, p. 559-584
DOI number (of the published article): 10.1007/s00220-008-0440-6
MSC-Numbers: 81-xx, 60-xx, 37-xx
Keywords and phrases: (quantum) large deviations, quantum Sanov's theorem, correlated quantum lattice systems, (quantum) hypothesis testing
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Discrete stationary classical processes as well as quantum lattice states are asymptotically confined to their respective typical support, the exponential growth rate of which is given by the (maximal ergodic) entropy. In the iid case the distinguishability of typical supports can be asymptotically specified by means of the relative entropy, according to Sanov's theorem. We give an extension to the correlated case, refering to the newly introduced class of HP-states.