Quantum Information Measures for Restricted Sets of Observables
Starts 6 Mar 2018 14:30
Ends 6 Mar 2018 16:00
Central European Time
Leonardo Building - Luigi Stasi Seminar Room
Abstract. In this talk I will consider the problem of defining measures of quantum information in cases where the space spanned by the set of accessible observables does not form an algebra, i.e. it is not closed under products. This setting is relevant for the study of localized quantum information in theories of gravity where the set of approximately-local operators in a region may not be closed under arbitrary products. While one cannot naturally associate a density matrix with a state in this setting, it is still possible to define a modular operator for a state, and distinguish between two states using a relative modular operator. These operators are defined on a 'little Hilbert space', which parameterizes small deformations of the system away from its original state, and they do not depend on the structure of the full Hilbert space of the theory. I will show how a novel class of relative-entropy-like quantities can be defined using the spectrum of these operators. I will also describe some applications of this formalism for studying bulk reconstruction and subregion-dualities in the AdS/CFT correspondence.
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