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Humboldt-Universität zu Berlin - Mathematisch-Naturwissen­schaft­liche Fakultät - Nanooptik

Humboldt-Universität zu Berlin | Mathematisch-Naturwissen­schaft­liche Fakultät | Institut für Physik | Nanooptik | Publications | From unambiguous quantum state discrimination to quantum state filtering

János A Bergou, Ulrike Herzog, and Mark Hillery (2003)

From unambiguous quantum state discrimination to quantum state filtering

Fortschritte der Physik, 51(2-3):74-80.

Unambiguous discrimination among nonorthogonal but linearly independent quantum states is possible with a certain probability of success. Here, we consider a new variant of that problem. Instead of discriminating among all of the N different states, we now ask for less. We want to unambiguously assign the state to one of two complementary subsets of the set of N given non-orthogonal quantum states, each occurring with given a priori probabilities. We refer to the special case when one subset contains only one state and the other contains the remaining N-1 states as unambiguous quantum state filtering. We present an optimal analytical solution for the special case of N=3, and discuss the optimal strategy to unambiguously distinguish |ψ1〉 from the set {|ψ2〉,|ψ3〉}. For unambiguous filtering the subsets need not be linearly independent. We briefly discuss how to construct generalized interferometers (multiports) which provide a fully linear optical implementation of the optimal strategy.