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Strong Complementarity in Quantum Computing

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If you have a question about this talk, please contact Neel Krishnaswami.

Loosely speaking, a pair of quantum observables is called “complementary” when knowledge of one implies ignorance of the other. Complementarity is responsible for much of the “weirdness” in quantum theory. The classic example is position and momentum, however finite dimensional examples such as the Z and X spins are used throughout quantum information processing.

Thanks to a theorem of Coecke, Pavlovic and Vicary, quantum observables can be identified with certain Frobenius algebras; from this perspective complementary observables are those whose algebras satisfy some additional equations. For strongly complementary observables these equations have a succinct form: the Frobenius algebras jointly form a Hopf algebra. This purely algebraic characterisation belies their power: strongly complementary observables can be used for many purposes in quantum information processing, and as I will show, strong complementarity is at the heart of quantum non-locality.

This talk is part of the Theoretical computer science seminar series.

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