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arXiv · 1902.11039

Quantum and classical bounds for two-state overlaps

Ernesto F. Galvão·Daniel J. Brod
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Abstract

Suppose we have $N$ quantum systems in unknown states $\lvertψ_i \rangle $, but know the value of some pairwise overlaps $\left| \langle ψ_k \lvert ψ_l \rangle \right|^2$. What can we say about the values of the unknown overlaps? We provide a complete answer to this problem for three pure states and two given overlaps, and a way to obtain bounds for the general case. We discuss how the answer contrasts from that of a classical model featuring only coherence-free, diagonal states, and describe three applications: basis-independent coherence witnesses, dimension witnesses, and characterisation of multi-photon indistinguishability.

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Ernesto F. Galvão, Daniel J. Brod. 2020-05-19. Quantum and classical bounds for two-state overlaps. https://doi.org/10.1103/physreva.101.062110

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