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arXiv:2206.08313quant-ph

A note on the inner products of pure states and their antidistinguishability

Vincent Russo, Jamie Sikora

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Abstract

A set of d quantum states is said to be antidistinguishable if there exists a d-outcome POVM that can perfectly identify which state was not measured. A conjecture by Havlíček and Barrett states that if a set of d pure states has small pair-wise inner products, then the set must be antidistinguishable. In this note we provide a certificate of antidistinguishability via semidefinite programming duality and use it to provide a counterexample to this conjecture when d = 4.

arXiv comments
3 pages. Comments welcome
Journal reference
DOI
doi:10.1103/PhysRevA.107.L030202
Subjects
quant-phQuantum Physics

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