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arXiv · 2403.15066

Unitary-invariant witnesses of quantum imaginarity

Carlos Fernandes·Rafael Wagner·Leonardo Novo·Ernesto F. Galvão
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Abstract

Quantum theory is traditionally formulated using complex numbers. This imaginarity of quantum theory has been quantified as a resource with applications in discrimination tasks, pseudorandomness generation, and quantum metrology. Here we propose witnesses for imaginarity that are basis-independent, relying on measurements of unitary-invariant properties of sets of states. For 3 pure states, we completely characterize the invariant values attainable by quantum theory, and give a partial characterization for 4 pure states. We show that simple pairwise overlap measurements suffice to witness imaginarity of sets of 4 states, but not for sets of 3. Our witnesses are experimentally friendly, opening up a new path for measuring and using imaginarity as a resource.

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Carlos Fernandes, Rafael Wagner, Leonardo Novo, Ernesto F. Galvão. 2024-03-22. Unitary-invariant witnesses of quantum imaginarity. https://doi.org/10.1103/physrevlett.133.190201

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