Unitary-invariant witnesses of quantum imaginarity

• URL: http://arxiv.org/abs/2403.15066v1
• Date: Fri, 22 Mar 2024 09:46:58 GMT
• Title: Unitary-invariant witnesses of quantum imaginarity
• Authors: Carlos Fernandes, Rafael Wagner, Leonardo Novo, Ernesto F. Galvão,
• Abstract summary: 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.
• Score: 8.700842317740943
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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