Unitary-invariant witnesses of quantum imaginarity
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912117994553344 |
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| author | Fernandes, Carlos Wagner, Rafael Novo, Leonardo Galvão, Ernesto F. |
| author_facet | Fernandes, Carlos Wagner, Rafael Novo, Leonardo Galvão, Ernesto F. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15066 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unitary-invariant witnesses of quantum imaginarity Fernandes, Carlos Wagner, Rafael Novo, Leonardo Galvão, Ernesto F. Quantum Physics 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. |
| title | Unitary-invariant witnesses of quantum imaginarity |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2403.15066 |