Chirality, magic, and quantum correlations in multipartite quantum states
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| Format: | Preprint |
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2025
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| author | Vardhan, Shreya Shi, Bowen Kim, Isaac H. Zou, Yijian |
| author_facet | Vardhan, Shreya Shi, Bowen Kim, Isaac H. Zou, Yijian |
| contents | We introduce a notion of chirality for generic quantum states. A chiral state is defined as a state which cannot be transformed into its complex conjugate in a local product basis using local unitary operations. We introduce a number of quantitative measures of chirality which vanish for non-chiral states. A faithful measure called the "chiral log-distance" is defined in terms of the maximum fidelity between the state and its complex conjugate under local unitary transformations. We further introduce a set of computable measures that involve nested commutators of modular Hamiltonians. We show general relations between chirality and the amount of "magic" or non-stabilizer resource in a state. We first show that stabilizer states of qubits are non-chiral. Furthermore, magic monotones such as the stabilizer nullity and the stabilizer fidelity are lower-bounded by the chiral log-distance. We further relate chirality to discord-like quantum correlations. We define a measure of discord-like correlations called the intrinsic interferometric power, and show that it is lower-bounded by a nested commutator chirality measure. One interesting aspect of chirality is that it is not monotonic under local partial traces, indicating that it is a unique kind of resource that is not captured by traditional quantum resource theories. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_10764 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chirality, magic, and quantum correlations in multipartite quantum states Vardhan, Shreya Shi, Bowen Kim, Isaac H. Zou, Yijian Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory We introduce a notion of chirality for generic quantum states. A chiral state is defined as a state which cannot be transformed into its complex conjugate in a local product basis using local unitary operations. We introduce a number of quantitative measures of chirality which vanish for non-chiral states. A faithful measure called the "chiral log-distance" is defined in terms of the maximum fidelity between the state and its complex conjugate under local unitary transformations. We further introduce a set of computable measures that involve nested commutators of modular Hamiltonians. We show general relations between chirality and the amount of "magic" or non-stabilizer resource in a state. We first show that stabilizer states of qubits are non-chiral. Furthermore, magic monotones such as the stabilizer nullity and the stabilizer fidelity are lower-bounded by the chiral log-distance. We further relate chirality to discord-like quantum correlations. We define a measure of discord-like correlations called the intrinsic interferometric power, and show that it is lower-bounded by a nested commutator chirality measure. One interesting aspect of chirality is that it is not monotonic under local partial traces, indicating that it is a unique kind of resource that is not captured by traditional quantum resource theories. |
| title | Chirality, magic, and quantum correlations in multipartite quantum states |
| topic | Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.10764 |