Chirality, magic, and quantum correlations in multipartite quantum states

• URL: http://arxiv.org/abs/2503.10764v1
• Date: Thu, 13 Mar 2025 18:00:08 GMT
• Title: Chirality, magic, and quantum correlations in multipartite quantum states
• Authors: Shreya Vardhan, Bowen Shi, Isaac H. Kim, Yijian Zou,
• Abstract summary: A chiral state cannot be transformed into its complex conjugate in a local product basis using local unitary operations.<n>A measure called the "chiral log-distance" is defined in terms of the maximum fidelity between the state and its complex conjugate.<n>We show general relations between chirality and the amount of "magic" or non-stabilizer resource in a state.
• Score: 10.878585241470166
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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