Chirality, magic, and quantum correlations in multipartite quantum states

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.