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arXiv · 2507.02188

Entanglement groups for mixed states

Xiaole Jiang·Daniel Kabat·Gilad Lifschytz·Aakash Marthandan
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Abstract

We extend an operational characterization of entanglement in terms of stabilizer groups from pure states to mixed states. For a density matrix $\rho_{AB}$, a stabilizer is a factorized unitary matrix $u_A \otimes u_B$ that, under conjugation, leaves $\rho_{AB}$ invariant. The entanglement group is a quotient of the stabilizer group, in which one-party stabilizers are considered trivial. This definition relates the entanglement of a density matrix to the entanglement of its purification. We give general properties of entanglement groups for mixed states, then discuss special properties for separable states. For a separable state, the entanglement group may be non-trivial. However it can only arise from multi-party entanglement with the purifying system.

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Xiaole Jiang, Daniel Kabat, Gilad Lifschytz, Aakash Marthandan. 2025-07-02. Entanglement groups for mixed states. https://arxiv.org/abs/2507.02188

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