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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.02188 |
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| _version_ | 1866913923728408576 |
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| author | Jiang, Xiaole Kabat, Daniel Lifschytz, Gilad Marthandan, Aakash |
| author_facet | Jiang, Xiaole Kabat, Daniel Lifschytz, Gilad Marthandan, Aakash |
| contents | We extend an operational characterization of entanglement in terms of stabilizer groups from pure states to mixed states. For a density matrix $ρ_{AB}$, a stabilizer is a factorized unitary matrix $u_A \otimes u_B$ that, under conjugation, leaves $ρ_{AB}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02188 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entanglement groups for mixed states Jiang, Xiaole Kabat, Daniel Lifschytz, Gilad Marthandan, Aakash Quantum Physics We extend an operational characterization of entanglement in terms of stabilizer groups from pure states to mixed states. For a density matrix $ρ_{AB}$, a stabilizer is a factorized unitary matrix $u_A \otimes u_B$ that, under conjugation, leaves $ρ_{AB}$ 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. |
| title | Entanglement groups for mixed states |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2507.02188 |