Exploring Non-Multiplicativity in the Geometric Measure of Entanglement
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916857765691392 |
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| author | Dilley, Daniel Chang, Jerry Larson, Jeffrey Chitambar, Eric |
| author_facet | Dilley, Daniel Chang, Jerry Larson, Jeffrey Chitambar, Eric |
| contents | The geometric measure of entanglement (GME) quantifies how close a multi-partite quantum state is to the set of separable states under the Hilbert-Schmidt inner product. The GME can be non-multiplicative, meaning that the closest product state to two states is entangled across subsystems. In this work, we explore the GME in two families of states: those that are invariant under bilateral orthogonal $(O \otimes O)$ transformations, and mixtures of singlet states. In both cases, a region of GME non-multiplicativity is identified around the anti-symmetric projector state. We employ state-of-the-art numerical optimization methods and models to quantitatively analyze non-multiplicativity in these states for d = 3. We also investigate a constrained form of GME that measures closeness to the set of real product states and show that this measure can be non-multiplicative even for real separable states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exploring Non-Multiplicativity in the Geometric Measure of Entanglement Dilley, Daniel Chang, Jerry Larson, Jeffrey Chitambar, Eric Quantum Physics The geometric measure of entanglement (GME) quantifies how close a multi-partite quantum state is to the set of separable states under the Hilbert-Schmidt inner product. The GME can be non-multiplicative, meaning that the closest product state to two states is entangled across subsystems. In this work, we explore the GME in two families of states: those that are invariant under bilateral orthogonal $(O \otimes O)$ transformations, and mixtures of singlet states. In both cases, a region of GME non-multiplicativity is identified around the anti-symmetric projector state. We employ state-of-the-art numerical optimization methods and models to quantitatively analyze non-multiplicativity in these states for d = 3. We also investigate a constrained form of GME that measures closeness to the set of real product states and show that this measure can be non-multiplicative even for real separable states. |
| title | Exploring Non-Multiplicativity in the Geometric Measure of Entanglement |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2503.23247 |