Insufficiency of Pure-State Ensembles in Characterizing Transformations of Entangled States under LOCC
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909975945674752 |
|---|---|
| author | Liu, C. L. Sun, Baoqing Zhou, D. L. |
| author_facet | Liu, C. L. Sun, Baoqing Zhou, D. L. |
| contents | The conditions for transforming pure entangled states under local operations and classical communication (LOCC) are well understood. A natural question then arises: Can we determine the transformation conditions for mixed entangled states under LOCC based on the properties of their pure-state ensembles? While much effort has been devoted to this issue, in this paper, we rule out this possibility. Our findings address several open questions, including: (i) The conditions \( E_f^{cr}(ρ) \geq E_f^{cr}(σ) \) for all convex roof entanglement measures \(E_f^{cr}\) is insufficient to guarantee the existence of an LOCC transformation \(Λ^L(\cdot)\) from \(ρ\) to \(σ\); and (ii) The inequalities \(\sum_j p_j E(φ_j) \geq \sum_l q_l E(ψ_l)\) for all entanglement monotones \(E\) are not sufficient to ensure the existence of an LOCC transformation from \(\{p_j, \ket{φ_j}\}\) to \(\{q_l, \ket{ψ_l}\}\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21665 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Insufficiency of Pure-State Ensembles in Characterizing Transformations of Entangled States under LOCC Liu, C. L. Sun, Baoqing Zhou, D. L. Quantum Physics The conditions for transforming pure entangled states under local operations and classical communication (LOCC) are well understood. A natural question then arises: Can we determine the transformation conditions for mixed entangled states under LOCC based on the properties of their pure-state ensembles? While much effort has been devoted to this issue, in this paper, we rule out this possibility. Our findings address several open questions, including: (i) The conditions \( E_f^{cr}(ρ) \geq E_f^{cr}(σ) \) for all convex roof entanglement measures \(E_f^{cr}\) is insufficient to guarantee the existence of an LOCC transformation \(Λ^L(\cdot)\) from \(ρ\) to \(σ\); and (ii) The inequalities \(\sum_j p_j E(φ_j) \geq \sum_l q_l E(ψ_l)\) for all entanglement monotones \(E\) are not sufficient to ensure the existence of an LOCC transformation from \(\{p_j, \ket{φ_j}\}\) to \(\{q_l, \ket{ψ_l}\}\). |
| title | Insufficiency of Pure-State Ensembles in Characterizing Transformations of Entangled States under LOCC |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.21665 |