Entanglement recovering under local non-positive reduced dynamics
Abstract
Consider a bipartite quantum system S=AB such that each part interacts only with its local environment. Under such circumstances, one expects that the entanglement between parts A and B does not increase after the time evolution. In fact, this is the case if the reduced dynamics of the system is given by ℰA⊗ ℰB, where ℰA and ℰB are quantum channels, i.e., completely positive trace-preserving maps. But, the reduced dynamics of the system may be given by a map as ΨA⊗ ΨB, where ΨA and ΨB are local non-positive maps. Then, the entanglement between A and B can exceed its initial value, as was shown in the case studied by Jordan et al. [Phys. Rev. A 76, 022102 (2007)]. In this paper, we first explore the general circumstances under which one can find such cases as they found. Next, we introduce another general procedure which leads to local non-positive maps that exhibit entanglement exceeding. Furthermore, we demonstrate that this apparent entanglement increase in the two above procedures corresponds physically to the retrieval of pre-existing inaccessible entanglement stored across the global system-environment degrees of freedom, rather than genuine generation of the entanglement ex nihilo.
Versions
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BibTeX
@misc{sargolzahi2026entanglement,
title = {{Entanglement recovering under local non-positive reduced dynamics}},
author = {Iman Sargolzahi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.08923},
eprint = {2605.08923},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.08923},
}
RIS
TY - UNPB
TI - Entanglement recovering under local non-positive reduced dynamics
AU - Iman Sargolzahi
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2605.08923
UR - https://arxiv.org/abs/2605.08923
AB - Consider a bipartite quantum system S=AB such that each part interacts only with its local environment. Under such circumstances, one expects that the entanglement between parts A and B does not increase after the time evolution. In fact, this is the case if the reduced dynamics of the system is given by ℰ_A⊗ ℰ_B, where ℰ_A and ℰ_B are quantum channels, i.e., completely positive trace-preserving maps. But, the reduced dynamics of the system may be given by a map as Ψ_A⊗ Ψ_B, where Ψ_A and Ψ_B are local non-positive maps. Then, the entanglement between A and B can exceed its initial value, as was shown in the case studied by Jordan et al. [Phys. Rev. A 76, 022102 (2007)]. In this paper, we first explore the general circumstances under which one can find such cases as they found. Next, we introduce another general procedure which leads to local non-positive maps that exhibit entanglement exceeding. Furthermore, we demonstrate that this apparent entanglement increase in the two above procedures corresponds physically to the retrieval of pre-existing inaccessible entanglement stored across the global system-environment degrees of freedom, rather than genuine generation of the entanglement ex nihilo.
ER -