Entanglement recovering under local non-positive reduced dynamics

arXiv:2605.08923v2 Announce Type: replace 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 $\mathcal{E}_{A}\otimes \mathcal{E}_{B}$, where $\mathcal{E}_{A}$ and $\mathcal{E}_{B}$ are quantum channels, i.e., completely positive trace-preserving maps. But, the reduced dynamics of the system may be given by a map as $\Psi_{A}\otimes \Psi_{B}$, where $\Psi_{A}$ and $\Psi_{B}$ 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 $\textit{ex nihilo}$.

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 $\mathcal{E}_{A}\otimes \mathcal{E}_{B}$, where $\mathcal{E}_{A}$ and $\mathcal{E}_{B}$ are quantum channels, i.e., completely positive trace-preserving maps. But, the reduced dynamics of the system may be given by a map as $\Psi_{A}\otimes \Psi_{B}$, where $\Psi_{A}$ and $\Psi_{B}$ 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 $\textit{ex nihilo}$.

arXiv:2605.08923 [quant-ph]

(or arXiv:2605.08923v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.08923 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1007/s13538-026-02153-0 Focus to learn more DOI(s) linking to related resources

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Entanglement recovering under local non-positive reduced dynamics

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