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arXiv:1803.11214 · Physical review. D/Physical review. D.

General no-go theorem for entanglement extraction

Petar Simidzija, Robert H. Jonsson, Eduardo Martín-Martínez

Published Jun 5, 2018• 53 citations
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Abstract

We study under what circumstances a separable bipartite system A-B can or cannot become entangled through local interactions with a bilocal entangled source ${\mathrm{S}}_{1}\text{\ensuremath{-}}{\mathrm{S}}_{2}$. We obtain constraints on the general forms of the interaction Hamiltonians coupling A with ${\mathrm{S}}_{1}$ and B with ${\mathrm{S}}_{2}$ necessary for A and B to become entangled. We are able to generalize and provide nonperturbative insight on several previous no-go theorems of entanglement harvesting from quantum fields using these general results. We also discuss the role of communication in the process of entanglement extraction, establishing a distinction between genuine entanglement extraction and communication-assisted entanglement generation.

DOI
10.1103/physrevd.97.125002

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We study under what circumstances a separable bipartite system A-B can or cannot become entangled through local interactions with a bilocal entangled source S1\ensuremath-S2{\mathrm{S}}_{1}\text{\ensuremath{-}}{\mathrm{S}}_{2}S1​\ensuremath-S2​. We obtain constraints on the general forms of the interaction Hamiltonians coupling A with S1{\mathrm{S}}_{1}S1​ and B with S2{\mathrm{S}}_{2}S2​ necessary for A and B to become entangled. We are able to generalize and provide nonperturbative insight on several previous no-go theorems of entanglement harvesting from quantum fields using these general results. We also discuss the role of communication in the process of entanglement extraction, establishing a distinction between genuine entanglement extraction and communication-assisted entanglement generation.
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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\mathcal{E}_{A}\otimes \mathcal{E}_{B}EA​⊗EB​, where EA\mathcal{E}_{A}EA​ and EB\mathcal{E}_{B}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⊗ΨBΨ_{A}\otimes Ψ_{B}ΨA​⊗ΨB​, where ΨAΨ_{A}ΨA​ and ΨBΨ_{B}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\textit{ex nihilo}ex nihilo.
We revisit the entanglement harvesting protocol when two detectors are in causal contact. We study the role of field-mediated communication in generating entanglement between the two detectors interacting with a quantum field. We provide a quantitative estimator of the relative contribution of communication versus genuine entanglement harvesting. For massless scalar fields in flat spacetime, we show that when two detectors can communicate via the field, the detectors do not really harvest entanglement from the field, and instead they get entangled only via the field-mediated communication channel. In other words, in these scenarios the entanglement harvesting protocol is truly ``harvesting entanglement'' from the field only when the detectors are not able to communicate. In contrast, for massive scalar fields both communication and genuine harvesting contribute equally to the bipartite entanglement when the detectors are causally connected. These results emphasize the importance of taking into account the causal relationships between two parties involved in this relativistic quantum information protocol before we can declare that it is truly entanglement harvesting.
States of sufficiently low purity are separable and cannot be entangled by unital (purity-non-generating) operations. Since high-purity states are experimentally demanding, it is natural to ask how much purity a state must possess to enable entanglement generation. Absolutely separable states remain separable under all deterministic unital channels, and so cannot deterministically generate entanglement in this setting. We show, however, that some absolutely separable states can generate entanglement via probabilistic protocols that do not produce purity. This motivates the study of states that fail to generate entanglement with any non-zero probability, which we call completely absolutely separable; we give a full characterization of this class. Along the way, we derive a novel sufficient condition for separability that depends only on the largest and smallest eigenvalues, along with the smallest local dimension and is independent of all previously known spectral separability criteria.