Universal embezzlers naturally emerge in critical fermion systems, study finds

Embezzlement of entanglement is an exotic phenomenon in quantum information science, describing the possibility of extracting entanglement from a resource system without changing its quantum state. In this context, the resource systems play the role of a catalyst, enabling a state transition that would otherwise be impossible, without being consumed in the process. For embezzlement of entanglement to be possible, the resource state needs to be highly entangled.

The term “universal embezzler” refers to the idea of a bipartite quantum system where every state is sufficiently entangled to make embezzlement possible. So far, it seemed highly questionable that physical systems exhibiting such strong entanglement properties could exist in the first place.

Yet researchers at Leibniz University Hannover have now shown that universal embezzlement emerges in all critical fermion chains, meaning one-dimensional fermion systems at quantum phase transitions. While their paper, published in Nature Physics, is merely theoretical, it could open new possibilities for the study of many-body physics and for the development of quantum technologies.

“We recently showed abstractly that the universal embezzlement phenomenon appears in relativistic quantum fields,” Alexander Stottmeister, co-author of the paper, told Phys.org. “However, after various talks, we were asked by colleagues with a quantum information or many-body physics background whether this would rather show that something was at odds in quantum field theory, and whether non-relativistic systems could also exhibit this phenomenon.

“Thus, we became curious whether universal embezzlement is in fact abundant and, for example, also materializes in the simpler setting of spin chains in many-body physics.”

Building on their earlier studies, Stottmeister and his colleagues set out to explore the possibility that critical spin chains always exhibit universal embezzlement. As part of their recent study, they demonstrated that this could be the case and showed that this property could naturally emerge in critical fermion systems.

“While our work shows that critical spin chains can embezzle entanglement, it does not provide a recipe for how to do so,” explained Lauritz van Luijk, co-author of the paper. “In ongoing work we describe explicit protocols that only use a certain class of operations, called Gaussian operations, which are in principle easier to implement.”

The researchers first started their exploration of universal embezzlement by focusing on the thermodynamic limit. This essentially means that rather than considering large but finite systems, they worked directly with infinite quantum systems (i.e., assuming that systems have an infinite number of particles or degrees of freedom).

“In the paper, we show that the subsystems corresponding to the left and right half chains in the thermodynamic limit satisfy a set of criteria, which we showed in previous work, correspond to universal embezzling quantum systems,” said van Luijk. “Finally, we demonstrate that the universal embezzlement property is not exclusive to the thermodynamic limit, but that it already emerges in large but finite fermion systems.”

The recent theoretical work by Stottmeister, van Luijk and their colleague Henrik Wilming suggests that universal quantum embezzlement could be a robust feature of well-known physical systems. In particular, it shows that critical free-fermionic many-body systems could naturally act as embezzlers.

“We showed that all critical spin chains, describing the critical points of quantum phase-transitions, that are translation-invariant and can be effectively described by non-interacting fermions show the universal embezzlement phenomenon,” said Wilming, co-author of the paper. “This comprises a large set of well-known models and shows that these models have much stronger entanglement properties than previously known.”

Notably, the researchers showed that embezzlement could also survive in an approximate form in finite systems, thus it is not a theoretical construct that only shows up in ideal infinite models, but instead could also emerge in real and finite quantum systems. In their next studies, they hope to further assess the validity of their theory.

“One plan is to investigate whether our results still hold true if we do not require an effective description in terms of non-interacting fermions,” added Wilming. “In this respect, it would also be interesting whether the embezzlement phenomenon persists in the presence of disorder. Another is to see whether critical systems could also show a form of embezzlement that involves more than two instead of just two parties.

“We have shown that the latter is in principle possible, but we haven’t found a natural physical model that allows for it.”

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