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1. Entanglement entropy from entanglement contour: higher dimensions

   https://doi.org/10.21468/SciPostPhysCore.5.2.020  

   Han, Muxin; Wen, Qiang (January 2022, SciPost Physics Core)

   We study the entanglement contour and partial entanglement entropy (PEE) in quantum field theories in 3 and higher dimensions. The entanglement entropy is evaluated from a certain limit of the PEE with a geometric regulator. In the context of the entanglement contour, we classify the geometric regulators, study their difference from the UV regulators. Furthermore, for spherical regions in conformal field theories (CFTs) we find the exact relation between the UV and geometric cutoff, which clarifies some subtle points in the previous literature. We clarify a subtle point of the additive linear combination (ALC) proposal for PEE in higher dimensions. The subset entanglement entropies in the ALC proposal should all be evaluated as a limit of the PEE while excluding a fixed class of local-short-distance correlation. Unlike the 2-dimensional configurations, naively plugging the entanglement entropy calculated with a UV cutoff will spoil the validity of the ALC proposal. We derive the entanglement contour function for spherical regions, annuli and spherical shells in the vacuum state of general-dimensional CFTs on a hyperplane. 

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2. Entanglement Holonomies

   Czech, Bartlomiej; Lamprou, Lampros; Susskind, Leonard (July 2018, arXiv.org)
3. Entanglement Dynamics From Random Product States: Deviation From Maximal Entanglement

   https://doi.org/10.1109/tit.2022.3140469  

   Huang, Yichen (May 2022, IEEE Transactions on Information Theory)
4. Entanglement-breaking superchannels

   https://doi.org/10.22331/q-2020-07-16-299  

   Chen, Senrui; Chitambar, Eric (July 2020, Quantum)

   In this paper we initiate the study of entanglement-breaking (EB) superchannels. These are processes that always yield separable maps when acting on one side of a bipartite completely positive (CP) map. EB superchannels are a generalization of the well-known EB channels. We give several equivalent characterizations of EB supermaps and superchannels. Unlike its channel counterpart, we find that not every EB superchannel can be implemented as a measure-and-prepare superchannel. We also demonstrate that many EB superchannels can be superactivated, in the sense that they can output non-separable channels when wired in series.We then introduce the notions of CPTP- and CP-complete images of a superchannel, which capture deterministic and probabilistic channel convertibility, respectively. This allows us to characterize the power of EB superchannels for generating CP maps in different scenarios, and it reveals some fundamental differences between channels and superchannels. Finally, we relax the definition of separable channels to include ( p , q ) -non-entangling channels, which are bipartite channels that cannot generate entanglement using p - and q -dimensional ancillary systems. By introducing and investigating k -EB maps, we construct examples of ( p , q ) -EB superchannels that are not fully entanglement breaking. Partial results on the characterization of ( p , q ) -EB superchannels are also provided. 

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5. Optimized Entanglement Purification

   https://doi.org/10.22331/q-2019-02-18-123  

   Krastanov, Stefan; Albert, Victor V.; Jiang, Liang (February 2019, Quantum)

   We investigate novel protocols for entanglement purification of qubit Bell pairs. Employing genetic algorithms for the design of the purification circuit, we obtain shorter circuits achieving higher success rates and better final fidelities than what is currently available in the literature. We provide a software tool for analytical and numerical study of the generated purification circuits, under customizable error models. These new purification protocols pave the way to practical implementations of modular quantum computers and quantum repeaters. Our approach is particularly attentive to the effects of finite resources and imperfect local operations - phenomena neglected in the usual asymptotic approach to the problem. The choice of the building blocks permitted in the construction of the circuits is based on a thorough enumeration of the local Clifford operations that act as permutations on the basis of Bell states. 

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