Entanglement-breaking superchannels

Senrui Chen; Eric Chitambar

doi:10.22331/q-2020-07-16-299

Entanglement-breaking superchannels

Senrui Chen^1,2 and Eric Chitambar³

¹Department of Electronic Engineering, Tsinghua University, Beijing 100084, China
²Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
³Department of Electrical and Computer Engineering, Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801

Published:	2020-07-16, volume 4, page 299
Eprint:	arXiv:1910.04647v2
Doi:	https://doi.org/10.22331/q-2020-07-16-299
Citation:	Quantum 4, 299 (2020).

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Abstract

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.

► BibTeX data

@article{Chen2020entanglement,
  doi = {10.22331/q-2020-07-16-299},
  url = {https://doi.org/10.22331/q-2020-07-16-299},
  title = {Entanglement-breaking superchannels},
  author = {Chen, Senrui and Chitambar, Eric},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {299},
  month = jul,
  year = {2020}
}

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[10] Markus Hasenöhrl and Matthias C. Caro, "Quantum and classical dynamical semigroups of superchannels and semicausal channels", Journal of Mathematical Physics 63 7, 072204 (2022).

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