Complete Characterization of Entanglement Embezzlement

Elia Zanoni; Thomas Theurer; Gilad Gour

doi:10.22331/q-2024-06-13-1368

Complete Characterization of Entanglement Embezzlement

Elia Zanoni, Thomas Theurer, and Gilad Gour

Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4, Canada
Institute for Quantum Science and Technology, University of Calgary, Calgary, AB T2N 1N4, Canada

Published:	2024-06-13, volume 8, page 1368
Eprint:	arXiv:2303.17749v3
Doi:	https://doi.org/10.22331/q-2024-06-13-1368
Citation:	Quantum 8, 1368 (2024).

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Abstract

Using local operations and classical communication (LOCC), entanglement can be manipulated but not created. However, entanglement can be $embezzled$. In this work, we completely characterize universal embezzling families and demonstrate how this singles out the original family introduced by van Dam and Hayden. To achieve this, we first give a full characterization of pure to mixed state LOCC-conversions. Then, we introduce a new conversion distance and derive a closed-form expression for it. These results might be of independent interest.

Featured image: Uniqueness of the van Dam and Hayden embezzling family

Popular summary

Quantum entanglement between two spatially separated parties, Alice and Bob, is a precious resource that cannot be created easily but enables many information-processing tasks. An interesting phenomenon occurs when Alice and Bob have access to a very specific set of entangled quantum states. Indeed, if they want to create an arbitrary entangled state, they can pick a state from the set, use it to create the desired entangled state, and at the end of the protocol the state that they picked at the beginning is almost unchanged. Moreover, by picking the right state, this difference can become arbitrarily small. This phenomenon is called entanglement embezzlement.

In our work, we completely characterize entanglement embezzlement. In other words, we describe all the sets of states that can be used for entanglement embezzlement, and we show that all these sets of states are very similar to the set of states proposed by van Dam and Hayden in their original paper about entanglement embezzlement. To achieve this, we derive a closed formula for the distance that measures how close to a desired target state Alice and Bob can convert an initial state, by using the best protocol and considering the limitations given by the fact that they are spatially separated.

► BibTeX data

@article{Zanoni2024complete,
  doi = {10.22331/q-2024-06-13-1368},
  url = {https://doi.org/10.22331/q-2024-06-13-1368},
  title = {Complete {C}haracterization of {E}ntanglement {E}mbezzlement},
  author = {Zanoni, Elia and Theurer, Thomas and Gour, Gilad},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1368},
  month = jun,
  year = {2024}
}

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