An Operational Environment for Quantum Self-Testing

Matthias Christandl; Nicholas Gauguin Houghton-Larsen; Laura Mancinska

doi:10.22331/q-2022-04-27-699

An Operational Environment for Quantum Self-Testing

Matthias Christandl, Nicholas Gauguin Houghton-Larsen, and Laura Mancinska

Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2200 Copenhagen, Denmark

Published:	2022-04-27, volume 6, page 699
Eprint:	arXiv:2108.06254v3
Doi:	https://doi.org/10.22331/q-2022-04-27-699
Citation:	Quantum 6, 699 (2022).

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Abstract

Observed quantum correlations are known to determine in certain cases the underlying quantum state and measurements. This phenomenon is known as $\textit{(quantum) self-testing}$.
Self-testing constitutes a significant research area with practical and theoretical ramifications for quantum information theory. But since its conception two decades ago by Mayers and Yao, the common way to rigorously formulate self-testing has been in terms of operator-algebraic identities, and this formulation lacks an operational interpretation. In particular, it is unclear how to formulate self-testing in other physical theories, in formulations of quantum theory not referring to operator-algebra, or in scenarios causally different from the standard one.
In this paper, we explain how to understand quantum self-testing operationally, in terms of causally structured dilations of the input-output channel encoding the correlations. These dilations model side-information which leaks to an environment according to a specific schedule, and we show how self-testing concerns the relative strength between such scheduled leaks of information. As such, the title of our paper has double meaning: we recast conventional quantum self-testing in terms of information-leaks to an environment – and this realises quantum self-testing as a special case within the surroundings of a general operational framework.
Our new approach to quantum self-testing not only supplies an operational understanding apt for various generalisations, but also resolves some unexplained aspects of the existing definition, naturally suggests a distance measure suitable for robust self-testing, and points towards self-testing as a modular concept in a larger, cryptographic perspective.

► BibTeX data

@article{Christandl2022operational,
  doi = {10.22331/q-2022-04-27-699},
  url = {https://doi.org/10.22331/q-2022-04-27-699},
  title = {An {O}perational {E}nvironment for {Q}uantum {S}elf-{T}esting},
  author = {Christandl, Matthias and Houghton-Larsen, Nicholas Gauguin and Mancinska, Laura},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {699},
  month = apr,
  year = {2022}
}

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[3] Arthur J. Parzygnat, "Reversing information flow: retrodiction in semicartesian categories", arXiv:2401.17447, (2024).

[4] Ernest Y. -Z. Tan, "Prospects for device-independent quantum key distribution", arXiv:2111.11769, (2021).

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