An operational environment for quantum self-testing
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An operational environment for quantum self-testing. / Christandl, Matthias; Larsen, Nicholas Gauguin Houghton; Mancinska, Laura.
In: Quantum, Vol. 6, 699, 2022, p. 1-67.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - An operational environment for quantum self-testing
AU - Christandl, Matthias
AU - Larsen, Nicholas Gauguin Houghton
AU - Mancinska, Laura
N1 - Publisher Copyright: © 2022 Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften. All Rights Reserved.
PY - 2022
Y1 - 2022
N2 - Observed quantum correlations are known to determine in certain cases the underlying quantum state and measurements. This phenomenon is known as (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.
AB - Observed quantum correlations are known to determine in certain cases the underlying quantum state and measurements. This phenomenon is known as (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.
UR - http://www.scopus.com/inward/record.url?scp=85132679111&partnerID=8YFLogxK
U2 - 10.22331/Q-2022-04-27-699
DO - 10.22331/Q-2022-04-27-699
M3 - Journal article
AN - SCOPUS:85132679111
VL - 6
SP - 1
EP - 67
JO - Quantum
JF - Quantum
SN - 2521-327X
M1 - 699
ER -
ID: 312622080