An Operational Environment for Quantum Self-Testing

• URL: http://arxiv.org/abs/2108.06254v3
• Date: Sun, 24 Apr 2022 10:05:25 GMT
• Title: An Operational Environment for Quantum Self-Testing
• Authors: Matthias Christandl, Nicholas Gauguin Houghton-Larsen and Laura Mancinska
• Abstract summary: We show how to understand quantum self-testing operationally. We recast conventional quantum self-testing in terms of information-leaks to an environment.
• Score: 2.3857747529378917
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Fine-Grained Uncertainty Relations for Quantum Testers [0.0]
  Fine-grained uncertainty relations (FGURs) are a contemporary interpretation of the uncertainty principle. In this study, we develop FGURs in terms of quantum testers. Specifically, we explore quantum testers involving maximally entangled states in detail.
  arXiv  Detail & Related papers  (2024-09-13T05:30:36Z)
• No-broadcasting characterizes operational contextuality [0.0]
  We show that the possibility of demonstrating contextuality is exactly characterized by non-commutativity. We also show how techniques from broadcasting can be used to simplify known foundational results in contextuality.
  arXiv  Detail & Related papers  (2024-06-11T14:33:06Z)
• A computational test of quantum contextuality, and even simpler proofs of quantumness [43.25018099464869]
  We show that an arbitrary contextuality game can be compiled into an operational "test of contextuality" involving a single quantum device. Our work can be seen as using cryptography to enforce spatial separation within subsystems of a single quantum device.
  arXiv  Detail & Related papers  (2024-05-10T19:30:23Z)
• A universal scheme to self-test any quantum state and extremal measurement [41.94295877935867]
  quantum network considered in this work is the simple star network, which is implementable using current technologies. For our purposes, we also construct a scheme that can be used to self-test the two-dimensional tomographically complete set of measurements with an arbitrary number of parties.
  arXiv  Detail & Related papers  (2023-12-07T16:20:28Z)
• A mathematical foundation for self-testing: Lifting common assumptions [0.0]
  We study the phenomenon of self-testing from the first principles, aiming to place this versatile concept on a rigorous mathematical footing. We identify a quantum correlation which is a self-test only if certain assumptions are made. Remarkably, this is also the first example of a correlation that cannot be implemented using projective measurements on a bipartite state of full Schmidt rank.
  arXiv  Detail & Related papers  (2023-10-19T11:41:31Z)
• A simple formulation of no-cloning and no-hiding that admits efficient and robust verification [0.0]
  Incompatibility is a feature of quantum theory that sets it apart from classical theory. The no-hiding theorem is another such instance that arises in the context of the black-hole information paradox. We formulate both of these fundamental features of quantum theory in a single form that is amenable to efficient verification.
  arXiv  Detail & Related papers  (2023-03-05T12:48:11Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)
• Self-adjointness in Quantum Mechanics: a pedagogical path [77.34726150561087]
  This paper aims to make quantum observables emerge as necessarily self-adjoint, and not merely hermitian operators. Next to the central core of our line of reasoning, the necessity of a non-trivial declaration of a domain to associate with the formal action of an observable.
  arXiv  Detail & Related papers  (2020-12-28T21:19:33Z)
• Quantum Mechanical description of Bell's experiment assumes Locality [91.3755431537592]
  Bell's experiment description assumes the (Quantum Mechanics-language equivalent of the classical) condition of Locality. This result is complementary to a recently published one demonstrating that non-Locality is necessary to describe said experiment. It is concluded that, within the framework of Quantum Mechanics, there is absolutely no reason to believe in the existence of non-Local effects.
  arXiv  Detail & Related papers  (2020-02-27T15:04:08Z)
• Symmetric Informationally Complete Measurements Identify the Irreducible Difference between Classical and Quantum Systems [0.0]
  We describe a general procedure for associating a minimal informationally-complete quantum measurement (or MIC) with a set of linearly independent post-measurement quantum states. We prove that the representation of the Born Rule obtained from a symmetric informationally-complete measurement (or SIC) minimizes this distinction in at least two senses.
  arXiv  Detail & Related papers  (2018-05-22T16:27:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.