Coming full circle -- A unified framework for Kochen-Specker contextuality

• URL: http://arxiv.org/abs/2501.09750v1
• Date: Thu, 16 Jan 2025 18:57:53 GMT
• Title: Coming full circle -- A unified framework for Kochen-Specker contextuality
• Authors: Markus Frembs,
• Abstract summary: Contextuality is a key distinguishing feature between classical and quantum physics. We introduce the conceptually new tool called context connections'', which allows to cast and analyse Kochen-Specker contextuality in new form. We show in detail how this framework subsumes the marginal and graph-theoretic approaches to contextuality.
• Score: 0.0
• License:
• Abstract: Contextuality is a key distinguishing feature between classical and quantum physics. It expresses a fundamental obstruction to describing quantum theory using classical concepts. In turn, when understood as a resource for quantum computation, it is expected to hold the key to quantum advantage. Yet, despite its long recognised importance in quantum foundations and, more recently, in quantum computation, the mathematics of contextuality has remained somewhat elusive - different frameworks address different aspects of the phenomenon, yet their precise relationship often is unclear. In fact, there is a glaring discrepancy already between the original notion of contextuality introduced by Kochen and Specker on the one side [J. Math. Mech., 17, 59, (1967)], and the modern approach of studying contextual correlations on the other [Rev. Mod. Phys., 94, 045007 (2022)]. In a companion paper [arXiv:2408.16764], we introduce the conceptually new tool called ``context connections'', which allows to cast and analyse Kochen-Specker (KS) contextuality in new form. Here, we generalise this notion, and based on it prove a complete characterisation of KS contextuality for finite-dimensional systems. To this end, we develop the framework of ``observable algebras". We show in detail how this framework subsumes the marginal and graph-theoretic approaches to contextuality, and thus that it offers a unified perspective on KS contextuality. In particular, we establish the precise relationships between the various notions of ``contextuality" used in the respective settings, and in doing so, generalise a number of results on the characterisation of the respective notions in the literature.

Related papers

• Event-based quantum contextuality theory [9.808029647992774]
  This paper overcomes the challenges faced by some known contextuality theories by establishing an event-based contextuality theory. Our theory provides a precise mathematical framework for quantum contextuality, which can handle the scenarios composed of general projectors. We conclude that the Kochen-Specker contextuality is equivalent to the state-independent strong contextuality for finite dimensional quantum systems.
  arXiv  Detail & Related papers  (2024-10-21T08:55:43Z)
• An algebraic characterisation of Kochen-Specker contextuality [0.0]
  Contextuality is a key distinguishing feature between classical and quantum physics. It expresses a fundamental obstruction to describing quantum theory using classical concepts. Different frameworks address different aspects of the phenomenon, yet their precise relationship often remains unclear.
  arXiv  Detail & Related papers  (2024-08-29T17:58:12Z)
• Quantum-inspired Interpretable Deep Learning Architecture for Text Sentiment Analysis [26.284684575675048]
  We propose a quantum-inspired deep learning architecture that combines QM principles with deep learning models for text sentiment analysis. Specifically, we analyze the commonalities between text representation and QM principles to design a quantum-inspired text representation method. We also design a feature extraction layer based on long short-term memory (LSTM) networks and self-attention mechanisms (SAMs)
  arXiv  Detail & Related papers  (2024-08-15T02:32:50Z)
• 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)
• Relaxation of first-class constraints and the quantization of gauge theories: from "matter without matter" to the reappearance of time in quantum gravity [72.27323884094953]
  We make a conceptual overview of an approach to the initial-value problem in canonical gauge theories. We stress how the first-class phase-space constraints may be relaxed if we interpret them as fixing the values of new degrees of freedom.
  arXiv  Detail & Related papers  (2024-02-19T19:00:02Z)
• State-independent all-versus-nothing arguments [1.223779595809275]
  Contextuality is a key feature of quantum information that challenges classical intuitions. This report provides a unified interpretation of contextuality by integrating Kochen-Specker type notions into the state-independent AvN argument.
  arXiv  Detail & Related papers  (2023-11-19T04:08:50Z)
• Quantum realism: axiomatization and quantification [77.34726150561087]
  We build an axiomatization for quantum realism -- a notion of realism compatible with quantum theory. We explicitly construct some classes of entropic quantifiers that are shown to satisfy almost all of the proposed axioms.
  arXiv  Detail & Related papers  (2021-10-10T18:08:42Z)
• From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality [0.0]
  We study the historical emergence of the concept from philosophical and logical issues. We present and compare the main theoretical frameworks that have been derived. We focus on the complex task of establishing experimental tests of contextuality.
  arXiv  Detail & Related papers  (2021-05-28T13:33:39Z)
• 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)
• The logic of contextuality [0.0]
  Contextuality is a key signature of quantum non-classicality. We study the logic of contextuality in the setting of partial Boolean algebras.
  arXiv  Detail & Related papers  (2020-11-05T19:04:04Z)
• Preferred basis, decoherence and a quantum state of the Universe [77.34726150561087]
  We review a number of issues in foundations of quantum theory and quantum cosmology. These issues can be considered as a part of the scientific legacy of H.D. Zeh.
  arXiv  Detail & Related papers  (2020-06-28T18:07:59Z)

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.