Form of Contextuality Predicting Probabilistic Equivalence between Two Sets of Three Mutually Noncommuting Observables

• URL: http://arxiv.org/abs/2309.13091v2
• Date: Thu, 4 Apr 2024 09:23:24 GMT
• Title: Form of Contextuality Predicting Probabilistic Equivalence between Two Sets of Three Mutually Noncommuting Observables
• Authors: Mirko Navara, Karl Svozil,
• Abstract summary: We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases within the Hilbert space, featuring a state-independent sum of probabilities. The measurement contextuality in this setup arises from the quantum realizations of the hypergraph, which adhere to a specific bound on the linear combination of probabilities.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases within the Hilbert space, featuring a state-independent sum of probabilities. In other words, regardless of the initial state preparation, the total probability remains constant but may be distinct from unity. The measurement contextuality in this setup arises from the quantum realizations of the hypergraph, which adhere to a specific bound on the linear combination of probabilities. In contrast, classical realizations can surpass this bound. The violation of quantum bounds stems from the inability of classical ontological models, specifically the set-theoretic representation of the hypergraph corresponding to the quantum observables' collections, to adhere to and explain the observed statistics.

Related papers

• A new class of exact coherent states: enhanced quantization of motion on the half-line [0.16385815610837165]
  We find a class of dynamically stable coherent states for motion on the half-line. The regularization of the half-line boundary and the consequent quantum motion are expounded within the framework of covariant affine quantization. Our discovery holds significant relevance in the field of quantum cosmology.
  arXiv  Detail & Related papers  (2023-10-25T13:19:24Z)
• Limitations of Classically-Simulable Measurements for Quantum State Discrimination [7.749391145337816]
  We investigate the limitations of classically-simulable measurements, specifically POVMs with positive discrete Wigner functions. Our results reveal similarities and distinctions between the quantum resource theory of magic states and entanglement in quantum state discrimination.
  arXiv  Detail & Related papers  (2023-10-17T15:01:54Z)
• A Universal Quantum Certainty Relation for Arbitrary Number of Observables [0.0]
  We derive by lattice theory a universal quantum certainty relation for arbitrary $M$ observables in $N$-dimensional system. We find that one cannot prepare a quantum state with PDVs of incompatible observables spreading out arbitrarily.
  arXiv  Detail & Related papers  (2023-08-10T16:44:10Z)
• Asymmetry and tighter uncertainty relations for R\'enyi entropies via quantum-classical decompositions of resource measures [0.0]
  It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is discussed.
  arXiv  Detail & Related papers  (2023-04-12T08:49:48Z)
• Non-standard entanglement structure of local unitary self-dual models as a saturated situation of repeatability in general probabilistic theories [61.12008553173672]
  We show the existence of infinite structures of quantum composite system such that it is self-dual with local unitary symmetry. We also show the existence of a structure of quantum composite system such that non-orthogonal states in the structure are perfectly distinguishable.
  arXiv  Detail & Related papers  (2021-11-29T23:37:58Z)
• Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
  Two particles are identical if all their intrinsic properties, such as spin and charge, are the same. Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
  arXiv  Detail & Related papers  (2021-05-10T13:11:59Z)
• Graph-Theoretic Framework for Self-Testing in Bell Scenarios [37.067444579637076]
  Quantum self-testing is the task of certifying quantum states and measurements using the output statistics solely. We present a new approach for quantum self-testing in Bell non-locality scenarios.
  arXiv  Detail & Related papers  (2021-04-27T08:15:01Z)
• An uncertainty view on complementarity and a complementarity view on uncertainty [0.0]
  We obtain a complete complementarity relation for quantum uncertainty, classical uncertainty, and predictability. We show that Brukner-Zeilinger's invariant information quantifies both the wave and particle characters of a quanton.
  arXiv  Detail & Related papers  (2020-07-09T20:40:25Z)
• Emergence of classical behavior in the early universe [68.8204255655161]
  Three notions are often assumed to be essentially equivalent, representing different facets of the same phenomenon. We analyze them in general Friedmann-Lemaitre- Robertson-Walker space-times through the lens of geometric structures on the classical phase space. The analysis shows that: (i) inflation does not play an essential role; classical behavior can emerge much more generally; (ii) the three notions are conceptually distinct; classicality can emerge in one sense but not in another.
  arXiv  Detail & Related papers  (2020-04-22T16:38:25Z)
• Inaccessible information in probabilistic models of quantum systems, non-contextuality inequalities and noise thresholds for contextuality [0.0]
  We quantify the inaccessible information of a model in terms of the maximum distinguishability of probability distributions. These bounds can be interpreted as a new class of robust preparation non-contextuality inequalities.
  arXiv  Detail & Related papers  (2020-03-12T19:23:14Z)
• Quantifying the unextendibility of entanglement [13.718093420358827]
  Entanglement is a striking feature of quantum mechanics, and it has a key property called unextendibility. We present a framework for quantifying and investigating the unextendibility of general bipartite quantum states.
  arXiv  Detail & Related papers  (2019-11-18T05:22:36Z)

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.