Information-Theoretic and Operational Measures of Quantum Contextuality

• URL: http://arxiv.org/abs/2512.11049v2
• Date: Wed, 17 Dec 2025 14:47:29 GMT
• Title: Information-Theoretic and Operational Measures of Quantum Contextuality
• Authors: Ali Can Günhan, Zafer Gedik,
• Abstract summary: Two complementary measures are introduced: the mutual information energy and a state-independent quantity.<n>We establish a hierarchy of bounds connecting these measures to the Robertson uncertainty relation.<n>The framework is applied to the Klyachko-Can-Biniciolu-Shumovsky (KCBS) scenario for spin-1 systems.
• Score: 0.7161783472741748
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We propose an information -- theoretic framework for quantifying Kochen-Specker contextuality. Two complementary measures are introduced: the mutual information energy, a state-independent quantity inspired by Onicescu's information energy that captures the geometric overlap between joint eigenspaces within a context; and an operational measure based on commutator expectation values that reflects contextual behavior at the level of measurement outcomes. We establish a hierarchy of bounds connecting these measures to the Robertson uncertainty relation, including spectral, purity-corrected, and operator norm estimates. The framework is applied to the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) scenario for spin-1 systems, where all quantities admit closed-form expressions. The Majorana-stellar representation furnishes a common geometric platform on which both the operational measure and the uncertainty products can be analyzed. For spin-1, this representation yields a three-dimensional Euclidean-like visualization of the Hilbert space in which, states lying on a plane exhibit maximum uncertainty for the observable along the perpendicular direction; simultaneous optimization across all KCBS contexts singles out a unique state on the symmetry axis. Notably, states achieving the optimal sum of uncertainty products exhibit vanishing operational contextuality, while states with substantial operational contextuality satisfy a nontrivial Robertson bound -- the two extremes are achieved by distinct quantum states.

Related papers

• Generalised state space geometry in Hermitian and non-Hermitian quantum systems [0.0]
  We show that it is possible to construct a family of connections that are dual to each other in a generalised sense.<n>We also elucidate the role of the metric in a quantum natural gradient descent problem.
  arXiv  Detail & Related papers  (2025-07-24T15:01:04Z)
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation.<n>We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue.<n>We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)
• Tightening the entropic uncertainty relations with quantum memory in a multipartite scenario [17.30562902622871]
  We introduce a tripartite quantum-memory-assisted entropic uncertainty relation.<n>We extend the relation to encompass multiple measurements conducted within multipartite systems.
  arXiv  Detail & Related papers  (2025-01-06T09:09:34Z)
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution [21.39913099096503]
  We introduce the concept of imaginary-time Lindbladian evolution as an alternative framework.<n>This new approach defines gapped quantum phases in open systems through the spectrum properties of the imaginary-Liouville superoperator.<n>Our findings demonstrate universal properties at quantum criticality, such as nonanalytic behaviors of steady-state observables, divergence of correlation lengths, and closing of the imaginary-Liouville gap.
  arXiv  Detail & Related papers  (2024-08-06T14:53:40Z)
• Finite-Depth Preparation of Tensor Network States from Measurement [0.0]
  We explore criteria on the local tensors for enabling deterministic state preparation via a single round of measurements. We use these criteria to construct families of measurement-preparable states in one and two dimensions. Our protocol even allows one to engineer preparable quantum states with a range of desired correlation lengths and entanglement properties.
  arXiv  Detail & Related papers  (2024-04-26T00:37:00Z)
• Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements [0.0]
  We characterize the patterns of many-body entanglement that can be deterministically created from measurement. We show this creates matrix product states and identify necessary and sufficient tensor conditions for preparability. We find a trade-off between the richness of the preparable entanglement spectrum and correlation functions, which leads to a no-go theorem for preparing certain quantum states.
  arXiv  Detail & Related papers  (2024-04-25T17:10:22Z)
• Overview of projective quantum measurements [0.0]
  We make use of a unitary "Stinespring" representation of measurements on a dilated Hilbert space. We explain how this unitary representation is guaranteed by the axioms of quantum mechanics.
  arXiv  Detail & Related papers  (2024-04-08T16:58:19Z)
• Unraveling the emergence of quantum state designs in systems with symmetry [15.699822139827916]
  We study the emergence of state designs from the random generator states exhibiting symmetries. We find faster convergence of the trace distance during the early time evolution in comparison to the cases when the symmetry is broken. We expect our findings to pave the way for further exploration of deep thermalization and equilibration of closed and open quantum many-body systems.
  arXiv  Detail & Related papers  (2024-02-14T05:35:03Z)
• The relative entropy of coherence quantifies performance in Bayesian metrology [0.21111026813272177]
  We show how a coherence measure can be applied to an ensemble of states. We then prove that during parameter estimation, the ensemble relative entropy of coherence is equal to the difference between the information gained, and the optimal Holevo information.
  arXiv  Detail & Related papers  (2024-01-29T10:11:15Z)
• Local Purity Distillation in Quantum Systems: Exploring the Complementarity Between Purity and Entanglement [41.94295877935867]
  We introduce and develop the framework of Gibbs-preserving local operations and classical communication.<n>We focus on systems with fully degenerate local Hamiltonians, where local cooling aligns with the extraction of local purity.<n>Our findings open doors to various practical applications, including techniques for entanglement detection and estimation.
  arXiv  Detail & Related papers  (2023-11-20T14:58:31Z)
• Quantification of Entanglement and Coherence with Purity Detection [16.01598003770752]
  Entanglement and coherence are fundamental properties of quantum systems, promising to power near future quantum technologies. Here, we demonstrate quantitative bounds to operationally useful entanglement and coherence. Our research offers an efficient means of verifying large-scale quantum information processing.
  arXiv  Detail & Related papers  (2023-08-14T11:03:40Z)
• Sequential sharing of two-qudit entanglement based on the entropic uncertainty relation [15.907303576427644]
  Entanglement and uncertainty relation are two focuses of quantum theory. We relate entanglement sharing to the entropic uncertainty relation in a $(dtimes d)$-dimensional system via weak measurements with different pointers.
  arXiv  Detail & Related papers  (2023-04-12T12:10:07Z)
• Regression of high dimensional angular momentum states of light [47.187609203210705]
  We present an approach to reconstruct input OAM states from measurements of the spatial intensity distributions they produce. We showcase our approach in a real photonic setup, generating up-to-four-dimensional OAM states through a quantum walk dynamics.
  arXiv  Detail & Related papers  (2022-06-20T16:16:48Z)
• Entropic uncertainty relations from equiangular tight frames and their applications [0.0]
  We derive uncertainty relations for a quantum measurement assigned to an equiangular tight frame. Also, we discuss applications of considered measurements to detect entanglement and other correlations.
  arXiv  Detail & Related papers  (2021-12-23T06:17:31Z)
• Entanglement detection in quantum many-body systems using entropic uncertainty relations [0.0]
  We study experimentally accessible lower bounds on entanglement measures based on entropic uncertainty relations. We derive an improved entanglement bound for bipartite systems, which requires measuring joint probability distributions in only two different measurement settings per subsystem.
  arXiv  Detail & Related papers  (2021-01-21T20:50:11Z)

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.