Graph structure of quantum mechanics

• URL: http://arxiv.org/abs/2411.18146v2
• Date: Mon, 02 Dec 2024 07:57:47 GMT
• Title: Graph structure of quantum mechanics
• Authors: Songyi Liu, Yongjun Wang, Baoshan Wang, Jian Yan, Heng Zhou,
• Abstract summary: The quantum mechanics is proved to admit no hidden-variable in 1960s, which means the quantum systems are contextual. We develop the approach of partial Boolean algebra to characterize the contextuality theory with local consistency and exclusivity. Our conclusions indicate that the quantum mechanics is a graph-structured combination of multiple hidden-variable theories, and provide a precise mathematical framework for quantum contextuality.
• Score: 3.9474648943255937
• License:
• Abstract: The quantum mechanics is proved to admit no hidden-variable in 1960s, which means the quantum systems are contextual. Revealing the mathematical structure of quantum mechanics is a significant task. We develop the approach of partial Boolean algebra to characterize the contextuality theory with local consistency and exclusivity, and then prove that the finite dimensional quantum systems are determined by atoms using two graph structure theorems. We also generalize our work to infinite dimensional cases. Our conclusions indicate that the quantum mechanics is a graph-structured combination of multiple hidden-variable theories, and provide a precise mathematical framework for quantum contextuality.

Related papers

• Embedded structure in quantum theory, functional operator and multiverse [0.0]
  We explore a wider theoretical framework that has quantum field theory built-in, taking the fact that quantum mechanics is reconstructed from quantum field theory as a hint. We formulate a quantum theory with an embedded structure by introducing functional operators, and we find that it could describe the level II multiverse.
  arXiv  Detail & Related papers  (2024-11-13T01:24:22Z)
• An Indeterminacy-based Ontology for Quantum Theory [0.0]
  I present and defend a new ontology for quantum theories (or sinterpretation'' of quantum theory) called Generative Quantum Interpretation (GQT) GQT provides a series of important benefits that current widely discussed lack, namely, wave function realism and primitive primitive, without some of their costs. I will argue that GQT should be taken seriously because it provides a series of important benefits that current widely discussed lack, namely, wave function realism and primitive primitive, without some of their costs.
  arXiv  Detail & Related papers  (2024-04-10T17:55:58Z)
• A vertical gate-defined double quantum dot in a strained germanium double quantum well [48.7576911714538]
  Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation. We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well. We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.
  arXiv  Detail & Related papers  (2023-05-23T13:42:36Z)
• VENUS: A Geometrical Representation for Quantum State Visualization [14.373238457656237]
  VENUS is a novel visualization for quantum state representation. We show that VENUS can effectively facilitate the exploration of quantum states for the single qubit and two qubits.
  arXiv  Detail & Related papers  (2023-03-15T04:56:23Z)
• No-signalling constrains quantum computation with indefinite causal structure [45.279573215172285]
  We develop a formalism for quantum computation with indefinite causal structures. We characterize the computational structure of higher order quantum maps. We prove that these rules, which have a computational and information-theoretic nature, are determined by the more physical notion of the signalling relations between the quantum systems.
  arXiv  Detail & Related papers  (2022-02-21T13:43:50Z)
• Quantum Information Dimension and Geometric Entropy [0.0]
  We introduce two analysis tools, inspired by Renyi's information theory, to characterize and quantify fundamental properties of geometric quantum states. We recount their classical definitions, information-theoretic meanings, and physical interpretations, and adapt them to quantum systems via the geometric approach.
  arXiv  Detail & Related papers  (2021-11-11T18:40:49Z)
• A thorough introduction to non-relativistic matrix mechanics in multi-qudit systems with a study on quantum entanglement and quantum quantifiers [0.0]
  This article provides a deep and abiding understanding of non-relativistic matrix mechanics. We derive and analyze the respective 1-qubit, 1-qutrit, 2-qubit, and 2-qudit coherent and incoherent density operators. We also address the fundamental concepts of quantum nondemolition measurements, quantum decoherence and, particularly, quantum entanglement.
  arXiv  Detail & Related papers  (2021-09-14T05:06:47Z)
• From Boolean Valued Analysis to Quantum Set Theory: Mathematical Worldview of Gaisi Takeuti [0.0]
  Gaisi Takeuti introduced Boolean valued analysis around 1974 to provide systematic applications of Boolean valued models of set theory to analysis. He then stepped forward to construct set theory based on quantum logic, as the first step to construct "quantum mathematics" We analyze Takeuti's mathematical world view underlying his program from two perspectives.
  arXiv  Detail & Related papers  (2021-02-07T17:17:06Z)
• Experimental Validation of Fully Quantum Fluctuation Theorems Using Dynamic Bayesian Networks [48.7576911714538]
  Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems. We experimentally verify detailed and integral fully quantum fluctuation theorems for heat exchange using two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup.
  arXiv  Detail & Related papers  (2020-12-11T12:55:17Z)
• One-shot quantum error correction of classical and quantum information [10.957528713294874]
  Quantum error correction (QEC) is one of the central concepts in quantum information science. We provide a form of capacity theorem for both classical and quantum information. We show that a demonstration of QEC by short random quantum circuits is feasible.
  arXiv  Detail & Related papers  (2020-11-02T01:24:59Z)
• Operational Resource Theory of Imaginarity [48.7576911714538]
  We show that quantum states are easier to create and manipulate if they only have real elements. As an application, we show that imaginarity plays a crucial role for state discrimination.
  arXiv  Detail & Related papers  (2020-07-29T14:03:38Z)

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.