Quantum Information Theory and Free Semialgebraic Geometry: One Wonderland Through Two Looking Glasses

• URL: http://arxiv.org/abs/2102.04240v1
• Date: Mon, 8 Feb 2021 14:36:40 GMT
• Title: Quantum Information Theory and Free Semialgebraic Geometry: One Wonderland Through Two Looking Glasses
• Authors: Gemma De Las Cuevas, Tim Netzer
• Abstract summary: We show how quantum information theory and free (i.e. noncommutative) semialgebraic geometry often study similar objects from different perspectives. We give examples in the context of positivity and separability, quantum magic squares, quantum correlations in non-local games, and positivity in tensor networks.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We illustrate how quantum information theory and free (i.e. noncommutative) semialgebraic geometry often study similar objects from different perspectives. We give examples in the context of positivity and separability, quantum magic squares, quantum correlations in non-local games, and positivity in tensor networks, and we show the benefits of combining the two perspectives. This paper is an invitation to consider the intersection of the two fields, and should be accessible for researchers from either field.

Related papers

• From Entanglement to Universality: A Multiparticle Spacetime Algebra Approach to Quantum Computational Gates Revisited [0.0]
  We focus on testing the usefulness of geometric algebras (GAs) techniques in two applications to quantum computing. First, we offer an explicit algebraic characterization of one- and two-qubit quantum states together with a MSTA description of one- and two-qubit quantum computational gates. In this first application, we devote special attention to the concept of entanglement, focusing on entangled quantum states and two-qubit entangling quantum gates.
  arXiv  Detail & Related papers  (2024-05-13T19:51:26Z)
• Antiparticles in non-relativistic quantum mechanics [55.2480439325792]
  Non-relativistic quantum mechanics was originally formulated to describe particles. We show how the concept of antiparticles can and should be introduced in the non-relativistic case without appealing to quantum field theory.
  arXiv  Detail & Related papers  (2024-04-02T09:16:18Z)
• A Geometry of entanglement and entropy [0.7373617024876725]
  We provide a comprehensive overview of entanglement, highlighting its crucial role in quantum mechanics. We discuss various methods for quantifying and characterizing entanglement through a geometric perspective. An example of entanglement as an indispensable resource for the task of state teleportation is presented at the end.
  arXiv  Detail & Related papers  (2024-02-24T18:26:32Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension [44.41126861546141]
  We provide a classification of Lie algebras generated by translation-invariant 2-local spin chain Hamiltonians. We consider chains with open and periodic boundary conditions and find 17 unique dynamical Lie algebras. In addition to the closed and open spin chains, we consider systems with a fully connected topology, which may be relevant for quantum machine learning approaches.
  arXiv  Detail & Related papers  (2023-09-11T17:59:41Z)
• Semidefinite programming relaxations for quantum correlations [45.84205238554709]
  We discuss how the core idea of semidefinite relaxations can be adapted for a variety of research topics in quantum correlations. These topics include nonlocality, quantum communication, quantum networks, entanglement, and quantum cryptography.
  arXiv  Detail & Related papers  (2023-07-05T18:00:07Z)
• Algebraic structures underlying quantum independences : Theory and Applications [0.0]
  We reconcile two approaches to quantum probabilities: one physical and coming directly from quantum mechanics, the other more algebraic. We provide a unified picture introducing jointly to several fields of applications, many of which are probably not all familiar. We take the opportunity to present various results obtained recently in the various noncommutative probability theories.
  arXiv  Detail & Related papers  (2022-10-17T17:12:04Z)
• Genuine multipartite entanglement and quantum coherence in an electron-positron system: Relativistic covariance [117.44028458220427]
  We analyze the behavior of both genuine multipartite entanglement and quantum coherence under Lorentz boosts. A given combination of these quantum resources is shown to form a Lorentz invariant.
  arXiv  Detail & Related papers  (2021-11-26T17:22:59Z)
• 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)
• 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)
• Quantum simulation of gauge theory via orbifold lattice [47.28069960496992]
  We propose a new framework for simulating $textU(k)$ Yang-Mills theory on a universal quantum computer. We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories.
  arXiv  Detail & Related papers  (2020-11-12T18:49:11Z)
• Euclidean formulation of relativistic quantum mechanics of N particles [0.0]
  Euclidean formulation of relativistic quantum mechanics for systems of a finite number of degrees of freedom is discussed. Theory can be formulated entirely in the Euclidean representation without the need for analytic continuation. Explicit formulas for generators of the Poincar'e group for any spin are constructed and shown to be self-adjoint on the Euclidean representation of the Hilbert space.
  arXiv  Detail & Related papers  (2020-10-20T15:27:50Z)

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.