Localizing quantum information

• URL: http://arxiv.org/abs/2609.01966v1
• Date: Wed, 02 Sep 2026 00:52:41 GMT
• Title: Localizing quantum information
• Abstract summary: In thermodynamics, entropy flows from one reservoir to another, and in quantum gravity, the entropy content of some spatial regions is bounded.<n>In quantum information theory, information is transmitted from one place to another, and entanglement can provide an advantage when there are constraints on such transmission.<n>We prove that an adjusted von Neumann entropy is the minimum quantum entropy that quantifies localizable information.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The idea that information can be localized is pervasive in physics. In thermodynamics, entropy flows from one reservoir to another, and in quantum gravity, the entropy content of some spatial regions is bounded. In quantum information theory, information is transmitted from one place to another, and entanglement can provide an advantage when there are constraints on such transmission. Shannon entropy quantifies localizable information in the sense that marginalization defines an outer measure on the set of parts of a classical multipartite system. In contrast, von Neumann entropy does not quantify localizable information in this sense. However, a variant of von Neumann entropy, which originates in noncommutative geometry, does. We prove that this adjusted von Neumann entropy is the minimum quantum entropy that quantifies localizable information. We also prove that this is the unique quantum entropy that characterizes Bell states in terms of redundant information, directly generalizing the classical case. We work with finite-dimensional $C^*$-algebras throughout, modeling finite quantum systems that may have superselection sectors.

Related papers

• Magic and entanglement in 1+1-dimensional SU(2) lattice gauge theory [37.724232080494424]
  Entanglement and non-stabilizerness (magic) quantify two distinct departures of quantum systems from classical description.<n>We calculate entanglement entropy and stabilizer Rényi entropy of the ground state of the (1+1)-dimensional SU(2) lattice gauge theory.<n>We find a crossover denoted by $g_star$ where the ground state passes from a more magic-rich regime into a regime with less magic.
  arXiv  Detail & Related papers  (2026-06-08T18:00:00Z)
• Hysteretic squashed entanglement in many-body quantum systems [42.085941481155295]
  Entanglement in many-body quantum systems is distributed across spatial regions.<n>We propose hysteretic entanglement $T_sq$, a conditional entanglement that measures the genuine quantum correlations between two subregions.<n>We show that $T_sq$ can detect genuine quantum correlations across both adjacent and long-range subsystems.
  arXiv  Detail & Related papers  (2026-03-10T17:00:49Z)
• Quantum information scrambling in adiabatically-driven critical systems [49.1574468325115]
  Quantum information scrambling refers to the spread of the initially stored information over many degrees of freedom of a quantum many-body system. Here, we extend the notion of quantum information scrambling to critical quantum many-body systems undergoing an adiabatic evolution.
  arXiv  Detail & Related papers  (2024-08-05T18:00:05Z)
• On dynamical measures of quantum information [0.0]
  We use the theory of quantum states over time to define an entropy $S(rho,mathcalE)$ associated with quantum processes. Such an entropy is then used to define formulations of the quantum conditional entropy and quantum mutual information.
  arXiv  Detail & Related papers  (2023-06-02T18:00:01Z)
• Which entropy for general physical theories? [44.99833362998488]
  We address the problem of quantifying the information content of a source for an arbitrary information theory. The functions that solve this problem in classical and quantum theory are Shannon's and von Neumann's entropy, respectively. In a general information theory there are three different functions that extend the notion of entropy, and this opens the question as to whether any of them can universally play the role of the quantifier for the information content.
  arXiv  Detail & Related papers  (2023-02-03T10:55:13Z)
• Shannon theory beyond quantum: information content of a source [68.8204255655161]
  We extend the definition of information content to operational probabilistic theories. We prove relevant properties as the subadditivity, and the relation between purity and information content of a state.
  arXiv  Detail & Related papers  (2021-12-23T16:36:06Z)
• Quantum logical entropy: fundamentals and general properties [0.0]
  We introduce the quantum logical entropy to study quantum systems. We prove several properties of this entropy for generic density matrices. We extend the notion of quantum logical entropy to post-selected systems.
  arXiv  Detail & Related papers  (2021-08-05T16:47:22Z)
• Quantum Entropy [0.12183405753834559]
  We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair of observables forming the quantum phase space. We conjecture an entropy law whereby that entropy of a closed system never decreases, implying a time arrow for particles physics.
  arXiv  Detail & Related papers  (2021-06-29T13:04:55Z)
• Information analysis in free and confined harmonic oscillator [0.0]
  In the last decade, information measures were investigated extensively in diverse quantum problems. The most prominent amongst these are: Fisher information, Shannon entropy, Renyi entropy, Tsallis entropy, Onicescu energy and several complexities. These have been invoked to explain several physico-chemical properties of a system under investigation.
  arXiv  Detail & Related papers  (2021-05-04T13:01:03Z)
• Taking the temperature of a pure quantum state [55.41644538483948]
  Temperature is a deceptively simple concept that still raises deep questions at the forefront of quantum physics research. We propose a scheme to measure the temperature of such pure states through quantum interference.
  arXiv  Detail & Related papers  (2021-03-30T18:18:37Z)
• Observation of thermalization and information scrambling in a superconducting quantum processor [24.685988382662803]
  We show that the $XX$ chain, as free fermions on a 1D lattice, fails to thermalize, and local information does not scramble in the integrable channel. Our experiments reveal ergodicity and scrambling in the controllable qubit ladder, and opens the door to further investigations on the thermodynamics and chaos in quantum many-body systems.
  arXiv  Detail & Related papers  (2021-01-20T09:00:09Z)
• A Topos Theoretic Notion of Entropy [1.827510863075184]
  We show how a notion of entropy can be defined within the topos formalism. We show how this construction unifies Shannon and von Neumann entropy as well as classical and quantum Renyi entropies.
  arXiv  Detail & Related papers  (2020-06-04T21:37:29Z)

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.