On the emergence of preferred structures in quantum theory

• URL: http://arxiv.org/abs/2512.07468v1
• Date: Mon, 08 Dec 2025 11:50:11 GMT
• Title: On the emergence of preferred structures in quantum theory
• Authors: Antoine Soulas, Guilherme Franzmann, Andrea Di Biagio,
• Abstract summary: We first focus on the question of whether the Hamiltonian can uniquely determine a tensor product structure.<n>The present paper reviews, clarifies, and critically examines two apparently conflicting theorems by Cotler et al. and Stoica.<n>We propose a correct mathematical way to address the general problem of preferred structures in quantum theory.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We assess the possibilities offered by Hilbert space fundamentalism, an attitude towards quantum physics according to which all physical structures (e.g. subsystems, locality, spacetime, preferred observables) should emerge from minimal quantum ingredients (typically a Hilbert space, Hamiltonian, and state). As a case study, we first mainly focus on the specific question of whether the Hamiltonian can uniquely determine a tensor product structure, a crucial challenge in the growing field of quantum mereology. The present paper reviews, clarifies, and critically examines two apparently conflicting theorems by Cotler et al. and Stoica. We resolve the tension, show how the former has been widely misinterpreted and why the latter is correct only in some weaker version. We then propose a correct mathematical way to address the general problem of preferred structures in quantum theory, relative to the characterization of emergent objects by unitary-invariant properties. Finally, we apply this formalism in the particular case we started with, and show that a Hamiltonian and a state are enough structure to uniquely select a preferred tensor product structure.

Related papers

• Observation of Quantum Darwinism and the Origin of Classicality with Superconducting Circuits [9.09683951826704]
  How can we rationalize everyday classical observations from an inherently quantum world?<n>Quantum Darwinism offers a compelling framework to explain this emergence of classicality.<n>We observe the highly structured branching quantum states that support classicality and the saturation of quantum mutual information.
  arXiv  Detail & Related papers  (2025-04-01T13:33:32Z)
• A Tutorial on Knots and Quantum Mechanics [0.0]
  Notes review a description of quantum mechanics in terms of the topology of spaces.<n>A topological classification of entanglement is discussed, as well as properties of entanglement entropy and basic quantum protocols.
  arXiv  Detail & Related papers  (2025-03-11T19:35:24Z)
• An explicit tensor notation for quantum computing [0.0]
  This paper introduces a formalism that aims to describe the intricacies of quantum computation. The focus is on providing a comprehensive representation of quantum states for multiple qubits and the quantum gates that manipulate them.
  arXiv  Detail & Related papers  (2024-09-16T17:21:17Z)
• Relaxation of first-class constraints and the quantization of gauge theories: from "matter without matter" to the reappearance of time in quantum gravity [72.27323884094953]
  We make a conceptual overview of an approach to the initial-value problem in canonical gauge theories. We stress how the first-class phase-space constraints may be relaxed if we interpret them as fixing the values of new degrees of freedom.
  arXiv  Detail & Related papers  (2024-02-19T19:00:02Z)
• On the tensorial structure of general covariant quantum systems [0.0]
  The structure of the observable algebra is related to a tensor product decomposition of the Hilbert space. It has been remarked that the Hamiltonian may determine this tensor product structure.
  arXiv  Detail & Related papers  (2023-12-20T19:03:23Z)
• 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)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• 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)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)
• Internal Boundary between Entanglement and Separability Within a Quantum State [5.439020425819001]
  We show that whether a quantum state is entangled or not is determined by a threshold within the quantum state. For an arbitrary quantum state, we provide operational algorithms to obtain its optimal entangled state, its optimal separable state, its best separable approximation (BSA) decomposition.
  arXiv  Detail & Related papers  (2020-03-01T23:06:53Z)
• Finite Deformations of Quantum Mechanics [0.0]
  We investigate modifications of quantum mechanics that replace the unitary group in a finite dimensional Hilbert space with a finite group. We show that Kornyak's proposal to understand QM as classical dynamics on a Hilbert space of one dimension higher than that describing the universe can probably be a model of the world we observe.
  arXiv  Detail & Related papers  (2020-01-21T17:35:03Z)

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.