Picturing general quantum subsystems

• URL: http://arxiv.org/abs/2511.09494v1
• Date: Thu, 13 Nov 2025 01:58:10 GMT
• Title: Picturing general quantum subsystems
• Authors: Octave Mestoudjian, Matt Wilson, Augustin Vanrietvelde, Pablo Arrighi,
• Abstract summary: We introduce a primitive notion of splitting maps within dagger symmetric monoidal categories.<n>We show that the comprehension preorder precisely captures the inclusion partial order between Von Neumann algebras.<n>We prove that the known equivalence between semi-causality and semi-localisability for factor subsystems extends to all (including non-factor) subsystems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We extend the usual process-theoretic view on locality and causality in subsystems (based on the tensor product case) to general quantum systems (i.e. possibly non-factor, finite-dimensional Von Neumann algebras). To do so, we introduce a primitive notion of splitting maps within dagger symmetric monoidal categories. Splitting maps give rise to subsystems that admit comparison via a preorder called comprehension, and support an adaptation of the usual categorical trace. We show that the comprehension preorder precisely captures the inclusion partial order between Von Neumann algebras, and that the splitting map trace captures the natural notion of Von Neumann algebra trace. As a consequence of the development of these diagrammatic tools, we prove that the known equivalence between semi-causality and semi-localisability for factor subsystems extends to all (including non-factor) subsystems.

Related papers

• Symmetry and localisation in causally constrained quantum operator dynamics [0.0]
  We study the structure of tri-partite unitaries ('walls') which permanently arrest local operator spreading in their time-periodic evolution.<n>We prove an entanglement area-law due to local constraints and we study its stability against projective measurements.<n>Our results offer a rigorous understanding of locally constrained quantum dynamics from a quantum information perspective.
  arXiv  Detail & Related papers  (2026-02-06T18:09:26Z)
• Random-Matrix-Induced Simplicity Bias in Over-parameterized Variational Quantum Circuits [72.0643009153473]
  We show that expressive variational ansatze enter a Haar-like universality class in which both observable expectation values and parameter gradients concentrate exponentially with system size.<n>As a consequence, the hypothesis class induced by such circuits collapses with high probability to a narrow family of near-constant functions.<n>We further show that this collapse is not unavoidable: tensor-structured VQCs, including tensor-network-based and tensor-hypernetwork parameterizations, lie outside the Haar-like universality class.
  arXiv  Detail & Related papers  (2026-01-05T08:04:33Z)
• Entanglement in von Neumann Algebraic Quantum Information Theory [1.6921396880325779]
  We use a framework in which subsystems are described by von Neumann algebras on the full system's Hilbert space.<n>We show that the type classification of von Neumann algebras is in one-to-one correspondence with a family of operational entanglement properties.
  arXiv  Detail & Related papers  (2025-10-08T21:18:08Z)
• Semantic Numeration Systems as Dynamical Systems [55.2480439325792]
  The cardinal abstract object (CAO) formed by them in a certain connectivity topology is proposed to be considered as a linear discrete dynamical system with nonlinear control.<n>The fundamental role of the configuration matrix, which combines information about the types of cardinal semantic operators in the CAO, their parameters and topology of connectivity, is demonstrated.
  arXiv  Detail & Related papers  (2025-07-28T19:29:36Z)
• Partitions in quantum theory [0.0]
  In quantum theory, subsystems are usually framed as sub-C* algebras of the algebra of operators on the global system.<n>We present a definition of partitions into an arbitrary number of parts, each of which is a possibly non-factor sub-C* algebra.<n>We discuss its physical interpretation and study its properties, in particular with regards to the structure of algebras' centres.
  arXiv  Detail & Related papers  (2025-06-27T13:36:48Z)
• Evolution of Gaussians in the Hellinger-Kantorovich-Boltzmann gradient flow [44.500314182711236]
  We derive explicit ordinary equations govern the evolution of mean, covariance, and mass under HK-Boltzmann flow.<n>We demonstrate exponential convergence to equilibrium through constructing a gradient structure associated with a Polyak-Lojasiewicz-type inequalities.<n>We extend our analysis to non-Gaussian targets exhibiting strong log-lambda-concavity.
  arXiv  Detail & Related papers  (2025-04-29T03:54:56Z)
• A Search for Classical Subsystems in Quantum Worlds [0.49478969093606673]
  We take a systematic approach to discover factorizations of a global Hilbert space that admit a quasi-classical description of subsystems. We show that every Hamiltonian admits a pointer basis in the factorization where the energy eigenvectors are separable. We derive several analytical forms that the Hamiltonian may take in such factorizations, each with its unique set of features.
  arXiv  Detail & Related papers  (2024-03-16T11:12:31Z)
• Enriching Diagrams with Algebraic Operations [49.1574468325115]
  We extend diagrammatic reasoning in monoidal categories with algebraic operations and equations. We show how this construction can be used for diagrammatic reasoning of noise in quantum systems.
  arXiv  Detail & Related papers  (2023-10-17T14:12:39Z)
• Coherence generation, symmetry algebras and Hilbert space fragmentation [0.0]
  We show a simple connection between classification of physical systems and their coherence generation properties, quantified by the coherence generating power (CGP) We numerically simulate paradigmatic models with both ordinary symmetries and Hilbert space fragmentation, comparing the behavior of the CGP in each case with the system dimension.
  arXiv  Detail & Related papers  (2022-12-29T18:31:16Z)
• Quantum Relativity of Subsystems [58.720142291102135]
  We show that different reference frame perspectives induce different sets of subsystem observable algebras, which leads to a gauge-invariant, frame-dependent notion of subsystems and entanglement. Such a QRF perspective does not inherit the distinction between subsystems in terms of the corresponding tensor factorizability of the kinematical Hilbert space and observable algebra. Since the condition for this to occur is contingent on the choice of QRF, the notion of subsystem locality is frame-dependent.
  arXiv  Detail & Related papers  (2021-03-01T19:00:01Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)

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.