Interval Effect Algebras and Holevo Instruments

• URL: http://arxiv.org/abs/2403.18925v1
• Date: Wed, 27 Mar 2024 18:16:24 GMT
• Title: Interval Effect Algebras and Holevo Instruments
• Authors: Stan Gudder,
• Abstract summary: This article begins with a study of convex effect-state spaces. We point out that such spaces are equivalent to interval effect algebras that generate an ordered linear space and possess an order-determining set of states. We then discuss operations and instruments on interval effect algebras under the assumption of an unrestrictive condition.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This article begins with a study of convex effect-state spaces. We point out that such spaces are equivalent to interval effect algebras that generate an ordered linear space and possess an order-determining set of states. We then discuss operations and instruments on interval effect algebras under the assumption of an unrestrictive condition. Effects measured by operations and sequential products of effects relative to operations are considered. Observables are introduced and coexistence of effects are discussed. We also present properties of sequential products of observables and conditioning of observables related to instruments. The final section is devoted to Holevo instruments. Pure and mixed Holevo operations are defined and extended to instruments. The Holevo sequential product of two observables is defined and the marginals of these products are computed. We define the commutant of two effects and derive its properties. Examples are given that illustrate the properties of previously presented concepts.

Related papers

• Nonparametric Partial Disentanglement via Mechanism Sparsity: Sparse Actions, Interventions and Sparse Temporal Dependencies [58.179981892921056]
  This work introduces a novel principle for disentanglement we call mechanism sparsity regularization. We propose a representation learning method that induces disentanglement by simultaneously learning the latent factors. We show that the latent factors can be recovered by regularizing the learned causal graph to be sparse.
  arXiv  Detail & Related papers  (2024-01-10T02:38:21Z)
• Is This the Subspace You Are Looking for? An Interpretability Illusion for Subspace Activation Patching [47.05588106164043]
  Mechanistic interpretability aims to understand model behaviors in terms of specific, interpretable features. Recent studies have explored subspace interventions as a way to manipulate model behavior and attribute the features behind it to given subspaces. We demonstrate that these two aims diverge, potentially leading to an illusory sense of interpretability.
  arXiv  Detail & Related papers  (2023-11-28T18:32:19Z)
• Dual Quantum Instruments and Sub-observables [0.0]
  We show that although a dual instruments measures a unique observable, it determines many sub-observables. Sub-observable effect algebras are characterized and studied. The sequential product of instruments is discussed.
  arXiv  Detail & Related papers  (2023-02-23T18:58:29Z)
• Dual Instruments and Sequential Products of Observables [0.0]
  We show that every operation possesses a unique dual operation and measures an unique effect. We extend this work to the theory of instruments and observables.
  arXiv  Detail & Related papers  (2022-08-16T19:44:45Z)
• Self-adjoint extension schemes and modern applications to quantum Hamiltonians [55.2480439325792]
  monograph contains revised and enlarged materials from previous lecture notes of undergraduate and graduate courses and seminars delivered by both authors over the last years on a subject that is central both in abstract operator theory and in applications to quantum mechanics. A number of models are discussed, which are receiving today new or renewed interest in mathematical physics, in particular from the point of view of realising certain operators of interests self-adjointly.
  arXiv  Detail & Related papers  (2022-01-25T09:45:16Z)
• Sequential Products of Quantum Measurements [0.0]
  We introduce sequential products of effect and operations. The results are generalized to include observables and instruments. Finally, we consider conditioning and coexistence of observables and instruments.
  arXiv  Detail & Related papers  (2021-08-18T01:44:20Z)
• Quantum asymmetry and noisy multi-mode interferometry [55.41644538483948]
  Quantum asymmetry is a physical resource which coincides with the amount of coherence between the eigenspaces of a generator. We show that the asymmetry may emphincrease as a result of a emphdecrease of coherence inside a degenerate subspace.
  arXiv  Detail & Related papers  (2021-07-23T07:30:57Z)
• Six-point functions and collisions in the black hole interior [71.67770216265583]
  We consider two signals sent from the boundaries into the black hole interior shared between the two regions. We compute three different out-of-time-order six-point functions to quantify various properties of the collision.
  arXiv  Detail & Related papers  (2021-05-26T18:01:23Z)
• Combinations of Quantum Observables and Instruments [0.0]
  We study parts of observables, post-processing, generalized convex combinations, sequential products and tensor products. We consider properties of observables measured by combinations of instruments. In this work, we only consider finite-dimensional quantum systems.
  arXiv  Detail & Related papers  (2020-10-15T21:26:22Z)
• 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)
• Algebraic and geometric properties of local transformations [0.0]
  Some properties of physical systems can be characterized from their correlations. In this work, we single out the set of deterministic local maps as the one satisfying two equivalent constructions. Surprisingly, the study of these fundamental properties has deep and practical applications.
  arXiv  Detail & Related papers  (2020-04-20T16:01:31Z)

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.