Step-by-step derivation of the algebraic structure of quantum mechanics (or from nondisturbing to quantum correlations by connecting incompatible observables)

• URL: http://arxiv.org/abs/2303.04847v1
• Date: Wed, 8 Mar 2023 19:27:24 GMT
• Title: Step-by-step derivation of the algebraic structure of quantum mechanics (or from nondisturbing to quantum correlations by connecting incompatible observables)
• Authors: Alisson Tezzin
• Abstract summary: This paper provides a step-by-step derivation of the quantum formalism. It helps us to understand why this formalism is as it is.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently there has been much interest in deriving the quantum formalism and the set of quantum correlations from simple axioms. In this paper, we provide a step-by-step derivation of the quantum formalism that tackles both these problems and helps us to understand why this formalism is as it is. We begin with a structureless system that only includes real-valued observables, states and a (not specified) state update, and we gradually identify theory-independent conditions that make the algebraic structure of quantum mechanics be assimilated by it. In the first part of the paper, we derive essentially all the "commutative part" of the quantum formalism, i.e., all definitions and theorems that do not involve algebraic operations between incompatible observables, such as projections, Specker's principle, and the spectral theorem; at the statistical level, the system is nondisturbing and satisfies the exclusivity principle at this stage. In the second part of the paper, we connect incompatible observables by taking transition probabilities between pure states into account. This connection is the final step needed to embed our system in a Hilbert space and to go from nondisturbing to quantum correlations.

Related papers

• The composition rule for quantum systems is not the only possible one [0.0]
  We argue that the composition postulate deserves to be experimentally scrutinised independently of the other features of quantum theory. We formulate a family of operational theories that are solely distinguished from quantum theory by their system-composition rule.
  arXiv  Detail & Related papers  (2024-11-24T19:31:13Z)
• What is "quantum" about quantum gravity? [0.0]
  We argue that if both the equivalence principle and quantum mechanics continue to survive experimental tests, that this favors epistemic'' interpretations of quantum mechanics.
  arXiv  Detail & Related papers  (2024-05-13T21:19:50Z)
• A Quantum Theory with Non-collapsing Measurements [0.0]
  A collapse-free version of quantum theory is introduced to study the role of the projection postulate. We assume "passive" measurements that do not update quantum states while measurement outcomes still occur probabilistically. The resulting quantum-like theory has only one type of dynamics, namely unitary evolution.
  arXiv  Detail & Related papers  (2023-03-23T16:32:29Z)
• Principle of information causality rationalizes quantum composition [0.0]
  We show that the principle of information causality, a generalization of no signaling principle, plays significant role to this aim. In accordance with no-signaling condition, state and effect spaces of a composite system can allow different possible mathematical descriptions.
  arXiv  Detail & Related papers  (2022-08-30T05:41:42Z)
• On a foundational conceptual principle of quantum mechanics [0.0]
  Anton Zeilinger's "foundational conceptual principle" for quantum mechanics is an idealistic principle, which should be replaced by a realistic principle of contextuality. We argue that the assumption of non-locality is not required to explain quantum correlation. In contrast to Zeilinger's proposed principle of quantization of information, the principle of contextuality explains it realistically.
  arXiv  Detail & Related papers  (2022-03-26T11:24:14Z)
• Quantum realism: axiomatization and quantification [77.34726150561087]
  We build an axiomatization for quantum realism -- a notion of realism compatible with quantum theory. We explicitly construct some classes of entropic quantifiers that are shown to satisfy almost all of the proposed axioms.
  arXiv  Detail & Related papers  (2021-10-10T18:08:42Z)
• 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 Causal Inference in the Presence of Hidden Common Causes: an Entropic Approach [34.77250498401055]
  We put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. We apply our proposed framework to an experimentally relevant scenario of identifying message senders on quantum noisy links. This approach can lay the foundations of identifying originators of malicious activity on future multi-node quantum networks.
  arXiv  Detail & Related papers  (2021-04-24T22:45:50Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Self-adjointness in Quantum Mechanics: a pedagogical path [77.34726150561087]
  This paper aims to make quantum observables emerge as necessarily self-adjoint, and not merely hermitian operators. Next to the central core of our line of reasoning, the necessity of a non-trivial declaration of a domain to associate with the formal action of an observable.
  arXiv  Detail & Related papers  (2020-12-28T21:19:33Z)
• Entropic Uncertainty Relations and the Quantum-to-Classical transition [77.34726150561087]
  We aim to shed some light on the quantum-to-classical transition as seen through the analysis of uncertainty relations. We employ entropic uncertainty relations to show that it is only by the inclusion of imprecision in our model of macroscopic measurements that we can prepare a system with two simultaneously well-defined quantities.
  arXiv  Detail & Related papers  (2020-03-04T14:01:17Z)

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.