Quantum Conditional Stochastic Processes

• URL: http://arxiv.org/abs/2603.27369v1
• Date: Sat, 28 Mar 2026 18:31:09 GMT
• Title: Quantum Conditional Stochastic Processes
• Abstract summary: We derive quantum mechanics by employing a correspondence called a textitdictionary<n>We also show that the converse holds. That is, beginning with a quantum system, we employ the dictionary to derive a CSP.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave functions, Born's rule for probabilities and others. If we accept that quantum mechanics is probabilistic, then these concepts can be derived and they become secondary. In this work, we begin with what we call a \textit{conditional stochastic process} (CSP) which is based on real numbers and probabilities. As we shall see, such processes are defined by three simple axioms. We then use CSP to derive quantum mechanics by employing a correspondence called a \textit{dictionary}. We also show that the converse holds. That is, beginning with a quantum system, we employ the dictionary to derive a CSP.

Related papers

• Quantum Analytical Mechanics: Quantum Mechanics with Hidden Variables [0.0]
  Quantum analytical mechanics derives equations of motion for so-called hidden'' variables.<n>The theory is not a replacement of Hilbert space quantum mechanics but a mathematical completion enriching our toolset for the description of quantum phenomena.
  arXiv  Detail & Related papers  (2025-11-26T14:26:16Z)
• The Quantum Wave Function as a Complex Probability Distribution [0.0]
  We show that the wave function and its complex conjugate can be interpreted as complex probability distributions.<n>It is suggested that embracing the idea of processes in quantum theory may explain the reasons for the appearance of classical behavior in large objects.
  arXiv  Detail & Related papers  (2025-02-14T19:39:06Z)
• Quantum decoherence from complex saddle points [0.0]
  Quantum decoherence is the effect that bridges quantum physics to classical physics.<n>We present some first-principle calculations in the Caldeira-Leggett model.<n>We also discuss how to extend our approach to general models by Monte Carlo calculations.
  arXiv  Detail & Related papers  (2024-08-29T15:35:25Z)
• Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
  We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
  arXiv  Detail & Related papers  (2024-08-19T09:15:54Z)
• A vertical gate-defined double quantum dot in a strained germanium double quantum well [48.7576911714538]
  Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation. We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well. We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.
  arXiv  Detail & Related papers  (2023-05-23T13:42:36Z)
• Simple Tests of Quantumness Also Certify Qubits [69.96668065491183]
  A test of quantumness is a protocol that allows a classical verifier to certify (only) that a prover is not classical. We show that tests of quantumness that follow a certain template, which captures recent proposals such as (Kalai et al., 2022) can in fact do much more. Namely, the same protocols can be used for certifying a qubit, a building-block that stands at the heart of applications such as certifiable randomness and classical delegation of quantum computation.
  arXiv  Detail & Related papers  (2023-03-02T14:18:17Z)
• Quantum entanglement without superposition [0.0]
  Superposition states are at the origin of many paradoxes in quantum mechanics. quantum jumps are a key feature of this approach, in blatant contrast with the continuity of the deterministic Schr"odinger equation.
  arXiv  Detail & Related papers  (2022-12-09T13:56:35Z)
• Schr\"odinger cat states of a 16-microgram mechanical oscillator [54.35850218188371]
  The superposition principle is one of the most fundamental principles of quantum mechanics. Here we demonstrate the preparation of a mechanical resonator with an effective mass of 16.2 micrograms in Schr"odinger cat states of motion. We show control over the size and phase of the superposition and investigate the decoherence dynamics of these states.
  arXiv  Detail & Related papers  (2022-11-01T13:29:44Z)
• Quantum mechanics? It's all fun and games until someone loses an $i$ [0.0]
  QBism regards quantum mechanics as an addition to probability theory. Recent work has demonstrated that reference devices employing symmetric informationally complete POVMs (or SICs) achieve a minimal quantumness. We attempt to identify the optimal reference device in the first real dimension without a SIC.
  arXiv  Detail & Related papers  (2022-06-30T15:15:16Z)
• The Logic of Quantum Programs [77.34726150561087]
  We present a logical calculus for reasoning about information flow in quantum programs. In particular we introduce a dynamic logic that is capable of dealing with quantum measurements, unitary evolutions and entanglements in compound quantum systems.
  arXiv  Detail & Related papers  (2021-09-14T16:08:37Z)
• 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)
• Tossing Quantum Coins and Dice [0.0]
  This case is an important example of a quantum procedure because it presents a typical framework employed in quantum information processing and quantum computing. The emphasis is on the clarification of the difference between quantum and classical conditional probabilities.
  arXiv  Detail & Related papers  (2021-03-31T11:39:56Z)
• Operational Resource Theory of Imaginarity [48.7576911714538]
  We show that quantum states are easier to create and manipulate if they only have real elements. As an application, we show that imaginarity plays a crucial role for state discrimination.
  arXiv  Detail & Related papers  (2020-07-29T14:03:38Z)

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.