Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1311.3408

The phenomenon of state reduction

Petr Hájíček

Published Nov 14, 2013• 2 citations
arXivHTMLPDF

Abstract

A theory of quantum measurement was introduced some time ago that was based on the notion of the so-called separation status. This separation status had a spatial, local character, so that the theory worked only in special cases. Nevertheless, it enabled a description of state reduction process that was specific in where, when and under which objective conditions the process occurs and that preserved the unitary transformation symmetry of quantum mechanics. Now, in an accompanying paper (arxiv:1411.5524), a completely general mathematical definition of the status is given and analyzed. The present paper reformulates the theory of state reduction accordingly. A general mathematical form of the process is postulated and illustrated by examples of Stern-Gerlach experiment and of screening.

DOI
10.48550/arxiv.1311.3408

Related papers

On the theory of quantum measurement

Petr Hájíček

The notion of state reduction employed by the standard quantum theory of measurement is difficult to accept for two reasons: It leaves open where and when the reduction takes place and it does not give any objective conditions under which the reduction occurs. Some recently published ideas on this problem are developed an improved. The disturbance of measurement due to identical particles in the environment is shown to make any POV measure non-measurable. Truncated POV (TPOV) measures are introduced that can be measurable if object systems satisfy the additional requirement of having separation status. The separation status is generalised from domain of space to domain of phase space. Starting from the previously introduced distinction between ancillas and detectors, further study of experiments suggests that a thermodynamic mixing within a detector and the consequent loss of separation status is the objective condition for the occurrence of the state reduction. The conjecture is simple, specific and testable. The theory is illustrated by a model of a real measurement.

arXiv:1307.0694•Jul 2, 2013•0 citations

QUANTUM THEORY OF STATE REDUCTION AND MEASUREMENT.

Izuru Fujiwara

The central problem in the quantum theory of measurement, how to describe the process of state reduction in terms of the quantum mechanical formalism, is solved on the basis of the relativity of quantal states, which implies that once the apparatus is detected in a well-defined state, the object state must reduce to a corresponding one. This is a process termed by Schrodinger disentanglement. Here, it is essential to observe that Renninger's negative result does constitute an actual measurement process. From this point of view, Heisenberg's interpretation of his microscope experiment and the Einstein-Podolsky-Rosen arguments are reinvestigated. Satisfactory discussions are given to various experimental situations, such as the Stern-Gerlach-type experiment, successive measurements, macroscopic measurements, and Schrodinger's cat. Finally it is proposed to regard a state vector in quantum mechanics as an irreducible physical construct, in Margenau's sense, that is not further analyzable both mathematically and conceptually.

•Jan 1, 1971•0 citations

On the derivation of wave function reduction from Schrödinger's equation: A model

Roland L. Omnes

The possibility of consistency between the basic quantum principles and reduction (wave function reduction) is reexamined. The mathematical description of an organized macroscopic device is constructed explicitly as a convenient tool for this investigation. A derivation of reduction from quantum mechanics is proposed on a specific example, using standard methods of statistical physics. Although these methods are valid only "for all practical purposes", arguments are given to ascribe an emerging status to reduction (or the uniqueness of physical reality), similar to the status of classical physics. Examination of measurements of the particles in an EPR pair by two space-like separated apparatuses shows that the model is consistent with the non-separable character of quantum mechanics, although both measurements are local. Quantitative estimates are given.

arXiv:1006.3227•Jun 16, 2010•2 citations

Emergence of outcomes in quantum mechanics

Bradley A. Foreman

A persistent focus on the concept of emergence as a core element of the scientific method allows a clean separation, insofar as this is possible, of the physical and philosophical aspects of the problem of outcomes in quantum mechanics. The philosophical part of the problem is to explain why a closed system has definite experimental outcomes. The physical part is to show mathematically that there exists a limit in which the contradiction between unitary Schroedinger dynamics and a reduction process leading to distinct outcomes becomes negligible according to an explicitly stated criterion, and to make this criterion as objective as possible. The physical problem is solved here by redefining the notion of a quantum state and finding a suitable measure for the change of state upon reduction. The appropriate definition of the quantum state is not as a ray or density operator in Hilbert space, but rather as an equivalence class consisting of all density operators in a given subspace, the members of which all describe the same experimental outcome. For systems containing only subsystems that are integrated with their environments, these equivalence classes can be represented mathematically by projection operators, and the resulting formalism is closely related to that used by von Neumann to study the increase of entropy predicted by the second law of thermodynamics. However, nearly isolated subsystems are reduced only indirectly, as a consequence of their interaction with integrated subsystems. The reduced states of isolated subsystems are the same conditional states used in the definition of quantum discord. The key concepts of decoherence theory can all be adapted to fit this definition of a quantum state, resulting in a unified theory capable of resolving, in principle, all aspects of the quantum measurement problem. The theory thus obtained is weakly objective but not strongly objective.

arXiv:1907.03456•Jul 8, 2019•1 citation

Space localization of the quantum particle

Alexey Yur'evich Samarin

It is shown, that in addition to the evolution quantum object motion wave equation in the integral form can describe the wave function reduction as a physical process. Such description is represented for the space localization process, taking place when the space coordinate is measured, and it is shown, that collapse arises, as the result of the quantum particle and corresponding measuring instrument interaction. This physical phenomenon mathematical image looks like the instantaneous transformation of the virtual paths set to the subset, determined by the measuring process conditions, when the macroscopic changes appears in the measuring instrument.In conventional quantum mechanics such Hilbert space collapse itself corresponds to such reduction phenomenon.

•Dec 1, 2013•3 citations

Measurement in Quantum Mechanics. II

Hitoshi Wakita

The theory of measurement is reasonably interpreted without any abrupt and noncausal change of a state, namely, with no “reduction of a wave packet”, in the framework of quantum mechanics. Though a process of measurement is causal in the usual quantum-mechanical sense, it is possible to utilize the concept of the “reduction of a wave packet” without any loss of compatibility. The Stern-Gerlach experiment is put to a careful study to show that the present interpretation is consistent with experiment.

Progress of Theoretical Physics•Jan 1, 1962•7 citations
A theory of quantum measurement was introduced some time ago that was based on the notion of the so-called separation status. This separation status had a spatial, local character, so that the theory worked only in special cases. Nevertheless, it enabled a description of state reduction process that was specific in where, when and under which objective conditions the process occurs and that preserved the unitary transformation symmetry of quantum mechanics. Now, in an accompanying paper (arxiv:1411.5524), a completely general mathematical definition of the status is given and analyzed. The present paper reformulates the theory of state reduction accordingly. A general mathematical form of the process is postulated and illustrated by examples of Stern-Gerlach experiment and of screening.
The notion of state reduction employed by the standard quantum theory of measurement is difficult to accept for two reasons: It leaves open where and when the reduction takes place and it does not give any objective conditions under which the reduction occurs. Some recently published ideas on this problem are developed an improved. The disturbance of measurement due to identical particles in the environment is shown to make any POV measure non-measurable. Truncated POV (TPOV) measures are introduced that can be measurable if object systems satisfy the additional requirement of having separation status. The separation status is generalised from domain of space to domain of phase space. Starting from the previously introduced distinction between ancillas and detectors, further study of experiments suggests that a thermodynamic mixing within a detector and the consequent loss of separation status is the objective condition for the occurrence of the state reduction. The conjecture is simple, specific and testable. The theory is illustrated by a model of a real measurement.
The central problem in the quantum theory of measurement, how to describe the process of state reduction in terms of the quantum mechanical formalism, is solved on the basis of the relativity of quantal states, which implies that once the apparatus is detected in a well-defined state, the object state must reduce to a corresponding one. This is a process termed by Schrodinger disentanglement. Here, it is essential to observe that Renninger's negative result does constitute an actual measurement process. From this point of view, Heisenberg's interpretation of his microscope experiment and the Einstein-Podolsky-Rosen arguments are reinvestigated. Satisfactory discussions are given to various experimental situations, such as the Stern-Gerlach-type experiment, successive measurements, macroscopic measurements, and Schrodinger's cat. Finally it is proposed to regard a state vector in quantum mechanics as an irreducible physical construct, in Margenau's sense, that is not further analyzable both mathematically and conceptually.
The possibility of consistency between the basic quantum principles and reduction (wave function reduction) is reexamined. The mathematical description of an organized macroscopic device is constructed explicitly as a convenient tool for this investigation. A derivation of reduction from quantum mechanics is proposed on a specific example, using standard methods of statistical physics. Although these methods are valid only "for all practical purposes", arguments are given to ascribe an emerging status to reduction (or the uniqueness of physical reality), similar to the status of classical physics. Examination of measurements of the particles in an EPR pair by two space-like separated apparatuses shows that the model is consistent with the non-separable character of quantum mechanics, although both measurements are local. Quantitative estimates are given.
A persistent focus on the concept of emergence as a core element of the scientific method allows a clean separation, insofar as this is possible, of the physical and philosophical aspects of the problem of outcomes in quantum mechanics. The philosophical part of the problem is to explain why a closed system has definite experimental outcomes. The physical part is to show mathematically that there exists a limit in which the contradiction between unitary Schroedinger dynamics and a reduction process leading to distinct outcomes becomes negligible according to an explicitly stated criterion, and to make this criterion as objective as possible. The physical problem is solved here by redefining the notion of a quantum state and finding a suitable measure for the change of state upon reduction. The appropriate definition of the quantum state is not as a ray or density operator in Hilbert space, but rather as an equivalence class consisting of all density operators in a given subspace, the members of which all describe the same experimental outcome. For systems containing only subsystems that are integrated with their environments, these equivalence classes can be represented mathematically by projection operators, and the resulting formalism is closely related to that used by von Neumann to study the increase of entropy predicted by the second law of thermodynamics. However, nearly isolated subsystems are reduced only indirectly, as a consequence of their interaction with integrated subsystems. The reduced states of isolated subsystems are the same conditional states used in the definition of quantum discord. The key concepts of decoherence theory can all be adapted to fit this definition of a quantum state, resulting in a unified theory capable of resolving, in principle, all aspects of the quantum measurement problem. The theory thus obtained is weakly objective but not strongly objective.
It is shown, that in addition to the evolution quantum object motion wave equation in the integral form can describe the wave function reduction as a physical process. Such description is represented for the space localization process, taking place when the space coordinate is measured, and it is shown, that collapse arises, as the result of the quantum particle and corresponding measuring instrument interaction. This physical phenomenon mathematical image looks like the instantaneous transformation of the virtual paths set to the subset, determined by the measuring process conditions, when the macroscopic changes appears in the measuring instrument.In conventional quantum mechanics such Hilbert space collapse itself corresponds to such reduction phenomenon.
The theory of measurement is reasonably interpreted without any abrupt and noncausal change of a state, namely, with no “reduction of a wave packet”, in the framework of quantum mechanics. Though a process of measurement is causal in the usual quantum-mechanical sense, it is possible to utilize the concept of the “reduction of a wave packet” without any loss of compatibility. The Stern-Gerlach experiment is put to a careful study to show that the present interpretation is consistent with experiment.