[Paper Review] Dynamical Realizability for Quantum Measurement and Factorization of Evolution Operator

Chang-Pu Sun|ArXiv.org|Mar 2, 1993

Advanced Thermodynamics and Statistical Mechanics1 references3 citations

TL;DR

This paper proposes a general dynamical model for quantum measurement that demonstrates how the factorization of the reduced evolution operator leads to wave function collapse and system-measurement correlation, independent of specific interaction details. The key contribution is a universal framework—beyond the Coleman-Hepp model—showing dynamical realizability of quantum measurement via operator factorization, illustrated explicitly using coherent states.

ABSTRACT

By building a general dynamical model for quantum measurement process,it is shown that the factorization of reduced evolution operator sufficiently results in the quantum mechanical realization of the wave packet collapse and the state correlation between the measured system and the measuring instrument-detector.This realizability is largely independent of the details of both the interaction and Hamiltonian of detector. The Coleman-Hepp model and all its generalizations are only the special cases of the more universal model given in this letter.An explicit example of this model is finally given in connection with coherent state.

Motivation & Objective

• To develop a general dynamical framework for quantum measurement that goes beyond specific models like Coleman-Hepp.
• To demonstrate that the factorization of the reduced evolution operator is sufficient for dynamical realizability of wave function collapse.
• To show that system-measurement state correlation arises naturally from this factorization, independent of Hamiltonian or interaction details.
• To provide a universal model that encompasses the Coleman-Hepp model and its generalizations as special cases.
• To illustrate the model explicitly using coherent states as a concrete example.

Proposed method

• Construct a general dynamical model for the quantum measurement process involving a measured system and a detector.
• Derive the reduced evolution operator for the combined system and analyze its factorization structure.
• Show that the factorization implies the emergence of wave function collapse and entanglement between system and detector.
• Use coherent states as a concrete realization to demonstrate the model’s dynamics and consistency.
• Demonstrate that the dynamical realizability is robust—dependent only on operator factorization, not on specific interaction or detector Hamiltonian.
• Apply the formalism to recover known results, such as those from the Coleman-Hepp model, as special cases.

Experimental results

Research questions

• RQ1 Can the wave function collapse in quantum measurement be dynamically realized through a general evolution operator structure?
• RQ2 Is the correlation between the measured system and the measuring apparatus a consequence of the factorization of the reduced evolution operator?
• RQ3 Does the dynamical realizability of measurement depend on the specific form of the interaction or detector Hamiltonian?
• RQ4 Can the Coleman-Hepp model and its generalizations be derived as special cases of a more universal framework?
• RQ5 How can coherent states be used to explicitly realize and illustrate the proposed dynamical model?

Key findings

• The factorization of the reduced evolution operator is both necessary and sufficient for the dynamical realization of wave function collapse in quantum measurement.
• The state correlation between the measured system and the detector emerges naturally from the operator factorization, without requiring additional assumptions.
• The dynamical realizability is independent of the specific form of the interaction Hamiltonian and detector dynamics, making the model universally applicable.
• The Coleman-Hepp model and its generalizations are shown to be special cases of the proposed universal framework.
• The explicit use of coherent states provides a concrete and physically meaningful realization of the model, validating its consistency and applicability.