Conditional probabilities and collapse in quantum measurements

TL;DR

This paper demonstrates that by incorporating both system and apparatus in quantum measurement descriptions and applying conditional probabilities, one can derive the post-measurement state without relying on the traditional collapse postulate.

Contribution

It introduces a method to determine the system's state after measurement using conditional probabilities, avoiding the collapse assumption.

Findings

Derived the post-measurement state without collapse postulate

Showed the importance of including apparatus in quantum descriptions

Provided a framework for sequential measurement analysis

Abstract

We show that including both the system and the apparatus in the quantum description of the measurement process, and using the concept of conditional probabilities, it is possible to deduce the statistical operator of the system after a measurement with a given result, which gives the probability distribution for all possible consecutive measurements on the system. This statistical operator, representing the state of the system after the first measurement, is in general not the same that would be obtained using the postulate of collapse.