Zurek's envariance derivation of Born's rule and measurement

TL;DR

This paper extends Zurek's envariance-based derivation of Born's rule from measurement scenarios to general composite quantum states, linking probability and measurement in a unified framework.

Contribution

It reinterprets Zurek's approach to derive Born's rule for arbitrary composite states and closed systems, emphasizing the interdependence of probability and measurement.

Findings

Extended Zurek's derivation to arbitrary composite states.

Linked probability and measurement concepts.

Provided a unified view of Born's rule in quantum mechanics.

Abstract

Zurek's derivation of Born's rule using envariance (invariance due to entanglement) is considered to capture the probability in full generality, but only as applied to measurement of a quantum observable. Contrariwise, textbook formulations of Born's rule begin with a pure state of a closed, undivided system. The task of this study is to show that a rearrangement of the Zurek approach is possible in which the latter is viewed as giving the probabilities for Schmidt states of an arbitrary composite state vector, and afterwards it is extended to probabilities in a closed, undivided system. This is achieved by determining simultaneously probability and measurement based on the fact that the physical meaning of probability and that of measurement are inextricably dependent on each other.