# Environment-assisted invariance does not necessitate Born's rule for quantum measurement

## TL;DR

This paper challenges the common assumption that environment-assisted invariance (envariance) guarantees Born's rule in quantum measurement, showing that envariance alone does not ensure all measurements follow Born's rule, especially in linear models.

## Contribution

It identifies an inconsistency in envariance-based arguments and demonstrates that envariance only guarantees Born's rule for specific measurement setups, not universally.

## Key findings

- Envariance does not imply all measurements follow Born's rule.
- Linear collapse models cannot produce Born's rule.
- Constructed measurement models can yield Born's rule for specific states.

## Abstract

The argument of environment-assisted invariance (known as envariance) implying Born's rule is widely used in models for quantum measurement to reason that they must yield the correct statistics, specifically for linear models. However, it has recently been shown that linear collapse models can never give rise to Born's rule. Here, we address this apparent contradiction and point out an inconsistency in the assumptions underlying the arguments based on envariance. We use a construction in which the role of the measurement machine is made explicit and show that the presence of envariance does not imply every measurement will behave according to Born's rule. Rather, it implies that every quantum state allows a measurement machine to be constructed, which yields Born's rule when measuring that particular state. This resolves the paradox and is in agreement with the recent result of objective collapse models necessarily being non-linear.