# Underlying non-Hermitian character of the Born rule in open quantum systems

## TL;DR

This paper reveals that in open quantum systems, the Born rule's probability interpretation can be exactly expressed through non-Hermitian resonance states, highlighting an underlying non-Hermitian structure.

## Contribution

It introduces an exact analytical expansion of the Born rule probabilities in open systems using non-Hermitian resonance states, uncovering their fundamental role.

## Key findings

- Exact expansion of probabilities in terms of non-Hermitian states
- Reveals non-Hermitian structure underlying the Born rule
- Provides analytical tools for open quantum system analysis

## Abstract

The absolute value squared of the probability amplitude corresponding to the overlap of an initial state with a continuum wave solution to the Schr\"odinger equation of the problem, has the physical interpretation provided by the Born rule. Here, it is shown that for an open quantum system, the above probability may be written in an exact analytical fashion as an expansion in terms of the non-Hermitian resonance (quasinormal) states and complex poles to the problem which provides an underlying non-Hermitian character of the Born rule.