Quantum Mechanics of Consecutive Measurements

TL;DR

This paper explores the causal structure of consecutive quantum measurements, demonstrating their equivalence to quantum Markov chains and identifying measurable differences between collapse and unitary models.

Contribution

It introduces a framework linking sequential measurements to quantum Markov chains and highlights experimentally detectable distinctions between collapse and unitary evolution.

Findings

Sequential measurements form quantum Markov chains.

Differences between collapse and unitary models are experimentally measurable.

Sequential measurements exhibit non-Markovian behavior.

Abstract

Consecutive quantum measurements performed on the same system can reveal fundamental insights into quantum theory's causal structure, and probe different aspects of the quantum measurement problem. According to the Copenhagen interpretation, measurements affect the quantum system in such a way that the quantum superposition collapses after the measurement, erasing any knowledge of the prior state. We show that a sequence of measurements in a collapse picture is equivalent to a quantum Markov chain, and that considering the unitary evolution of quantum wavefunctions interacting consecutively with more than two detectors reveals an experimentally measurable difference between a collapse and unitary picture. The non-Markovian nature of sequential measurements that we report is consistent with earlier discoveries in optimal quantum state discrimination.