Retrodiction of a sequence of measurement results in qubit interferometers

TL;DR

This paper investigates how well one can retrodict previous measurement results in qubit interferometers by analyzing the information gained from measurements on the final state, considering different measurement scenarios.

Contribution

It introduces a detailed analysis of retrodicting measurement results in qubit interferometers, including models with multiple measurements and different retrodiction objectives.

Findings

Retrodiction ranges from no information to perfect knowledge depending on system parameters.

Analysis of a specific case with two two-outcome measurements and a projective measurement.

Evaluation of retrodicting one, all, or unperformed measurement results.

Abstract

We study how well we can retrodict results of measurements made on a quantum system if we can make measurements on its final state. We know what measurements were made, but not their results. An initial examination shows that we can gain anywhere from no information to perfect information about the results of previous measurements, depending on the measurements and the initial state of the system. The case of two two-outcome measurements, the second of which is a projective measurement, is examined in some detail. We then look at a model of a qubit interferometer in which measurements are made in order to determine the path the qubit followed. The measurement made on the final state of the qubit depends on the information about previous measurement results that we are trying to determine. One can attempt to find the result of just one of the measurements, all of them, or find a measurement sequence that was not realized. We study all three possibilities.