Probing qubit by qubit: properties of the POVM and the information/disturbance tradeoff

TL;DR

This paper investigates the properties of a specific class of qubit POVMs generated by coupling a signal qubit with a probe qubit and performing measurements, analyzing their information-disturbance tradeoff and optimality.

Contribution

It characterizes the simplest class of qubit POVMs derived from probe coupling, detailing their properties and the tradeoff between information gain and disturbance.

Findings

Typical tradeoff values are near optimal

Maximally mixed probes can achieve optimal tradeoff

Detailed analysis of POVM matrix elements

Abstract

We address the class of positive operator-valued measures (POVMs) for qubit systems that are obtained by coupling the signal qubit with a probe qubit and then performing a projective measurement on the sole probe system. These POVMs, which represent the simplest class of qubit POVMs, depends on 3+3+2=8 free parameters describing the initial preparation of the probe qubit, the Cartan representative of the unitary coupling, and the projective measurement at the output, respectively. We analyze in some details the properties of the POVM matrix elements, and investigate their values for given ranges of the free parameters. We also analyze in details the tradeoff between information and disturbance for different ranges of the free parameters, showing, among other things, that i) typical values of the tradeoff are close to optimality and ii) even using a maximally mixed probe one may achieve optimal tradeoff.