Adversarial Information Gain in Non-ideal Quantum Measurements

TL;DR

This paper investigates how noise in quantum measurement devices affects the amount of information an adversary can extract, providing conditions for compatibility and maximum information gain in non-ideal quantum measurement scenarios.

Contribution

It introduces necessary and sufficient conditions for the compatibility of non-ideal quantum instruments with noisy meters, quantifying adversarial information gain in quantum measurements.

Findings

Derived conditions for quantum instrument compatibility.

Quantified maximum adversarial information based on noise parameters.

Provided a device implementation scenario for the adversary.

Abstract

Performing a quantum measurement yields two different results: a classical outcome drawn from a probability distribution, according to Born's rule, and a quantum outcome corresponding to the post-measurement state. Quantum devices that provide both outcomes can be described through quantum instruments. In a realistic scenario, one can expect that the observer's obtained classical and quantum outcomes are non-ideal: this can be due to experimental limitations, but could also be explained by adversarial interference, that is, a second party that disturbs the device through a concealed measurement to obtain information. The second scenario can be interpreted through quantum compatibility, as it implies that both the observer's instrument and the adversary's measurement can be performed simultaneously. In this work, we show how the noise of the observer's device relates to the amount of information that the adversary can obtain. We study scenarios in which the adversary aims to acquire information on the same basis as the observer's measurement, or on a mutually unbiased basis with respect to the observer's basis. In both cases, we derive necessary and sufficient conditions for the compatibility of a single qubit non-ideal quantum instrument and a noisy meter, from which we obtain the maximum amount of information that the adversary can extract in terms of the noise parameters of the observer's instrument. Finally, we provide the device implementation from the adversary's point of view for the same basis scenario.