A model independent approach towards resource count and precision limits in a general measurement

TL;DR

This paper introduces a model-independent method to quantify resource count and measurement precision limits in general measurement schemes, applicable to both quantum and classical systems, based on the number of outcomes.

Contribution

It proposes a unique probability distribution that minimizes measurement error and establishes a fundamental resource bound proportional to the number of outcomes.

Findings

Measurement error scales as 1/M

Resource count R equals the number of outcomes M

Provides a universal, model-independent resource estimation method

Abstract

A formulation towards quantifying resource count used in a measurement, that is independent of the model of the measurement dynamics(Quantum/Classical), is considered. For any general measurement with $(M+1)$ discrete outcomes, it is found that there is a unique probability distribution that minimizes the measurement error, with the error scaling as $1/M$. For a measurement with a finite resource$(R)$, this absolute bound implies the resource count to be equal to the possible outcomes i.e. $R=M$. This formulation therefore provides a model independent route towards estimating resource count used in any general measurement scheme.