Error tradeoff relation for estimating the unitary-shift parameter of a relativistic spin-1/2 particle

TL;DR

This paper explores the fundamental quantum limitations on estimating two parameters of a relativistic spin-1/2 particle, revealing that moving observers face a tradeoff preventing simultaneous precise estimation, analyzed through quantum Fisher information.

Contribution

It introduces a novel indicator to detect and evaluate the strength of the tradeoff relation in relativistic quantum parameter estimation.

Findings

Moving observers cannot estimate two parameters simultaneously.

A new indicator effectively detects and measures the tradeoff relation.

The transition from classical to quantum models affects parameter estimation capabilities.

Abstract

The purpose of this paper is to discuss the existence of a nontrivial tradeoff relation for estimating two unitary-shift parameters in a relativistic spin-1/2 system. It is shown that any moving observer cannot estimate two parameters simultaneously, even though a parametric model is classical in the rest frame. This transition from the classical model to a genuine quantum model is investigated analytically using a one-parameter family of quantum Fisher information matrices. This paper proposes to use an indicator that can not only detect the existence of a tradeoff relation but can also evaluate its strength. Based on the proposed indicator, this paper investigates the nature of the tradeoff relation in detail.