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

• URL: http://arxiv.org/abs/2308.00669v2
• Date: Tue, 5 Dec 2023 02:44:55 GMT
• Title: Error tradeoff relation for estimating the unitary-shift parameter of a relativistic spin-1/2 particle
• Authors: Shin Funada, Jun Suzuki
• Abstract summary: 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.
• Score: 20.44391436043906
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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