Effective state as compatibility between agents

TL;DR

This paper introduces a decision-theoretical approach to coarse-graining in quantum systems, providing necessary and sufficient conditions for the existence of a well-defined effective state by reinterpreting the problem through quantum state pooling.

Contribution

It offers a novel decision-theoretical framework and conditions for coarse-graining, moving beyond the traditional quantum channels perspective.

Findings

Derived necessary and sufficient conditions for effective coarse-grained states

Reinterpreted coarse-graining as quantum state pooling

Utilized conditional quantum states toolkit for tangible criteria

Abstract

Shedding a new light in the coarse-graining scenario, in this contribution we came up with different necessary and sufficient conditions for the existence of a well-defined coarse-grained state. For doing so, we had to break apart with the usual quantum channels perspective and assume a more decision-theoretical posture. Broadly speaking, we reinterpret the coarse-graining problem in the language of quantum state pooling, and by make an extensive use of the conditional quantum states toolkit we have been able to derive more tangible conditions for the emergence of a compatible, effective coarse-grained state.