Wigner's friend scenarios: on what to condition and how to verify the predictions

TL;DR

This paper explores the Wigner's friend thought experiment, revealing the fundamental differences in information accessible to observers and proposing a game-theoretic approach to understanding state assignment and verification.

Contribution

It introduces a symmetrical perspective on observer information in Wigner's friend scenarios and proposes a game-based framework for state verification considering all accessible information.

Findings

Observers have fundamentally different information that cannot be shared.

Objectivity of quantum states is relative to each observer's information bubble.

Conditioning on all available information allows verification of other observers' state assignments.

Abstract

Wigner's friend experiment and its modern extensions display the ambiguity of the quantum mechanical description regarding the assignment of quantum states. While the friend applies the state-update rule to the system upon observing an outcome of her measurement in a quantum system, Wigner describes the friend's measurement as a unitary evolution, resulting in an entangled state for the composite system of the friend and the system. In this respect, Wigner is often referred to as a "superobserver" who has the supreme technological ability to keep the friend's laboratory coherent. As such, it is often argued that he has the "correct" description of the state. Here we show that the situation is more symmetrical than is usually thought: there are different types of information that each of the observers has that the other fundamentally cannot have - they reside in different "bubbles" (in Calvalcanti's terminology). While this can explain why the objectivity of the state assignment is only relative to the bubble, we consider more elaborated situations in the form of a game in which the players can switch between bubbles. We find that, in certain circumstances, observers may be entitled to adopt and verify the state assignment from another bubble if they condition their predictions on \textit{all} information that is in principle available to them.