Recasting Schrödinger's Cat Thought Experiment as a Remote Measurement Problem

TL;DR

This paper reframes Schrödinger's cat within the Conditional States Approach (CSA), treating quantum theory as a Bayesian generalization of classical probability and modeling the setup as a remote measurement between two spatially separated agents. By mapping CPTP maps to conditional states via the Jamiołkowski isomorphism and employing the star-product, it derives the joint and conditional states that describe how Bob's box measurements update Alice's cat state through quantum Bayesian inversion. The key contribution is an explicit construction of the conditional state $\rho_{A|Y}$ and a concrete measurement protocol that shows how Bob's observed outcome determines whether the cat is dead or alive in Alice's lab, highlighting the subjective, agent-centric nature of quantum state assignments. The work offers an educational, technically explicit perspective on quantum foundations, illustrating how a classic thought experiment can illuminate Bayesian inference in quantum theory and its interpretation within the CSA framework.

Abstract

With 2025 being declared the Year of Quantum Science and Technology, our contribution seeks to provide a fresh perspective on Schrödinger's cat thought experiment. We reinterpret this experiment by viewing it through the lens of quantum theory as a generalisation of classical probability, rooted in a Bayesian subjectivist framework. In this revised approach, we treat the experiment as a remote measurement problem. Specifically, we explore how the beliefs of two agents, Alice and Bob, who are spatially separated yet share a quantum state, are updated when local measurements are conducted on their respective systems. Through this reinterpretation of the well-known experiment, we also aim to offer an educational perspective that will be beneficial for young scientists interested in the field of quantum theory.

Figures (3)

• Figure 1: A not-so-fine work of art representing the original setup of Schrödinger's cat thought experiment. Taking a cross-section of the hermetically sealed box, we can see the representation of the "diabolical device" consisting of the Geiger counter, the poison, the hammer, and the radioactive atom. Also represented are the two possible states of the cat: alive and dead.
• Figure 2: Diagrammatic representation of the recasting of Schrödinger's cat. Alice, located in region $A$, is in the presence of the cat, which was allowed to interact with the box for a limited time. The box is in region $B$, where Bob resides and can perform selected measurements on it. The dashed line between regions $A$ and $B$ indicates that they are spatially separated, while the continuous arrow from region $B$ to region $Y$ represents the measurement process that Bob can perform over the box and therefore, we have the same region at two different instants of time.
• Figure 3: Diagrammatic representation of the recasting with the conditional states used to seek for our solution. In the lower part of the diagram we have the joint conditional state $\rho_{AB}$ between the regions of Alice and Bob and their associated conditional state $\rho_{B|A}$ obtained through the quantum rule for joint/conditional states. In the vertical branch of the diagram, we have the measurement process represented by the hybrid conditional state $\varrho_{Y|B}$.

Theorems & Definitions (6)

• definition 1: Jamioł kowski Isomorphism
• proposition 2
• definition 3: $\star-$Product
• proposition 4
• proof
• proof