Beyond the Box: Rethinking Schrödinger’s Cat

Author: Denis Avetisyan

A new analysis reframes the famous thought experiment as a problem of remote measurement, focusing on how observations of entangled systems update our understanding of quantum states.

This work recasts Schrödinger’s cat as a remote measurement problem within a Bayesian framework, leveraging conditional states and entanglement to model belief updates.

The enduring paradox of Schrödinger’s cat highlights the challenges of interpreting quantum measurement within classical frameworks. This paper, ‘Recasting Schrödinger’s Cat Thought Experiment as a Remote Measurement Problem’, offers a novel perspective by reframing the thought experiment as a scenario of spatially separated observers updating their beliefs about an entangled system. Through a Bayesian approach, we demonstrate how local measurements by these observers-Alice and Bob-effectively constitute a remote measurement, revealing the evolution of conditional states. Could this reinterpretation offer a more intuitive pathway for understanding quantum mechanics and its implications for quantum information science?

The Elegance of Indeterminacy

Despite its extraordinary predictive power, quantum mechanics grapples with fundamental conceptual difficulties, most notably the measurement problem. This challenge centers on the perplexing relationship between observation and reality, questioning how the act of measuring a quantum system forces it to ‘choose’ a definite state from a superposition of possibilities. Prior to measurement, a quantum entity exists in a probabilistic haze, described by a wave function; however, the precise moment observation occurs seems to collapse this wave function, yielding a single, concrete outcome. This isn’t simply a matter of lacking information; rather, the theory itself doesn’t fully explain how this transition from probabilistic potentiality to definite actuality arises. The core of the issue isn’t whether predictions are accurate, but whether the theory adequately describes what is happening to the system during measurement, prompting ongoing debate about the nature of reality itself and the role of the observer within it.

The famous Schrödinger’s Cat thought experiment, traditionally framed as a paradox of quantum superposition, receives a novel interpretation in this work as a problem of remote measurement. Rather than focusing on the cat being simultaneously alive and dead until observed, the analysis centers on the possibility of acquiring information about the system – the cat’s state – without any direct physical interaction. This reframing suggests that the challenge isn’t necessarily the indeterminacy of the quantum state itself, but the act of gaining knowledge about it from a distance. By considering measurement as an informational process decoupled from physical intervention, the study proposes a new lens through which to examine the measurement problem, potentially sidestepping long-held assumptions about the role of the observer and offering a pathway towards resolving the foundational ambiguities within quantum mechanics. The implications extend beyond the thought experiment, suggesting that many quantum phenomena might be better understood as consequences of information transfer rather than inherent indeterminacy.

This work fundamentally reconsiders the quantum measurement problem not as a consequence of inherent indeterminacy within the system itself, but as a challenge rooted in the acquisition of information. By shifting the emphasis from what is being measured to how information about the system is obtained, researchers propose a new framework for understanding quantum reality. This approach suggests that the act of measurement isn’t about collapsing a wave function representing all possibilities, but rather a process of extracting specific information that was always present, albeit inaccessible. Consequently, this reframing opens entirely new avenues of investigation, encouraging exploration of the role of information theory, signal processing, and even the limits of computation in defining the boundary between the quantum and classical realms. The implications extend beyond foundational physics, potentially informing advancements in quantum technologies and our understanding of the nature of information itself.

The Language of Correlation

A quantum joint state mathematically describes the combined state of two or more quantum systems, moving beyond individual system descriptions to capture correlations. Represented as a vector in a combined Hilbert space – the tensor product of the individual system Hilbert spaces – a joint state, denoted as $|\psi\rangle_{AB}$, specifies the probabilities of measuring different outcomes when both systems A and B are measured. The formalism allows for the quantification of correlations; if the joint state cannot be factored into a product of individual system states, $|\psi\rangle_{AB} \neq |\psi\rangle_A \otimes |\psi\rangle_B$, it indicates the presence of entanglement, a non-classical correlation crucial for quantum technologies. The density matrix, $\rho_{AB}$, fully characterizes the joint state, including mixed states which represent probabilistic ensembles of pure states.

Quantum conditional states describe the state of a quantum system A given a specific measurement outcome on another system B. Mathematically, if a joint state $ \rho_{AB} $ exists for systems A and B, and a measurement is performed on system B yielding outcome ‘i’, the conditional state of A is given by $ \rho_{A|i} = \text{Tr}_B(\Pi_i \rho_{AB}) $, where $ \Pi_i $ is the projector onto the outcome ‘i’ of the measurement on B, and $ \text{Tr}_B $ denotes the partial trace over system B. This process effectively reduces the combined system’s description to a state solely representing system A, reflecting the information gained from the measurement on B. The resulting conditional state is not necessarily pure, and its properties depend on the initial joint state $ \rho_{AB} $ and the measurement performed on system B.

Bell states, represented by the four maximally entangled states $ \left| \Phi^+ \right\rangle = \frac{1}{\sqrt{2}} \left( \left| 00 \right\rangle + \left| 11 \right\rangle \right)$, $ \left| \Phi^- \right\rangle = \frac{1}{\sqrt{2}} \left( \left| 00 \right\rangle – \left| 11 \right\rangle \right)$, $ \left| \Psi^+ \right\rangle = \frac{1}{\sqrt{2}} \left( \left| 01 \right\rangle + \left| 10 \right\rangle \right)$, and $ \left| \Psi^- \right\rangle = \frac{1}{\sqrt{2}} \left( \left| 01 \right\rangle – \left| 10 \right\rangle \right)$, demonstrate complete correlation between two qubits. These states are critical resources for quantum information protocols, including quantum teleportation, superdense coding, and entanglement-based quantum key distribution. The maximal entanglement inherent in Bell states ensures that measurement on one qubit instantaneously determines the state of the other, regardless of the physical distance separating them, forming the basis for these applications.

Belief as the Foundation

The Bayesian Inversion Rule, central to Quantum Bayesian Inference, mathematically describes how prior probabilities regarding a quantum system’s state are updated following a measurement. Specifically, if $P(\rho)$ represents the initial probability of the system being in state $\rho$, and $P(x| \rho)$ is the probability of obtaining measurement outcome $x$ given the state $\rho$, then the posterior probability $P(\rho|x)$ – the probability of the system being in state $\rho$ given the observed outcome $x$ – is calculated using Bayes’ Theorem as $P(\rho|x) \propto P(x|\rho)P(\rho)$. This rule effectively allows for a consistent reassessment of belief in the system’s state based on empirical evidence, moving from a prior probability distribution to a posterior distribution that reflects the information gained from the measurement.

Quantum Bayesian Inference (QBI) reinterprets the conventional understanding of quantum states. Rather than representing objective, inherent properties of a physical system, QBI posits that quantum states, described mathematically as vectors in Hilbert space, function as subjective degrees of belief held by an agent about the possible outcomes of measurements. This perspective fundamentally shifts the ontological status of the wavefunction, viewing it as an expression of knowledge rather than a direct representation of reality. Consequently, the probabilities derived from the wavefunction reflect the agent’s confidence in specific measurement results, and updates to these probabilities occur via Bayesian conditioning as measurement data becomes available. This approach necessitates a probabilistic framework where quantum mechanics describes what an agent knows about a system, not the system itself.

The evolution of probabilistic beliefs within the Quantum Bayesian Inference framework is governed by Completely Positive Trace-Preserving (CPTP) maps, which mathematically describe the physical processes acting on the quantum system. These maps, represented as superoperators, transform the initial probability distribution – typically a density operator $ \rho $ – into a new distribution reflecting the outcome of a physical interaction. Specifically, a CPTP map $\mathcal{E}$ acts on $ \rho $ to produce a new density operator $ \mathcal{E}(\rho)$, ensuring that the transformed state remains valid – that is, it is positive semi-definite and has a trace of 1. The properties of the CPTP map thus dictate how probabilities are updated based on the physical process, formalizing the Bayesian update rule within the quantum context.

The Observer’s Universe

The conventional portrayal of quantum mechanics often prioritizes an objective, observer-independent reality, but an agent-centric perspective fundamentally shifts this focus. This approach posits that a quantum system’s properties aren’t definitively determined until viewed through the lens of an agent – an entity possessing beliefs about the system. It’s not simply that observation collapses the wave function, but rather that the agent’s pre-existing beliefs, combined with the measurement outcome, actively shape the perceived state of the system. Consequently, different agents, holding differing prior beliefs, could legitimately assign different probabilities to the same quantum event, highlighting the subjective nature of quantum reality. This isn’t to suggest a relativistic free-for-all, but that the agent’s informational state is crucial; the quantum world, from this viewpoint, is understood not as a set of ‘things’ but as a landscape of possibilities conditioned by who – or what – is asking the question and what they already believe to be true.

This work introduces the Conditional States Approach, a novel framework for interpreting quantum theory that moves away from purely objective descriptions of reality. Rather than assigning inherent properties to quantum systems, this approach posits that a system’s state is defined by an agent’s beliefs and the probabilities they assign to potential measurement outcomes. This isn’t simply a matter of epistemic uncertainty; the framework demonstrates how these probabilities are updated dynamically as the agent gains information through measurement, effectively personalizing the quantum state. Consequently, the observed quantum reality isn’t a fixed entity, but a subjective assignment of probabilities conditioned on the agent’s knowledge and beliefs, offering a compelling agent-centric perspective on the foundations of quantum mechanics and challenging traditional interpretations of $ \Psi $ as an objective physical state.

Quantum mechanics traditionally portrays reality as an objective system evolving independently of observation. However, a shift in focus toward how an agent’s beliefs are updated during measurement reveals a fundamentally different picture. This approach doesn’t deny the existence of a physical reality, but rather frames its description through the lens of subjective probability assignments. Each measurement isn’t simply revealing a pre-existing value, but actively revising an agent’s understanding of the system’s state, effectively collapsing the wave function from the perspective of that agent. Consequently, quantum reality isn’t a fixed entity ‘out there,’ but a continually refined internal model constructed by the observer. This nuanced view allows for a richer interpretation of quantum phenomena, moving beyond purely objective descriptions to embrace the inherent role of belief and information in shaping our understanding of the universe.

Formalizing the Quantum Dance

Quantum mechanics posits that the act of measurement fundamentally alters a system’s state, a process rigorously described by mathematical objects called Completely Positive Trace-Preserving (CPTP) maps. These maps don’t simply describe evolution; they define how quantum states transform during interaction, acting as a complete prescription for the measurement process. A CPTP map takes an initial density matrix, $ \rho $, representing the quantum state, and outputs a new density matrix representing the state after the measurement. Crucially, these maps ensure that probabilities remain positive and the total probability is conserved, adhering to the fundamental tenets of quantum theory. Understanding CPTP maps is therefore essential for modeling any quantum interaction, from the simplest observation of a particle’s spin to the complex dynamics within quantum computers, offering a precise mathematical language for describing how information is extracted from the quantum realm.

Within the mathematical formalism of quantum mechanics, predicting measurement outcomes isn’t about definite results, but rather probabilities. Positive Operator-Valued Measures, or POVMs, provide the crucial tools for calculating these probabilities. Unlike traditional projective measurements, POVMs allow for a more general description of measurement processes, accommodating situations where information is partially obtained or the measurement process itself disturbs the quantum system. Essentially, a POVM assigns a positive operator to each possible outcome of a measurement; the trace of this operator acting on the quantum state gives the probability of observing that particular outcome. This framework extends beyond simple yes/no questions, enabling the calculation of probabilities for a continuous range of measurement results and providing a complete probabilistic description of any quantum measurement, even those that don’t neatly fit into the framework of traditional quantum mechanics.

The famed thought experiment of Schrödinger’s cat is reinterpreted as a problem of remote quantum measurement within this work, utilizing the tools of Bayesian probability. Rather than focusing on superposition as a paradox of macroscopic objects, the analysis frames the situation as an observer updating their beliefs about a system based on measurements performed on a correlated, spatially separated component. This approach employs ‘conditional states’ to mathematically describe how the observer’s knowledge evolves-essentially, the probability of the cat being alive or dead is not determined until a measurement is made on the entangled system, and this probability is updated according to Bayesian inference. The study demonstrates that the cat’s state remains indefinite not due to inherent quantum weirdness, but because the observer’s information is incomplete until a correlated measurement resolves the uncertainty, offering a novel perspective on the measurement problem and the role of observation in quantum mechanics.

The study meticulously reframes the Schrödinger’s cat paradox, shifting focus from the cat’s ambiguous state to the observer’s evolving knowledge. This approach, grounded in Bayesian inference and remote measurement, highlights that reality isn’t a fixed entity but a continually updated probability. It echoes the sentiment expressed by Louis de Broglie: “It is in the interplay between the wave and the particle that we find the true nature of reality.” The paper demonstrates this interplay by showing how measurement on an entangled system-a remote observation-collapses the wave function and defines the observed state, aligning with de Broglie’s insight into the fundamental duality at the heart of quantum mechanics. The reduction of complexity through conditional states offers clarity, revealing the information inherent in entanglement.

Where Does This Leave Us?

The exercise of framing Schrödinger’s cat as a remote measurement problem, while conceptually neat, does not, predictably, dissolve the core difficulty. It merely relocates it. The Bayesian accounting offers a precise method for updating beliefs, but the initial assignment of probabilities remains stubbornly subjective. One is left to wonder if the true obstacle isn’t a lack of mathematical rigor, but a fundamental inability to relinquish the notion of objective reality – a ghost haunting the formalism.

Future work will likely focus on refining the connection between Bayesian inference and the physical processes governing decoherence. However, a more radical approach might prove fruitful. Perhaps the persistent discomfort arises from insisting on a single, complete description. Could it be that the quantum state is not a ‘thing’ to be known, but a relational construct, valid only within a specific frame of reference?

Ultimately, the continued dissection of this thought experiment serves not to unveil a definitive answer, but to expose the limits of current understanding. If one cannot explain, simply, what constitutes ‘measurement’, further complication – be it in the form of Bayesian updates or entangled auxiliaries – offers little solace. The problem isn’t complexity; it’s a misplaced faith in it.

Original article: https://arxiv.org/pdf/2512.17991.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/