[Paper Review] Qubits are not observers -- a no-go theorem

Časlav Brukner|arXiv (Cornell University)|Jul 7, 2021

Quantum Mechanics and ApplicationsPhysics and Astronomy21 references26 citations

TL;DR

The paper proves a no-go theorem in relational quantum mechanics (RQM) showing that a system’s description relative to an observer cannot amount to conventional knowledge about the observer, due to basis-dependence ambiguities in relative states.

ABSTRACT

The relational approach to quantum states asserts that the physical description of quantum systems is always relative to something or someone. In relational quantum mechanics (RQM) it is relative to other quantum systems, in the (neo-)Copenhagen interpretation of quantum theory to measurement contexts, and in QBism to the beliefs of the agents. In contrast to the other two interpretations, in RQM any interaction between two quantum systems counts as a "measurement", and the terms "observer" and "observed system" apply to arbitrary systems. We show, in the form of a no-go theorem, that in RQM the physical description of a system relative to an observer cannot represent knowledge about the observer in the conventional sense of this term. The problem lies in the ambiguity in the choice of the basis with respect to which the relative states are to be defined in RQM. In interpretations of quantum theory where observations play a fundamental role, the problem does not arise because the experimental context defines a preferred basis.

Motivation & Objective

• Clarify how relational quantum states are defined relative to another system.
• Demonstrate a consistency constraint (no-go) on interpreting observer-relative states as knowledge about the observer.
• Identify the role of a preferred basis and how it limits relational knowledge in RQM.
• Differentiate RQM from neo-Copenhagen and QBism in terms of how observations are treated.

Proposed method

• Analyze a bipartite entangled state between a system S and an observer O.
• Introduce Definite Relative State (DefRS) and Distinct Relative States (DisRS) assumptions.
• Show that, under the joint state, DefRS and DisRS lead to inconsistency due to basis dependence.
• Represent the same joint state in two different bases to reveal the preferred-basis ambiguity.
• Argue that a preferred basis (e.g., a macroscopic measurement basis) resolves the ambiguity, aligning with neo-Copenhagen/QBism.
• Conclude that RQM cannot consistently treat relational states as knowledge about the observer.

Experimental results

Research questions

• RQ1 Can a system’s relative state, as defined in RQM, be interpreted as knowledge about the observer in the conventional sense?
• RQ2 Does the freedom to choose different bases for expressing a joint system-observer state lead to inconsistencies in what the observer allegedly knows?
• RQ3 Is there a basis (preferred basis) that prevents the ambiguity and aligns RQM with other interpretations?
• RQ4 How do decoherence and macroscopic measurement contexts influence the Relational Quantum Mechanics framework?
• RQ5 What distinguishes RQM’s relational states from observer-based interpretations like neo-Copenhagen and QBism?

Key findings

• A no-go theorem shows DefRS and DisRS cannot be simultaneously valid in quantum mechanics.
• Different basis representations of the same joint state yield observer knowledge that is not orthogonal, preventing copying or unconditional use for actions.
• Without a preferred basis, RQM allows multiple, non-orthogonal observer knowledge states, undermining conventional knowledge about the observer.
• The existence of a preferred basis (as in decoherence-supported or measurement-based contexts) avoids the inconsistency, aligning with neo-Copenhagen and QBism.
• Qubits cannot play the role of observers in RQM without violating foundational assumptions about knowledge and distinguishability.