[Paper Review] Consistency in the description of quantum measurement: Quantum theory can consistently describe the use of itself

Joseph M. Renes|arXiv (Cornell University)|Jul 5, 2021

Quantum Mechanics and Applications37 references33 citations

TL;DR

The paper adds two rules to standard quantum theory to parse when dynamics count as measurements and to determine when multiple observers’ descriptions can be treated consistently, thereby resolving the Frauchiger–Renner paradox.

ABSTRACT

Recent extended formulations of the Wigner's friend thought experiment throw the measurement problem of quantum mechanics into sharper relief. Here I respond to an invitation by Renner to provide a consistent and concrete set of rules for quantum mechanics which can avoid the apparent paradox formulated by Frauchiger and Renner [Nat. Comm. 9, 3711 (2018)]. I propose a slight addition to standard textbook quantum mechanics, in the form of two rules, which avoids the paradox. The first specifies when a given quantum dynamics can be interpreted as a measurement. Potentially any dynamics can, but doing so depends on the context of other performed operations. The second requires that a joint context be used to determine whether several different dynamical evolutions can all be interpreted as measurement. The paradox is then avoided because not every participant in the Frauchiger-Renner thought experiment regards the stated dynamical descriptions of the experiment as measurements.

Motivation & Objective

• Motivate and address the measurement problem through extended formulations of Wigner’s friend and the FR paradox.
• Propose precise rules that decide when a dynamical evolution can be interpreted as a measurement.
• Introduce a context-based rule for combining multiple isometries as measurements to maintain consistency.
• Demonstrate how these rules break the paradox without abandoning unitary descriptions.
• Discuss connections to existing interpretations and approaches in quantum foundations.

Proposed method

• Formulate a parsing rule that identifies when an isometry can be understood as a POVM measurement within a given context.
• Impose a context rule requiring joint consideration of multiple isometries to ensure commuting measurement observables.
• Illustrate with examples including the quantum eraser to show how certain descriptions count as measurements only in compatible contexts.
• Apply the rules to the extended Wigner’s friend scenario to show how the paradox is avoided.
• Discuss how the rules relate to existing frameworks like consistent histories and relational/neo-Copenhagen interpretations.

Experimental results

Research questions

• RQ1 Can every dynamical evolution be interpreted as a measurement, and how does context constrain this interpretation?
• RQ2 How must multiple observers’ descriptions be combined to form a consistent set of measurements and inferences?
• RQ3 Does enforcing a joint context for several potential measurements prevent FR-like contradictions?
• RQ4 How do these rules interact with known quantum eraser phenomena and Wigner’s friend setups?
• RQ5 What are the broader interpretational implications of acknowledging context-dependent, non-absolute measurements?

Key findings

• A parsing rule permits a dynamics to be read as a measurement only if a corresponding observable with commuting post-measurement operations exists.
• A context rule requires that the set of all considered isometries parses as measurements only in the joint context, ensuring a commuting algebra of observables.
• Applying the rules to Wigner’s friend and the quantum eraser shows that certain dynamical descriptions do not count as measurements in all contexts, avoiding paradoxical inferences.
• In the extended FR scenario, Bob cannot regard certain isometries as describing his measurement in the context of Wigner’s measurement, breaking the chain of inferences that leads to the paradox.
• The approach preserves the unitary descriptions while avoiding absolute, context-free measurements, shifting the discussion toward a relational or contextual understanding.