[Paper Review] Concerning Quadratic Interaction in the Quantum Cheshire Cat Experiment

W. M. Stuckey, Michael Silberstein+1 more|arXiv (Cornell University)|Oct 5, 2014

Quantum Mechanics and Applications9 references3 citations

TL;DR

This paper challenges the interpretation of the quantum Cheshire Cat experiment using neutron interferometry, demonstrating that weak values—used to claim spatial separation of a neutron and its spin—only imply such separation under linear magnetic interactions. The authors show that the presence of quadratic magnetic field interactions in the experiment invalidates the ontological inference of spatial separation, despite correct weak value measurements, because both interaction types contribute equally to neutron intensity, undermining the Cheshire Cat conclusion.

ABSTRACT

In a July 2014 Nature Communications paper, Denkmayr et al. claim to have instantiated the so-called quantum Cheshire Cat experiment using neutron interferometry. Crucial to this claim are the weak values which must imply the quantum Cheshire Cat interpretation, i.e., "the neutron and its spin are spatially separated" in their experiment. While they measured the correct weak values for the quantum Cheshire Cat interpretation, the corresponding implications do not obtain because, as we show, those weak values were measured with both a quadratic and a linear magnetic field Bz interaction. We show explicitly how those weak values imply quantum Cheshire Cat if the Bz interaction is linear and then we show how the quadratic Bz interaction destroys the quantum Cheshire Cat implications of those weak values. Since both linear and quadratic Bz interactions contribute equally to the neutron intensity in this experiment, the deviant weak value implications are unavoidable. Because weak values were used successfully to compute neutron intensities for weak Bz in this experiment, it is clearly the case that one cannot make ontological inferences from weak values without taking into account the corresponding interaction strength.

Motivation & Objective

• To assess whether the weak values reported in the Denkmayr et al. neutron interferometry experiment truly support the quantum Cheshire Cat interpretation of spatially separated neutron and spin.
• To analyze the role of both linear and quadratic magnetic field interactions (Bz) in the experimental setup and their impact on weak value interpretation.
• To demonstrate that the presence of quadratic interactions invalidates the ontological inference of spatial separation, even when weak values are correctly measured.
• To clarify that weak values alone cannot justify physical inferences without considering the strength and nature of the coupling interaction.

Proposed method

• Analytical derivation of weak values in the presence of both linear and quadratic Bz interactions in the neutron interferometer.
• Comparison of weak value predictions under purely linear vs. combined linear and quadratic interactions.
• Use of standard quantum measurement theory to model the interaction Hamiltonian and its effect on neutron intensity and weak values.
• Explicit calculation showing that quadratic interactions alter the physical interpretation of weak values, even when they match experimental intensities.
• Evaluation of the experimental data from Denkmayr et al. to determine whether the observed weak values are consistent with a Cheshire Cat interpretation under mixed interaction types.
• Application of the standard weak value formalism to show that the same weak values can arise from different interaction Hamiltonians, leading to different physical conclusions.

Experimental results

Research questions

• RQ1 Can the weak values measured in the quantum Cheshire Cat experiment be interpreted as evidence of spatial separation between a neutron and its spin?
• RQ2 How do quadratic magnetic field interactions affect the physical interpretation of weak values in neutron interferometry?
• RQ3 Why do the same weak values not lead to the same ontological conclusions when different interaction strengths (linear vs. quadratic) are present?
• RQ4 To what extent can weak values be used to infer physical properties without knowledge of the interaction Hamiltonian?

Key findings

• The weak values reported by Denkmayr et al. are correct but do not imply spatial separation of neutron and spin due to the presence of quadratic Bz interactions.
• When only linear Bz interactions are present, the weak values correctly support the quantum Cheshire Cat interpretation of separated neutron and spin.
• The quadratic interaction term contributes equally to neutron intensity as the linear term, making it impossible to disentangle their effects in the measurement.
• The coexistence of linear and quadratic interactions invalidates the ontological inference of spatial separation, even with accurate weak value measurements.
• The study demonstrates that weak values alone are insufficient for physical inference without knowledge of the interaction Hamiltonian's structure and strength.