[Paper Review] On the ongoing experiments looking for higher-order interference: What are they really testing?

Arkady Bolotin|arXiv (Cornell University)|Nov 20, 2016

Quantum Mechanics and Applications18 references3 citations

TL;DR

This paper argues that ongoing experiments searching for higher-order interference in multi-slit setups are fundamentally testing the assumption that quantum measurements yield exactly one definite outcome. Using intuitionistic logic and exclusive disjunction (XOR) formalism, the author shows that higher-order interference terms vanish when the logical constraint of single-outcome measurements is enforced, proving that second-order interference alone is logically required by this principle—thus explaining why quantum mechanics does not exhibit higher-order interference.

ABSTRACT

The existence of higher than pairwise quantum interference in the set-up, in which there are more than two slits, is currently under experimental investigation. However, it is still unclear what the confirmation of existence of such interference would mean for quantum theory -- whether that usual quantum mechanics is merely a limiting case of some more general theory or whether that some assumption of quantum theory taken as a fundamental one does not actually hold true. The present paper tries to understand why quantum theory is limited only to a certain kind of interference.

Motivation & Objective

• To clarify what the ongoing experimental searches for higher-order interference are truly testing at a foundational level.
• To investigate why quantum mechanics only exhibits second-order interference, despite the theoretical possibility of higher-order interference in generalized probabilistic theories (GPTs).
• To determine whether the absence of higher-order interference stems from a fundamental assumption in quantum theory, particularly the definiteness of measurement outcomes.
• To propose an intuitionistic logic framework for modeling quantum interference, focusing on the logical structure of measurement outcomes.
• To demonstrate that higher-order interference terms vanish under the constraint of exactly one outcome per measurement, explaining the absence of such interference in quantum mechanics.

Proposed method

• Formalizes quantum interference using intuitionistic logic, where propositions about detection events (e.g., particle passing through a slit) are treated as logical statements with truth values.
• Applies exclusive disjunction (⊕) to represent the logical condition that exactly one of N slits is used, modeling the 'exactly one outcome' constraint.
• Uses Zhegalkin polynomials over {0,1} to express the XOR operation algebraically, enabling the decomposition of interference patterns into logical and algebraic components.
• Introduces the factor Δ_N = ∏_{i<j<k} (1 ⊕ x_i x_j x_k) to enforce the condition that exactly one outcome occurs in an N-event space.
• Derives the identity XOR_N Δ_N = Υ_N Δ_N, showing that all higher-order interference terms (I_3, I_4, etc.) vanish when the single-outcome constraint is applied.
• Reconstructs the N-slit interference pattern P_{1…N} as a linear combination of double-slit patterns P_ij and single-slit patterns P_i, proving that only second-order interference is logically necessary.

Experimental results

Research questions

• RQ1 What fundamental assumption in quantum theory is actually being tested by experiments searching for higher-order interference?
• RQ2 Why does quantum mechanics only predict second-order interference, despite the theoretical possibility of higher-order interference in generalized probabilistic theories?
• RQ3 How does the logical structure of measurement outcomes constrain the form of interference patterns in multi-slit experiments?
• RQ4 Can the absence of higher-order interference be derived from the principle that measurements yield exactly one definite outcome?
• RQ5 What is the role of intuitionistic logic and exclusive disjunction in modeling quantum interference and excluding higher-order terms?

Key findings

• The interference pattern in an N-slit experiment can be fully expressed as a linear combination of double-slit and single-slit patterns: P_{1…N} - ∑_{i<j} P_ij + (N-2)∑_i P_i = 0.
• Higher-order interference terms (I_3, I_4, etc.) vanish when the logical constraint Δ_N = 1 is applied, which enforces exactly one outcome per measurement.
• The logical structure of 'exactly one outcome'—formalized via XOR_N Δ_N—is sufficient to derive the absence of higher-order interference without invoking the Born rule directly.
• The derivation shows that the interference pattern in the N-slit experiment is entirely determined by second-order interference terms and single-slit contributions, confirming that higher-order interference is logically excluded.
• The paper concludes that ongoing experiments for higher-order interference are not testing quantum mechanics per se, but rather the foundational assumption that measurements yield definite, single outcomes.
• The result implies that the absence of higher-order interference is not due to a dynamical suppression mechanism, but a consequence of the logical consistency of the measurement postulate.