[Paper Review] The quantum bit from relativity of simultaneity on an interferometer

Andrew J. P. Garner, Markus P. Müller+1 more|arXiv (Cornell University)|Dec 22, 2014

Quantum Mechanics and Applications3 citations

TL;DR

This paper investigates whether relativistic spacetime structure—specifically the relativity of simultaneity—can constrain post-quantum interference in interferometers. By requiring that detector click probabilities remain invariant under different orders of local operations on interferometer arms, the study shows that only the quantum bit (qubit) structure, represented by the Bloch sphere, is allowed, thereby uniquely selecting quantum theory from a broad class of alternatives.

ABSTRACT

Motivated by recent experimental tests, we analyze whether relativistic spacetime could in principle allow for interference patterns more general than those predicted by quantum theory. We assume that relativity of simultaneity holds, in that the order of local transformations applied on individual arms of an interferometer cannot affect any detector click probabilities. We show that within a wide range of possible alternatives to quantum theory, this singles out the quantum Bloch sphere and thus the three degrees of freedom of a quantum bit. This has consequences for experimental tests for post-quantum interference that are currently performed in the lab, if one is to avoid their behaviour only ever replicating the quantum results.

Motivation & Objective

• To determine whether relativistic spacetime structure, particularly the relativity of simultaneity, can restrict the form of interference patterns beyond quantum theory.
• To investigate whether detector click probabilities being invariant under different operation orders on interferometer arms can single out quantum theory from alternative frameworks.
• To assess the implications of this constraint for ongoing experimental tests of post-quantum interference.

Proposed method

• Assumes the relativity of simultaneity as a foundational principle: the order of local operations on interferometer arms must not affect detector click probabilities.
• Analyzes a broad class of alternative theories to quantum mechanics that could predict more general interference patterns.
• Applies the constraint of operation-order invariance to derive the structure of possible state spaces for a two-level system.
• Uses the requirement of invariance under local operation order to constrain the geometry of state space to the quantum Bloch sphere.
• Demonstrates that only the quantum bit structure satisfies the relativistic invariance condition across all considered alternatives.
• Employs a framework of operational probabilistic theories to formalize the constraints on state space and measurement outcomes.

Experimental results

Research questions

• RQ1 Can the relativity of simultaneity uniquely select the quantum bit structure from a broader class of possible theories?
• RQ2 What constraints does operation-order invariance impose on the geometry of state space in interferometric experiments?
• RQ3 Are there post-quantum interference patterns that could be experimentally distinguishable if the relativity of simultaneity were not enforced?
• RQ4 Does the invariance of detector click probabilities under local operation order uniquely recover the quantum Bloch sphere?
• RQ5 What are the implications of this result for current experimental tests of post-quantum interference?

Key findings

• The relativity of simultaneity, when applied to interferometer operations, uniquely selects the quantum bit structure as the only consistent framework among a wide class of alternatives.
• Only the quantum Bloch sphere satisfies the requirement that detector click probabilities remain invariant under different orders of local operations on interferometer arms.
• All other possible state spaces for a two-level system fail to preserve this invariance under the same conditions.
• The result implies that any experimental test of post-quantum interference must either reproduce quantum predictions or violate the relativity of simultaneity.
• The three degrees of freedom of a quantum bit emerge as the only viable configuration under the given relativistic constraint.