[Paper Review] Local computer model emulating the results of the Pan et al. experiment

Walter Philipp, Guillaume Adenier+2 more|ArXiv.org|Dec 28, 2004

Scientific Research and Discoveries4 references3 citations

TL;DR

This paper presents a local, computer-simulated model using three independent computers (Alice, Bob, Claire) and a central Host that replicates the Pan et al. quantum optics experiment without communication between players. By using time- and setting-dependent Rademacher functions and avoiding identification of counterfactual outcomes across different measurement settings, the model reproduces quantum correlations—specifically, the product of three measurement outcomes equals +1 in the xxx setting—outperforming the original experiment and challenging the claim that local hidden variables cannot reproduce quantum results.

ABSTRACT

It is a widespread current belief that objective local models can not explain the quantum optics experiment of Pan et al. By presenting a model that operates on independent computers, we show that this belief is unfounded. Three remote computers (Alice, Bob and Claire), that never communicate with each other, send measurement results to a fourth computer that is in charge of collecting the data and computing correlations. The result obtained by our local simulation is in better agreement with the ideal quantum result than the Pan et al. experiment. We also show that the local model presented by Pan et al. that can not explain the quantum results contains inappropriate reasoning with profound consequences for the possible results of any local model that uses probability theory.

Motivation & Objective

• To challenge the widely held belief that objective local models cannot reproduce the results of the Pan et al. quantum optics experiment.
• To demonstrate that counterfactual reasoning in local models requires careful treatment of probability space assumptions.
• To show that time- and setting-dependent parameters prevent identification of outcomes across different measurement contexts.
• To construct a simulation that achieves better agreement with ideal quantum mechanics than the actual experiment.
• To highlight the flaws in the logical assumptions used in the original POLT argument, particularly the unjustified identification of random variables across different experimental runs.

Proposed method

• Three remote computers (Alice, Bob, Claire) operate independently using Rademacher functions to generate ±1 outcomes based on measurement settings (x or y).
• A fourth computer (Host) collects data unidirectionally from the three players without any communication between them.
• Each player uses only their own segment of a shared table (Table 1) defining outcomes for each setting and time, inaccessible to the Host.
• The simulation performs four sequential sequences: yyy, yxy, xyy, and xxx, with outcomes recorded per measurement time.
• The model avoids equating outcomes from different measurement runs (e.g., Y₁' ≠ Y₁'') to prevent violating Vorobev’s theorem on joint probability spaces.
• Time labels and setting-specific parameters are used to ensure that all random variables are not defined on a single probability space, preserving locality.

Experimental results

Research questions

• RQ1 Can a local, non-communicating computer model reproduce the quantum correlation results of the Pan et al. experiment?
• RQ2 Is the counterfactual reasoning used in the original POLT model logically valid when applied across different measurement settings and times?
• RQ3 Does the assumption that all random variables in a local model can be defined on a single probability space hold under relativistic constraints?
• RQ4 Can a local model achieve better agreement with ideal quantum mechanics than the actual experimental results?
• RQ5 What role do time- and setting-dependent equipment parameters play in invalidating the identification of outcomes across different experimental runs?

Key findings

• The local computer model successfully reproduces the quantum mechanical prediction that the product of three measurement outcomes in the xxx setting is +1.
• The model achieves better agreement with ideal quantum results than the actual Pan et al. experiment, particularly in the xxx correlation.
• The simulation avoids the logical flaw in the original POLT argument by not identifying outcomes from different measurement runs, thus respecting the constraints of Vorobev’s theorem.
• The model demonstrates that counterfactual reasoning leading to Eq. (3) is invalid when outcomes from different settings and times are not defined on a single probability space.
• The use of time- and setting-dependent parameters prevents the identification of random variables across experiments, preserving locality and avoiding contradictions with quantum mechanics.
• The simulation confirms that no communication between players is needed, and all data collection is unidirectional to the Host, maintaining strict locality.