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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

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Partial Independence Suffices to Rule Out Real Quantum Theory Experimentally.

Mirjam Weilenmann^1,2, Nicolas Gisin^2,3, Pavel Sekatski²

¹Institut Polytechnique de Paris, LTCI, Télécom Paris, Inria, -, 91120 Palaiseau, France.

Physical Review Letters

|November 17, 2025

Summary

Complex Hilbert spaces may not be essential for quantum experiments. This study shows partial source independence is enough to prove Real Quantum Theory inadequate, revealing a tradeoff between independence and Bell values.

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Area of Science:

Foundational Quantum Physics
Quantum Information Theory
Quantum Foundations

Background:

Quantum theory traditionally relies on complex Hilbert spaces, raising questions about the necessity of complex numbers.
Previous work demonstrated that complex quantum theory's predictions are unavoidable in network scenarios with independent sources.
The inadequacy of Real Quantum Theory was shown under strict independence assumptions.

Purpose of the Study:

To investigate if partial source independence is sufficient to demonstrate the limitations of Real Quantum Theory.
To explore the relationship between source independence and achievable Bell values in Real Quantum Theory.
To determine the entanglement requirements for simulating complex quantum correlations within a real quantum framework.

Main Methods:

Revisiting and relaxing the independence assumption from previous studies.
Deriving a tradeoff relation between source independence and Bell values in Real Quantum Theory.
Analyzing entanglement requirements for simulating complex quantum correlations using real quantum systems.

Main Results:

Partial source independence is sufficient to demonstrate the inadequacy of Real Quantum Theory.
A tradeoff is established between source independence and the Bell value in Real Quantum Theory.
One bit of real-valued entanglement is shown to be necessary and sufficient for recovering complex quantum correlations in a specific scenario.
A construction is provided to simulate complex quantum setups with 'm' independent sources using 'm' real-qubit entangled states.

Conclusions:

The necessity of complex Hilbert spaces in quantum theory can be demonstrated even with relaxed independence assumptions.
Real Quantum Theory faces limitations that can be quantified by a tradeoff involving source independence and Bell inequalities.
Entanglement, specifically real-valued entanglement, plays a crucial role in bridging the gap between real and complex quantum descriptions.