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Partial Independence Suffices to Rule Out Real Quantum Theory Experimentally
Mirjam Weilenmann1,2, Nicolas Gisin2,3, 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.
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.
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