A real-valued framework based on Kähler space with a symplectic composition rule exactly reproduces all standard quantum mechanics predictions, including maximal CHSH violation.
Locality Implies Complex Numbers in Quantum Mechanics
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abstract
We show that the presented real-number quantum theories, compatible with the independent source assumption, require the inclusion of a nonlocal map. This means that if the independent source assumption holds, in these models, complex-number quantum theory is equivalent to a real-number quantum theory with hidden nonlocal degrees of freedom. Our results suggest that complex numbers may be indispensable for describing the process involving entanglement between two independent systems.
fields
quant-ph 2years
2026 2representative citing papers
The quotient-space real formulation of quantum mechanics is shown to be standard complex QM in real notation, not an independent real-amplitude theory, because it requires a hidden complex structure J, a superselection rule, and a balanced tensor product isomorphic to the complex tensor product.
citing papers explorer
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Quantum mechanics over real numbers fully reproduces standard quantum theory
A real-valued framework based on Kähler space with a symplectic composition rule exactly reproduces all standard quantum mechanics predictions, including maximal CHSH violation.
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Hidden Complex Structure in Quotient-Space Real Quantum Mechanics
The quotient-space real formulation of quantum mechanics is shown to be standard complex QM in real notation, not an independent real-amplitude theory, because it requires a hidden complex structure J, a superselection rule, and a balanced tensor product isomorphic to the complex tensor product.