Quantum theory based on real numbers can be experimentally falsified

Area of Science:

• Quantum Physics
• Foundations of Quantum Mechanics
• Mathematical Physics

Background:

• Physical experiments are typically described using probabilities and real numbers.
• Quantum theory, uniquely, is formulated using complex Hilbert spaces, a departure from other physical theories.
• A 'real quantum theory' using real operators has been shown to reproduce outcomes for experiments with shared real quantum states.

Purpose of the Study:

• To investigate the necessity of complex numbers within the quantum mechanical formalism.
• To determine if complex numbers are fundamentally required for quantum theory.
• To differentiate between real and complex formulations of quantum theory through experimental predictions.

Main Methods:

• Theoretical analysis comparing real and complex Hilbert-space formulations of quantum mechanics.
• Devising a Bell-like experiment to distinguish between the two formulations.
• Investigating predictions in network scenarios with independent states and measurements.

Main Results:

• Real and complex Hilbert-space formulations of quantum theory yield different predictions in specific network scenarios.
• A Bell-like experiment is proposed to experimentally test these differing predictions.
• The study demonstrates that complex numbers are indeed necessary for the quantum formalism.

Conclusions:

• Complex numbers are not merely a mathematical convenience but are essential for the predictive power of quantum theory.
• The proposed experiment can serve as a crucial test to falsify real quantum theory.
• This work clarifies the fundamental role of complex numbers in quantum mechanics, akin to how Bell experiments clarified locality.