Optimal discrimination between real and complex quantum theories

Abstract

We find the minimal number of settings to test quantum theory based on real numbers, assuming separability of the sources, modifying the recent proposal [M.-O. Renou et al., Nature 600, 625 (2021)]. The test needs only three settings for observers $A$ and $C$, but the ratio of complex to real maximum is smaller than in the existing proposal. We also found that two settings and two outcomes for both observes are insufficient.

arXiv comment7 pages, 4 figures, MATLAB script in anciliary files

References in corpus (22)

• Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
• Significant-loophole-free test of Bell's theorem with entangled photons
• A strong loophole-free test of local realism
• Separability criterion and inseparable mixed states with positive partial transposition
• On the reality of the quantum state
• Unextendible Product Bases and Bound Entanglement
• Direct Measurement of the Quantum Wavefunction
• Event-Ready Bell Test Using Entangled Atoms Simultaneously Closing Detection and Locality Loopholes
• Quantum theory based on real numbers can be experimentally falsified
• Operational Resource Theory of Imaginarity
• Maximal violation of the I3322 inequality using infinite dimensional quantum systems
• Optimal randomness certification from one entangled bit
• Convergent relaxations of polynomial optimization problems with non-commuting variables
• Testing real quantum theory in an optical quantum network
• Ruling out real-valued standard formalism of quantum theory
• Construction of quantum states with bound entanglement
• Simulating quantum systems using real Hilbert spaces
• Entanglement 25 years after Quantum Teleportation: testing joint measurements in quantum networks
• Self-testing of Pauli observables for device-independent entanglement certification
• Efficiency of higher dimensional Hilbert spaces for the violation of Bell inequalities
• The Platonic solids and fundamental tests of quantum mechanics
• Second-second moments and two observers testing quantum nonlocality

Cited by in corpus (1)

• Resource Theory of Imaginarity: New Distributed Scenarios