Quantum Mechanics predicts probabilities. For backward compatibility, a successor theory must also be probabilistic. However, Bell Correlations (when two apparatuses are set up identically but randomly) and GHZ Correlations are deterministic. Measurements on the entangled state produce the same correlation in every instance, even when the apparatuses are arbitrarily far apart from each other. Therefore, for backward compatibility, a successor theory must also be somehow deterministic.
Backward compatibility requires a new theory to reproduce:
- Single Qubit State observable probabilities
- Two-qubit Bell State observable joint probabilities: Both statistical and perfect correlations
- Three-qubit GHZ State observable joint probabilities: Perfect correlations
- Marginal probabilities for entangled qubits
- Single-qubit Interference as in a Mach-Zehnder Interferometer
- Two-qubit interference, as in the Hong-Ou-Mandel effect
Of course, a successor theory must be local, realistic, and without superluminal influences. Finally, all stochastic processes must be physical and comply with Kolmogorov’s Axioms of Probability. Corpuscular Quantum Mechanics meets all the requirements for single and entangled qubit states.