Operational probability theory (OPT) provides a unified framework to study classical mechanics, quantum mechanics and any probabilistic theory. In the framework of certain OPTâ€™s of single systems, we identify various nonclassical features such as incompatibility, multiple pure-state decomposability, measurement disturbance, no-cloning and the impossibility of certain universal operations, with the non-simpliciality of the state space. This is shown to naturally suggest an underlying simplex as an ontological model. Contextuality turns out to be an independent nonclassical feature, arising from the intransitivity of compatibility.
The question concerning the physical realizability of a probability distribution is of quite importance in Quantum foundations. Specker first pointed out that this question cannot be answered from Kolmogorov's axioms alone. We study Specker's observation in the simplest scenario involving three inputs each with two outputs. Then using only linear constraints imposed on joint probabilities by this principle, we reveal unphysical nature of Garg-Mermin (GM) correlation. Our result establishes that, unlike in the CH scenario, the local orthogonality principle at single copy level is not equivalent to the no-signaling condition in the GM scenario.
1. â€œOn the origin of nonclassicality in single systemsâ€ - S. Aravinda, R. Srikanth and A. Pathak, J. Phys. A: Math. Theor. 50, 465303 (2017).
2. â€œExclusivity and the un-physicality of Garg-Mermin correlationsâ€ - S. Aravinda, A. Mukherjee, and M. Banik, Phys. Rev. A 98, 012116 (2018).
3. â€œImpossible process of non-interacting identical particlesâ€ - S. Aravinda, arXiv:1808.01820 [quant-ph]