Probability and Entanglement in Quantum Mechanics

Stephan Hartmann, Patrick Suppes

Vladimir N. Chernega, Olga V. Man’ko, Vladimir I. Man’ko

Concept of entangled probability distribution of several random variables is introduced. These probability distributions describe multimode quantum states in probability representation of quantum mechanics. Example of entangled probability distribution is considered.

F.J. Duarte, T S Taylor

Jincheng Zhang

Quantum entanglement, a peculiar phenomenon where two or more particles become linked in such a way that they share the same fate, is a cornerstone of quantum mechanics. This paper explores the potential of leveraging this entanglement to revolutionize probability theory, proposing a formalization of probability based on quantum entanglement as a fundamental building block. We aim to develop a set of operators representing entanglement, enabling precise calculation of probabilities and correlations within quantum systems. The core claim is that this framework offers a deeper and more rigorous understanding of randomness and uncertainty inherent in quantum mechanics.

Vladimir N. Chernega, Olga V. Man’ko, Vladimir I. Man’ko

The superposition states of two qubits including entangled Bell states are considered in the probability representation of quantum mechanics. The superposition principle formulated in terms of the nonlinear addition rule of the state density matrices is formulated as a nonlinear addition rule of the probability distributions describing the qubit states. The generalization of the entanglement properties to the case of superposition of two-mode oscillator states is discussed using the probability representation of quantum states.