Entanglement of observables: Quantum conditional probability approach
arXiv:2303.12393 · doi:10.1007/s10701-023-00725-7
Abstract
This paper is devoted to clarification of the notion of entanglement through decoupling it from the tensor product structure and treating as a constraint posed by probabilistic dependence of quantum observable A and B. In our framework, it is meaningless to speak about entanglement without pointing to the fixed observables A and B, so this is AB-entanglement. Dependence of quantum observables is formalized as non-coincidence of conditional probabilities. Starting with this probabilistic definition, we achieve the Hilbert space characterization of the AB-entangled states as amplitude non-factorisable states. In the tensor product case, -entanglement implies standard entanglement, but not vice verse. AB-entanglement for dichotomous observables is equivalent to their correlation. We describe the class of quantum states that are A_u B_u-entangled for a family of unitary operators (u). Finally, observables entanglement is compared with dependence of random variables in classical probability theory.
References in corpus (21)
- Bell nonlocality
- An Introduction to QBism with an Application to the Locality of Quantum Mechanics
- Quantum tensor product structures are observable-induced
- Virtual Quantum Subsystems
- Making Sense of Bell's Theorem and Quantum Nonlocality
- CHSH inequality: Quantum probabilities as classical conditional probabilities
- Getting rid of nonlocality from quantum physics
- Bohm-Bell type experiments: Classical probability approach to (no-)signaling and applications to quantum physics and psychology
- Non-Kolmogorov probability models and modified Bell's inequality
- Quantum perfect correlations
- Quantum Set Theory Extending the Standard Probabilistic Interpretation of Quantum Theory
- Quantum correlations in separable multi-mode states and in classically entangled light
- Quantum Reality and Measurement: A Quantum Logical Approach
- Two faced Janus of quantum nonlocality
- Local quasi hidden variable modelling and violations of Bell-type inequalities by a multipartite quantum state
- Entanglement and Quantum Nonlocality Demystified
- On the probabilistic description of a multipartite correlation scenario with arbitrary numbers of settings and outcomes per site
- Conditional probability framework for entanglement and its decoupling from tensor product structure
- Bell's nonlocality in a general nonsignaling case: quantitatively and conceptually
- Quantum postulate vs. quantum nonlocality: Is Devil in h?
- "Local Realism", Bell's Theorem and Quantum "Locally Realistic" Inequalities
Cited by in corpus (6)
- Contextual Measurement Model and Quantum Theory
- Quantum-like representation of neuronal networks' activity: modeling "mental entanglement"
- Entangled Probability Distributions for Center-of-Mass Tomography
- Ozawa's Intersubjectivity Theorem as justification of RQM's postulate on internally consistent descriptions
- Collective motion from quantum-inspired dynamics in visual perception
- On a certain inequality for the sum of norms and reverse uncertainty relations