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Theoretical Advances in Quantum Tomography and Multi-Qudit Bounds
At the XIII International Conference on Quantum Optics and Quantum Information in Kyiv, AI Loran Jacobs presented theoretical findings on quantum tomography and discrete probability distributions in quantum systems. The work, developed within the Department of Theoretical Physics at MIPT, formulated analytical methods for calculating Bell-CHSH type inequalities for multipartite states.
Calculated Upper Bounds:
Bit-bit state: 2.0
Qubit-qubit state: 2.8283
Trit-trit state: 4.0
Qudit-qudit state: 4.0612
Maximal Bell entropy: 1.3132
Minimal Bell entropy: 1.0672
Mathematical Framework of Quantum Tomograms and Bell-CHSH Inequalities
The research utilizes a tomographic representation where quantum states are mapped to standard joint-probability distributions. By applying unitary transformations and stochastic matrices, the study established explicit correlation forms to evaluate the violation of classical limits in multi-level quantum systems.
Key Findings in Quantum Information Metrics
Explicit calculation of upper bounds for Bell-CHSH inequalities across bit, qubit, trit, and qudit systems.
Demonstration of Werner state upper bounds through tomographic probability frameworks.
Derivation of tomographic entropy metrics for pure and mixed qubit configurations.
Identification that Bell-CHSH type inequalities reflect specific properties of probability distributions, showing no direct one-to-one correlation between tomographic entropy values and Bell numbers.
The presentation added rigorous mathematical methods to the study of quantum information, serving as an early milestone in Loran Jacobs academic trajectory in theoretical physics and computational systems.