Disclosing Quantum Contextuality: A Geometric Approach to N-Qubit Configurations
Résumé
In the intriguing realm of quantum physics, the concept of contextuality raises interesting questions about the nature of quantum systems. Since the commutation relation in the N-qubits Pauli group corresponds to the colinearity relation in the symplectic polar space W(2N − 1, 2), we study subgeometries of this space in order to discover new contextual quantum configurations.
We have developed algorithms and a corresponding software in C language, that can effectively determine quantum contextuality and quantify it, by charting these symplectic polar spaces of various ranks.
This tool allowed us to uncover new insights that go beyond the achievements of earlier work, such as that of de Boutray et al (J. Phys. A: Math. Theor. 55 475301, 2022). Our study spans across these geometric structures of ranks from two to seven, offering significant findings.
In my talk I will explicitly illustrate the concept of quantum contextuality on certain wellknown finite-geometric configurations living in W(5,2), like the doily (and its two-spread), an elliptic quadric (and its spread of lines) and a hyperbolic quadric (and its associated Heawood
graph); I will also consider configurations whose contexts are all the subspaces with a given dimension k < N.
Origine : Fichiers produits par l'(les) auteur(s)