New and improved bounds on the contextuality degree of multi-qubit configurations - Université de Technologie de Belfort-Montbeliard
Article Dans Une Revue Mathematical Structures in Computer Science Année : 2024

New and improved bounds on the contextuality degree of multi-qubit configurations

Résumé

We present algorithms and a C code to reveal quantum contextuality and evaluate the contextuality degree (a way to quantify contextuality) for a variety of point-line geometries located in binary symplectic polar spaces of small rank. With this code we were not only able to recover, in a more efficient way, all the results of a recent paper by de Boutray et al. [(2022). Journal of Physics A: Mathematical and Theoretical 55 475301], but also arrived at a bunch of new noteworthy results. The paper first describes the algorithms and the C code. Then it illustrates its power on a number of subspaces of symplectic polar spaces whose rank ranges from 2 to 7. The most interesting new results include: (i) non-contextuality of configurations whose contexts are subspaces of dimension 2 and higher, (ii) non-existence of negative subspaces of dimension 3 and higher, (iii) considerably improved bounds for the contextuality degree of both elliptic and hyperbolic quadrics for rank 4, as well as for a particular subgeometry of the three-qubit space whose contexts are the lines of this space, (iv) proof for the non-contextuality of perpsets and, last but not least, (v) contextual nature of a distinguished subgeometry of a multi-qubit doily, called a two-spread, and computation of its contextuality degree. Finally, in the three-qubit polar space we correct and improve the contextuality degree of the full configuration and also describe finite geometric configurations formed by unsatisfiable/invalid constraints for both types of quadrics as well as for the geometry whose contexts are all 315 lines of the space.
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Dates et versions

hal-04755721 , version 1 (28-10-2024)

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Axel Muller, Metod Saniga, Alain Giorgetti, Henri de Boutray, Frédéric Holweck. New and improved bounds on the contextuality degree of multi-qubit configurations. Mathematical Structures in Computer Science, 2024, 34 (4), pp.322 -343. ⟨10.1017/S0960129524000057⟩. ⟨hal-04755721⟩
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