arXiv subjects

S. P. Toh

Publications and source records attributed to S. P. Toh.

4 recordsLinked to original sources

arXiv2013

Kochen-Specker Sets with a Mixture of 16 Rank-1 and 14 Rank-2 Projectors for a Three-Qubit System

Kochen-Specker (KS) theorem denies the possibility for the noncontextual hidden variable theories to reproduce the predictions of quantum mechanics. A set of projection operators (projectors) and bases used to show the impossibility of noncontextual definite values assignment is named as the KS set. Since one KS set with a mixture of 16 rank-1 projectors and 14 rank-2 projectors proposed in 1995 [Kernaghan M and Peres A 1995 Phys. Lett.\ A \textbf{198} 1] for a three-qubit system, there are plenty of the same type KS sets and we propose a systematic way to produce them. We also propose a probabilistic state-dependent proof of the KS theorem that mainly focuses on the values assignment for all the rank-2 projectors.

quant-ph↗

arXiv2013

State Independent Proof of Kochen-Specker Theorem with Thirty Rank-Two Projectors

The Kochen-Specker theorem states that noncontextual hidden variable theories are incompatible with quantum mechanics. We provide a state independent proof of the Kochen-Specker theorem using the smallest number of projectors, i.e., thirty rank-2 projectors, associated with the Mermin pentagram for a three-qubit system.

quant-ph↗

arXiv2013

Kochen-Specker Sets with Thirty Rank-Two Projectors in Three-Qubit System

A simple three rules supplemented by five steps scheme is proposed to produce Kochen-Specker (KS) sets with 30 rank-2 projectors that occur twice each. The KS sets provide state-independent proof of KS theorem based on a system of three qubits. A small adjustment of the scheme enables us to manually generate a large number of KS sets with a mixture of rank-1 and rank-2 projectors.

quant-ph↗

arXiv2013

Generating the Kochen-Specker Sets with 36, 38 and 40 Rays in Three-qubit System: Three Simple Algorithms

We put forward three simple algorithms to generate Kochen-Specker sets used for parity proof of Kochen-Specker theorem in three-qubit system. These algorithms enables us to generate 320, 640 and 64 Kochen-Specket sets with 36, 38 and 40 rays, respectively. No any computer calculation is required, every step in the algorithms is determined by the method of picking the rays that repeat 4 times in the KS sets.

quant-ph↗