1302.4801 (Mordecai Waegell et al.)

Proofs of the Kochen-Specker theorem based on the N-qubit Pauli group    [PDF]

Mordecai Waegell, P. K. Aravind

We present a number of observables-based proofs of the Kochen-Specker (KS) theorem based on the N-qubit Pauli group for N >= 4, thus adding to the proofs that have been presented earlier based on the two- and three-qubit groups. These proofs have the attractive feature that they can be represented in the form of diagrams from which they are obvious by inspection. They are also irreducible, in the sense that they cannot be reduced to smaller proofs by ignoring any subset of qubits and/or observables in them. A simple algorithm is given for transforming any observables-based KS proof into a large number of projectors-based KS proofs. For any observables-based proof in which each of the O observables occurs in exactly two commuting sets and any two commuting sets have at most one observable in common, the total number of projectors-based parity proofs is given by 2^O. We introduce symbols for both the observables- and projectors-based proofs that capture their important characteristics and also help convey a feeling for the enormous variety of both these types of proofs within the Pauli group. We discuss an infinite family of observables-based proofs that applies to any number of qubits from two up, and show that its members can be used to generate projectors-based KS proofs involving only nine bases (or experimental contexts) in any dimension of the form 2^N for N >= 2. Some implications of our results are discussed.

View original: http://arxiv.org/abs/1302.4801