Corpus ID: 162184307

Kochen-Specker sets in four-dimensional spaces

@article{Elford2019KochenSpeckerSI,
  title={Kochen-Specker sets in four-dimensional spaces},
  author={Brandon Elford and Petr Lisonek},
  journal={arXiv: Combinatorics},
  year={2019}
}
For the first time we construct an infinite family of Kochen-Specker sets in a space of fixed dimension, namely in R^4. While most of the previous constructions of Kochen-Specker sets have been based on computer search, our construction is analytical and it comes with a short, computer-free proof. 

References

SHOWING 1-9 OF 9 REFERENCES
Kochen-Specker sets and Hadamard matrices
  • P. Lisonek
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 2019
TLDR
A new class of complex Hadamard matrices which have not been studied previously are introduced and it is shown that the recently discovered simple parity proof of the Kochen-Specker theorem is the initial member of this infinite family of parity proofs. Expand
A Proof with 18 Vectors of the Bell-Kochen-Specker Theorem
A state-independent, additive proof of the Bell-Kochen-Specker theorem with 18 four-dimensional vectors is presented. These vectors can be physically interpreted as a set of 18 propositionsExpand
Kochen-Specker set with seven contexts
The Kochen-Specker (KS) theorem is a central result in quantum theory and has applications in quantum information. Its proof requires several yes-no tests that can be grouped in contexts or subsetsExpand
Minimal complexity of Kochen-Specker sets does not scale with dimension
A Kochen-Specker (KS) set is a specific set of projectors and measurement contexts that prove the Bell-Kochen-Specker contextuality theorem. The simplest known KS sets in Hilbert space dimensionsExpand
Applying the simplest Kochen-Specker set for quantum information processing.
TLDR
An input state-independent experimental technique is reported to certify whether a set of measurements is actually accessing a preestablished quantum six-dimensional space encoded in the transverse momentum of single photons. Expand
Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets
Quantum contextuality turns out to be a necessary resource for universal quantum computation and important in the field of quantum information processing. It is therefore of interest both forExpand
On the Problem of Hidden Variables in Quantum Mechanics
The demonstrations of von Neumann and others, that quantum mechanics does not permit a hidden variable interpretation, are reconsidered. It is shown that their essential axioms are unreasonable. ItExpand
Contextuality supplies the ‘magic’ for quantum computation
TLDR
This work proves a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via ‘magic state’ distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer. Expand
P
  • Badzia̧g, J.R. Portillo, A. Cabello, Kochen-Specker set with seven contexts. Phys. Rev. A 89
  • 2014