Quantum Computers, Discrete Space, and Entanglement
arXiv:quant-ph/0207003
Abstract
We consider algebras underlying Hilbert spaces used by quantum information algorithms. We show how one can arrive at equations on such algebras which define n-dimensional Hilbert space subspaces which in turn can simulate quantum systems on a quantum system. In doing so we use MMP diagrams and linear algorithms. MMP diagrams are tractable since an n-block of an MMP diagram has n elements while an n-block of a standard lattice diagram has 2^n elements. An immediate test for such an approach is a generation of minimal and arbitrary Kochen-Specker vectors and we present a minimal state-independent Kochen-Specker set of seven vectors from a Hilbert space with more than four dimensions.
6 pages, RevTeX, Author's http://m3k.grad.hr/pavicic
References in corpus (15)
- Quantum computation over continuous variables
- Bell-Kochen-Specker theorem: A proof with 18 vectors
- Finite precision measurement nullifies the Kochen-Specker theorem
- A feasible "Kochen-Specker" experiment with single particles
- Proposed experimental tests of the Bell-Kochen-Specker theorem
- Non-Contextual Hidden Variables and Physical Measurements
- Kochen-Specker theorem for 8-dimensional space
- Hidden-variable theorems for real experiments
- Finite-precision measurement does not nullify the Kochen-Specker theorem
- Interferometry with Two Pairs of Spin Correlated Photons
- Spin-correlated interferometry with beam splitters: preselection of spin-correlated photons
- Spin correlated interferometry for polarized and unpolarized photons on a beam splitter
- A Kochen-Specker Theorem for Imprecisely Specified Measurement
- Kochen-Specker theorem and experimental test on hidden variables
- New variants of the Bell-Kochen-Specker theorem