Quantumness without quantumness: entanglement as classical correlations in higher dimensions

Details Quantumness without quantumness: entanglement as classical correlations in higher dimensions Quantumness without quantumness: entanglement as classical correlations in higher dimensions

2007-01-15

arxiv.org/abs/quant-ph/0701101v1

Physics

Quantum Physics

6 pages, no figures, special issue of Journal of Modern Optics in honour of Peter Knight

Scientific paper

I exploit the formal equivalence between the ground state of a $d$ dimensional quantum system and a d+1 dimensional classical Ising chain to represent quantum entanglement in terms of classical correlations only. This offers a general "local hidden variable model" for all quantum phenomena existing in one dimension lower than the (hidden variable) classical model itself. The local hidden variable model is not contradicted by the implications of Bell's theorem. Formal theory is presented first and then exemplified by the quantum Ising spin chain in a transverse magnetic field. Here I explicitely show how to derive any two site entanglement in the transverse model from the partition function of the classical Ising spin chain existing in two dimensions. Some speculations are then presented regarding possible fundamental implications of these results.

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