Parallel transport in an entangled ring

Details Parallel transport in an entangled ring Parallel transport in an entangled ring

2002-02-07

arxiv.org/abs/quant-ph/0202048v2

Physics

Quantum Physics

31 pages, no figures; v2 includes a new example of a qubit ring

Scientific paper

10.1063/1.1499207

This paper defines a notion of parallel transport in a lattice of quantum particles, such that the transformation associated with each link of the lattice is determined by the quantum state of the two particles joined by that link. We focus particularly on a one-dimensional lattice--a ring--of entangled rebits, which are binary quantum objects confined to a real state space. We consider states of the ring that maximize the correlation between nearest neighbors, and show that some correlation must be sacrificed in order to have non-trivial parallel transport around the ring. An analogy is made with lattice gauge theory, in which non-trivial parallel transport around closed loops is associated with a reduction in the probability of the field configuration. We discuss the possibility of extending our result to qubits and to higher dimensional lattices.

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