dorsal/arxiv
View SchemaParallel transport in an entangled ring
| Authors | William K. Wootters |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0202048 |
| URL | https://arxiv.org/abs/quant-ph/0202048 |
| DOI | 10.1063/1.1499207 |
Abstract
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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"abstract": "This paper defines a notion of parallel transport in a lattice of quantum\nparticles, such that the transformation associated with each link of the\nlattice is determined by the quantum state of the two particles joined by that\nlink. We focus particularly on a one-dimensional lattice--a ring--of entangled\nrebits, which are binary quantum objects confined to a real state space. We\nconsider states of the ring that maximize the correlation between nearest\nneighbors, and show that some correlation must be sacrificed in order to have\nnon-trivial parallel transport around the ring. An analogy is made with lattice\ngauge theory, in which non-trivial parallel transport around closed loops is\nassociated with a reduction in the probability of the field configuration. We\ndiscuss the possibility of extending our result to qubits and to higher\ndimensional lattices.",
"arxiv_id": "quant-ph/0202048",
"authors": [
"William K. Wootters"
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"quant-ph"
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"doi": "10.1063/1.1499207",
"title": "Parallel transport in an entangled ring",
"url": "https://arxiv.org/abs/quant-ph/0202048"
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