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arXiv:quant-ph/0003020

Parallel and Anti-Parallel Spins: More Differences

Sibasish Ghosh A, Roy, Anirban, Ujjwal Sen

Published Mar 6, 2000• 0 citations
arXivHTMLPDF

Abstract

The authors have withdrawn this paper.
DOI
10.48550/arxiv.quant-ph/0003020

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Gisin and Popescu [PRL, 83, 432 (1999)] have shown that more information about their direction can be obtained from a pair of anti-parallel spins compared to a pair of parallel spins, where the first member of the pair (which we call the pointer member) can point equally along any direction in the Bloch sphere. They argued that this was due to the difference in dimensionality spanned by these two alphabets of states. Here we consider similar alphabets, but with the first spin restricted to a fixed small circle of the Bloch sphere. In this case, the dimensionality spanned by the anti-parallel versus parallel alphabet is now equal. However, the anti-parallel alphabet is found to still contain more information in general. We generalize this to having N parallel spins and M anti-parallel spins. When the pointer member is restricted to a small circle these alphabets again span spaces of equal dimension, yet in general, more directional information can be found for sets with smaller |N-M| for any fixed total number of spins. We find that the optimal POVMs for extracting directional information in these cases can always be expressed in terms of the Fourier basis. Our results show that dimensionality alone cannot explain the greater information content in anti-parallel combinations of spins compared to parallel combinations. In addition, we describe an LOCC protocol which extract optimal directional information when the pointer member is restricted to a small circle and a pair of parallel spins are supplied.
The authors discuss parallelization strategies for the BSS (Blankenbecler-Sugar-Scalapino) algorithm, a quantum Monte Carlo technique for treating lattice fermions. They then present results obtained by applying the BSS algorithm to the one-dimensional Kondo insulator model on both vector and parallel machines. In particular they compare Kondo insulator spin correlations with RKKY predictions, investigate the opening of a charge gap, and consider the question of long-range anti-ferromagnetic order.