Equientangled Bases in Arbitrary Dimensions and Quadratic Gauss Sums
Abstract
Recently [Karimipour and Memarzadeh, PhysRevA 73, 012329 (2006)] posed the problem of finding a continuous family of orthonormal bases in a bipartite space of two identical systems with the following properties: i) in each basis, all states have to be equally entangled, and ii) the family continuously interpolate between the product basis and the maximally entangled basis. The authors provided a necessary condition and simple examples for relatively small dimensions, but questioned the existence of a general solution for arbitrary dimensions. Employing the properties of quadratic Gauss sums, we prove that such a family of bases exists for all dimensions and provide an explicit simple parametrization. We illustrate the behaviour of our solution with particular examples.
Cite
@article{arxiv.1003.4424,
title = {Equientangled Bases in Arbitrary Dimensions and Quadratic Gauss Sums},
author = {Vlad Gheorghiu},
journal= {arXiv preprint arXiv:1003.4424},
year = {2010}
}
Comments
This paper has been withdrawn due to the submission of a major revised version, arXiv:1004.1633 [quant-ph]. The latter provides an additional solution and contains significantly new material.