Mutually Unbiased Bases and Semi-definite Programming

TY - JOUR

T1 - Mutually Unbiased Bases and Semi-definite Programming

AU - Brierley, Stephen

AU - Weigert, Stefan

PY - 2010/12/1

Y1 - 2010/12/1

N2 - A complex Hilbert space of dimension six supports at least three but not more than seven mutually unbiased bases. Two computer-aided analytical methods to tighten these bounds are reviewed, based on a discretization of parameter space and on Gröbner bases. A third algorithmic approach is presented: the non-existence of more than three mutually unbiased bases in composite dimensions can be decided by a global optimization method known as semidefinite programming. The method is used to confirm that the spectral matrix cannot be part of a complete set of seven mutually unbiased bases in dimension six.

AB - A complex Hilbert space of dimension six supports at least three but not more than seven mutually unbiased bases. Two computer-aided analytical methods to tighten these bounds are reviewed, based on a discretization of parameter space and on Gröbner bases. A third algorithmic approach is presented: the non-existence of more than three mutually unbiased bases in composite dimensions can be decided by a global optimization method known as semidefinite programming. The method is used to confirm that the spectral matrix cannot be part of a complete set of seven mutually unbiased bases in dimension six.

KW - Mathematical Physics

UR - http://www.scopus.com/inward/record.url?scp=79952403571&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/254/1/012008

DO - 10.1088/1742-6596/254/1/012008

M3 - Article

VL - 254

JO - J. Phys.: Conf. Ser.

JF - J. Phys.: Conf. Ser.

IS - 1

M1 - 012008

ER -