Maximal Sets of Mutually Unbiased Quantum States in Dimension Six

TY - JOUR

T1 - Maximal Sets of Mutually Unbiased Quantum States in Dimension Six

AU - Brierley, Stephen

AU - Weigert, Stefan

PY - 2008/10/13

Y1 - 2008/10/13

N2 - We study sets of pure states in a Hilbert space of dimension d which are mutually unbiased (MU), that is, the squares of the moduli of their scalar products are equal to zero, one, or 1/d. These sets will be called a MU constellation, and if four MU bases were to exist for d=6, they would give rise to 35 different MU constellations. Using a numerical minimisation procedure, we are able to identify only 18 of them in spite of extensive searches. The missing MU constellations provide the strongest numerical evidence so far that no seven MU bases exist in dimension six.

AB - We study sets of pure states in a Hilbert space of dimension d which are mutually unbiased (MU), that is, the squares of the moduli of their scalar products are equal to zero, one, or 1/d. These sets will be called a MU constellation, and if four MU bases were to exist for d=6, they would give rise to 35 different MU constellations. Using a numerical minimisation procedure, we are able to identify only 18 of them in spite of extensive searches. The missing MU constellations provide the strongest numerical evidence so far that no seven MU bases exist in dimension six.

KW - Mathematical Physics

UR - http://www.scopus.com/inward/record.url?scp=54849426505&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.78.042312

DO - 10.1103/PhysRevA.78.042312

M3 - Article

SN - 1050-2947

VL - 78

JO - Physical Review A

JF - Physical Review A

IS - 4

M1 - 042312

ER -