Relation To Spherical T-designs
A spherical t-design is a set of vectors on the d-dimensional generalized hypersphere, such that the average value of any -order polynomial over is equal to the average of over all normalized vectors . Defining as the t-fold tensor product of the Hilbert spaces, and
as the t-fold tensor product frame operator, it can be shown that a set of normalized vectors with forms a spherical t-design if and only if
It then immediately follows that every SIC-POVM is a 2-design, since
which is precisely the necessary value that satisfies the above theorem.
Read more about this topic: SIC-POVM
Famous quotes containing the words relation to and/or relation:
“Light is meaningful only in relation to darkness, and truth presupposes error. It is these mingled opposites which people our life, which make it pungent, intoxicating. We only exist in terms of this conflict, in the zone where black and white clash.”
—Louis Aragon (1897–1982)
“Only in a house where one has learnt to be lonely does one have this solicitude for things. One’s relation to them, the daily seeing or touching, begins to become love, and to lay one open to pain.”
—Elizabeth Bowen (1899–1973)