1206.0356 (M. Revzen)

Geometrically Underpinned Maximally Entangled States Basis    [PDF]

M. Revzen

Finite geometry is used to underpin finite, two d-dimensional particles Hilbert space, d=prime $\ne2$. Central role are allotted to states with mutual unbiased bases (MUB) labelling. Dual affine plane geometry (DAPG) points underpin single particle, MUB labelled, product states. The DAPG lines are shown to underpin maximally entangled states which form an orthonormal basis spanning the space. The relevance of mutually unbiased collective coordinate bases (MUCB) for dealing with maximally entangled states is discussed and shown to provide an economic alternative mode of study. The maximally entangled, geometrically reasoned states, provide the means to a new more transparent solution of the Mean King Problem (MKP). Brief expositions of the topics considered: MUB, DAPG, MUCB and the MKP are included rendering the paper self contained.

View original: http://arxiv.org/abs/1206.0356