Projective Ring Line of an Arbitrary Single Qudit

Details Projective Ring Line of an Arbitrary Single Qudit Projective Ring Line of an Arbitrary Single Qudit

2007-10-04

arxiv.org/abs/0710.0941v2

Journal of Physics A Mathematical and Theoretical 41 (2008) 015302 (12pp)

Physics

Quantum Physics

Scientific paper

10.1088/1751-8113/41/1/015302

As a continuation of our previous work (arXiv:0708.4333) an algebraic geometrical study of a single $d$-dimensional qudit is made, with $d$ being {\it any} positive integer. The study is based on an intricate relation between the symplectic module of the generalized Pauli group of the qudit and the fine structure of the projective line over the (modular) ring $\bZ_{d}$. Explicit formulae are given for both the number of generalized Pauli operators commuting with a given one and the number of points of the projective line containing the corresponding vector of $\bZ^{2}_{d}$. We find, remarkably, that a perp-set is not a set-theoretic union of the corresponding points of the associated projective line unless $d$ is a product of distinct primes. The operators are also seen to be structured into disjoint `layers' according to the degree of their representing vectors. A brief comparison with some multiple-qudit cases is made.

Affiliated with

Also associated with

No associations

Rating

Projective Ring Line of an Arbitrary Single Qudit does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Projective Ring Line of an Arbitrary Single Qudit, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Projective Ring Line of an Arbitrary Single Qudit will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-563126