Notes on the Qubit Phase Space and Discrete Symplectic Structures

Details Notes on the Qubit Phase Space and Discrete Symplectic Structures Notes on the Qubit Phase Space and Discrete Symplectic Structures

2009-06-24

arxiv.org/abs/0906.4516v1

Physics

Quantum Physics

12 pages

Scientific paper

We start from Wootter's construction of discrete phase spaces and Wigner functions for qubits and more generally for finite dimensional Hilbert spaces. We look at this framework from a non-commutative space perspective and we focus on the Moyal product and the differential calculus on the discrete phase spaces. In particular, the qubit phase space provides the simplest example of a four-point non-commutative phase space. We give an explicit expression of the Moyal bracket as a differential operator. We then compare the quantum dynamics encoded by the Moyal bracket to the classical dynamics: we show that the classical Poisson bracket does not satisfy the Jacobi identity thus leaving the Moyal bracket as the only consistent symplectic structure. We finally generalizes our analysis to Hilbert spaces of prime dimensions d and their associated d*d phase spaces.

Affiliated with

Also associated with

No associations

Rating

Notes on the Qubit Phase Space and Discrete Symplectic Structures 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 Notes on the Qubit Phase Space and Discrete Symplectic Structures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Notes on the Qubit Phase Space and Discrete Symplectic Structures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-106427