Convexity of quantum $χ^2$-divergence

Details Convexity of quantum $χ^2$-divergence Convexity of quantum $χ^2$-divergence

2011-02-15

arxiv.org/abs/1102.2989v2

Physics

Mathematical Physics

Proof clarified, typos corrected

Scientific paper

The quantum \chi^2-divergence has recently been introduced and applied to quantum channels (quantum Markov processes). In contrast to the classical setting the quantum \chi^2-divergence is not unique but depends on the choice of quantum statistics. In the reference [11] a special one-parameter family of quantum \chi^2_\alpha(\rho,\sigma)-divergences for density matrices were studied, and it was established that they are convex functions in (\rho,\sigma) for parameter values \alpha\in [0,1], thus mirroring the classical theorem for the \chi^2(p,q)-divergence for probability distributions (p,q). We prove that any quantum \chi^2-divergence is a convex function in its two arguments.

Affiliated with

Also associated with

No associations

Rating

Convexity of quantum $χ^2$-divergence 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 Convexity of quantum $χ^2$-divergence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Convexity of quantum $χ^2$-divergence will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-378011