Quantum Orlicz spaces in information geometry

Details Quantum Orlicz spaces in information geometry Quantum Orlicz spaces in information geometry

2004-07-21

arxiv.org/abs/math-ph/0407046v1

Physics

Mathematical Physics

16 A4 pages; talk given at the 36 th Conf on Mathematical Physics, Torun, 2004

Scientific paper

A start is made to redefining the topology of the spaces of normal states (density operators) by a new norm which is finite only for states of finite entropy. It is shown that a symmetrized version of the free energy difference between states can be used as a quantum version of the cosh Young function used in the theory of Orlicz space. The results form a quantum version of the classical treatment of nonparametric estimation by information geometry, in the work of Pistone and Sempi. We succeed in constructing the Luxemburg norm, the tangent space carrying the (+1)-affine structure, and the cotangent space carrying the (-1) affine structure, and we demonstrate the Holder-Orlicz inequality.

Affiliated with

Also associated with

No associations

Rating

Quantum Orlicz spaces in information geometry 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 Quantum Orlicz spaces in information geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Orlicz spaces in information geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1072