Quantum Orlicz spaces in information geometry
Quantum Orlicz spaces in information geometry
复制标题
DOI：
10.1007/s11080-004-6626-2
复制
发表时间：
2004-12-01
影响因子：
0.8
通讯作者：
Streater, RF
中科院分区：
文献类型：
--
作者：
Streater, RF
设H-0是一个自伴算子，使得对于某个β < 1，Tre-（betaH_0）是迹类的，并且设chi（β）表示ε-有界形式的集合，即，平行于（H-0+C）X-1.2-π（H-0+C）（-1/2+ π）平行于< C for some C >0.令chi：= Span boolean OR（x）是（0，1/2\）chi（x）的元素。令M表示形式为rho（x）= e（-Ho-X-Psix，）的量子信息态流形的基础集合X是chi的元素。我们证明了如果Tr e（-Ho）= 1，1.映射Phi，Phi（X）= 1/2 Tr（e（-Ho+X）+ e（-Ho-x））-1是定义在X 2上的量子杨氏函数。由Phi定义的Orlicz空间是M在rho（o）处的切空间;其仿射结构由Amari 3的（+1）-联络定义。rho（o）的a 'hood的子集，由p附近的状态组成（这些sigma是M中服从C-1 rho（1+p）的元素）
Let H-0 be a selfadjoint opera tor such that Tre-(beta H0) is of trace class for some beta < 1, and let chi(epsilon) denote the set of epsilon-bounded forms, i.e., parallel to(H-0+C)X-1.2-epsilon(H-0+C)(-1/2+epsilon) parallel to < C for some C > 0. Let chi := Span boolean OR(epsilon is an element of(0,1/2\) chi(epsilon). Let M denote the underlying set of the quantum information manifold of states of the form rho(x) = e(-Ho-X-psi x,) X is an element of chi. We show that if Tr e(-Ho) = 1,1. the map Phi, Phi(X) = 1/2 Tr (e(-Ho+X) + e(-Ho-x))-1 is a quantum Young function defined on X2. The Orlicz space defined by Phi is the tangent space of M at rho(o); its affine structure is defined by the (+1)-connection of Amari3. The Subset of a 'hood of rho(o), consisting of p-nearby states (those sigma is an element of M obeying C-1 rho(1+p)