Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum logarithmic derivative bound on quantum state estimation as a
  dual of the Holevo bound   In quantum estimation theory, the Holevo bound is known as a lower bound of
weighed traces of covariances of unbiased estimators. The Holevo bound is
defined by a solution of a minimization problem, and in general, explicit
solution is not known. When the dimension of Hilbert space is two and the
number of parameters is two, a explicit form of the Holevo bound was given by
Suzuki. In this paper, we focus on a logarithmic derivative lies between the
symmetric logarithmic derivative (SLD) and the right logarithmic derivative
(RLD) parameterized by $\beta\in[0,1]$ to obtain lower bounds of weighted trace
of covariance of unbiased estimator. We introduce the maximum logarithmic
derivative bound as the maximum of bounds with respect to $\beta$. We show that
all monotone metrics induce lower bounds, and the maximum logarithmic
derivative bound is the largest bound among them. We show that the maximum
logarithmic derivative bound has explicit solution when the $d$ dimensional
model has $d+1$ dimensional $\mathcal{D}$ invariant extension of the SLD
tangent space. Furthermore, when $d=2$, we show that the maximization problem
to define the maximum logarithmic derivative bound is the Lagrangian duality of
the minimization problem to define Holevo bound, and is the same as the Holevo
bound. This explicit solution is a generalization of the solution for a two
dimensional Hilbert space given by Suzuki. We give also examples of families of
quantum states to which our theory can be applied not only for two dimensional
Hilbert spaces.

2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc