Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effect of nonnegativity on estimation errors in one-qubit state
  tomography with finite data   We analyze the behavior of estimation errors evaluated by two loss functions,
the Hilbert-Schmidt distance and infidelity, in one-qubit state tomography with
finite data. We show numerically that there can be a large gap between the
estimation errors and those predicted by an asymptotic analysis. The origin of
this discrepancy is the existence of the boundary in the state space imposed by
the requirement that density matrices be nonnegative (positive semidefinite).
We derive an explicit form of a function reproducing the behavior of the
estimation errors with high accuracy by introducing two approximations: a
Gaussian approximation of the multinomial distributions of outcomes, and
linearizing the boundary. This function gives us an intuition for the behavior
of the expected losses for finite data sets. We show that this function can be
used to determine the amount of data necessary for the estimation to be treated
reliably with the asymptotic theory. We give an explicit expression for this
amount, which exhibits strong sensitivity to the true quantum state as well as
the choice of measurement.

5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess