Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Informationally completed measurements: conditions, projective
  realizations, and optimalities   The physical problem behind informationally completed(IC) measurements is
determining an unknown state statistically by measurement outcomes, which is
known as state tomography. It is of central importance in quantum information
processing such as channel estimating, device testing, quantum key
distribution, etc. However, constructing such measurements with good properties
is a long standing problem. Previous constructions include completed sets of
mutually unbiased bases, which might not exist generally, as well as optimal IC
measurements, which can not be minimally projective. In this work, we
investigate IC measurements including conditions, projective realizations, and
optimalities. Although our results demonstrate the difficulty of constructing
minimal projective IC measurements(MPICM) in $C^{n}$, we present examples as
well as a general construction for even $n$, conjecture its validity for $n\geq
10$, with numerical examinations for $n\leq 100$. It might be the first general
construction of MPICM in no prime power dimensional systems. On the other hand,
a new kind of optimality, which indicates the efficiency of observables, is
investigated with an optimization scheme being presented. Finally, we
demonstrate that states in $C^n$ can be determined by a rank-one projective
measurement, which is optimal in both trace sense and frame potential sense, in
$C^{n^{2}}$. The measurement could perform better than previous ones such as
symmetric IC POVMs. Our results can be generalized to local state tomography.

19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph