Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Detection of Symmetric Mixed Quantum States   We develop a sufficient condition for the least-squares measurement (LSM), or
the square-root measurement, to minimize the probability of a detection error
when distinguishing between a collection of mixed quantum states. Using this
condition we derive the optimal measurement for state sets with a broad class
of symmetries.
  We first consider geometrically uniform (GU) state sets with a possibly
nonabelian generating group, and show that if the generator satisfies a certain
constraint, then the LSM is optimal. In particular, for pure-state GU ensembles
the LSM is shown to be optimal. For arbitrary GU state sets we show that the
optimal measurement operators are GU with generator that can be computed very
efficiently in polynomial time, within any desired accuracy.
  We then consider compound GU (CGU) state sets which consist of subsets that
are GU. When the generators satisfy a certain constraint, the LSM is again
optimal. For arbitrary CGU state sets the optimal measurement operators are
shown to be CGU with generators that can be computed efficiently in polynomial
time.

27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio