Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposition of any quantum measurement into extremals   We design an efficient and constructive algorithm to decompose any
generalized quantum measurement into a convex combination of extremal
measurements. We show that if one allows for a classical post-processing step
only extremal rank-1 POVMs are needed. For a measurement with $N$ elements on a
$d$-dimensional space, our algorithm will decompose it into at most $(N-1)d+1$
extremals, whereas the best previously known upper bound scaled as $d^2$. Since
the decomposition is not unique, we show how to tailor our algorithm to provide
particular types of decompositions that exhibit some desired property.

32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin