Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pooling quantum states obtained by indirect measurements   We consider the pooling of quantum states when Alice and Bob both have one
part of a tripartite system and, on the basis of measurements on their
respective parts, each infers a quantum state for the third part S. We denote
the conditioned states which Alice and Bob assign to S by alpha and beta
respectively, while the unconditioned state of S is rho. The state assigned by
an overseer, who has all the data available to Alice and Bob, is omega. The
pooler is told only alpha, beta, and rho. We show that for certain classes of
tripartite states, this information is enough for her to reconstruct omega by
the formula omega \propto alpha rho^{-1} beta. Specifically, we identify two
classes of states for which this pooling formula works: (i) all pure states for
which the rank of rho is equal to the product of the ranks of the states of
Alice's and Bob's subsystems; (ii) all mixtures of tripartite product states
that are mutually orthogonal on S.

10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph