Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closed formula for the relative entropy of entanglement   The long-standing problem of finding a closed formula for the relative
entropy of entanglement (REE) for two qubits is addressed. A compact-form
solution to the inverse problem, which characterizes an entangled state for a
given closest separable state, is obtained. Analysis of the formula for a large
class of entangled states strongly suggests that a compact analytical solution
of the original problem, which corresponds to finding the closest separable
state for a given entangled state, can be given only in some special cases. A
few applications of the compact-form formula are given to show additivity of
the REE, to relate the REE with the Rains upper bound for distillable
entanglement, and to show that a Bell state does not have a unique closest
separable state.

22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an