Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry and Entanglement of Two-Qubit States in the Quantum
  Probabilistic Representation   A new geometric representation of qubit and qutrit states based on
probability simplexes is used to describe the separability and entanglement
properties of density matrices of two qubits. The Peres--Horodecki positive
partial transpose (ppt)-criterion and the concurrence inequalities are
formulated as the conditions that the introduced probability distributions must
satisfy to present entanglement. A four-level system, where one or two states
are inaccessible, is considered as an example of applying the elaborated
probability approach in an explicit form. The areas of three Triadas of
Malevich's squares for entangled states of two qubits are defined through the
qutrit state, and the critical values of the sum of their areas are calculated.
We always find an interval for the sum of the square areas, which provides the
possibility for an experimental checkup of the entanglement of the system in
terms of the probabilities.

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The categories of this paper are: hep-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
2
The categories of this paper are: math
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph