Data-driven criteria for quantum correlations
Mateusz Krawczyk Jarosław Pawłowski Maciej M. Maśka Katarzyna Roszak
We build a machine learning model to detect correlations in a three-qubit
system using a neural network trained in an unsupervised manner on randomly
generated states. The network is forced to recognize separable states, and
correlated states are detected as anomalies. Quite surprisingly, we find that
the proposed detector performs much better at distinguishing a weaker form of
quantum correlations, namely, the quantum discord, than entanglement. In fact,
it has a tendency to grossly overestimate the set of entangled states even at
the optimal threshold for entanglement detection, while it underestimates the
set of discordant states to a much lesser extent. In order to illustrate the
nature of states classified as quantum-correlated, we construct a diagram
containing various types of states -- entangled, as well as separable, both
discordant and non-discordant. We find that the near-zero value of the
recognition loss reproduces the shape of the non-discordant separable states
with high accuracy, especially considering the non-trivial shape of this set on
the diagram. The network architecture is designed carefully: it preserves
separability, and its output is equivariant with respect to qubit permutations.
We show that the choice of architecture is important to get the highest
detection accuracy, much better than for a baseline model that just utilizes a
partial trace operation.