Learning entanglement breakdown as a phase transition by confusion
Quantum technologies require methods for preparing and manipulating entangled
multiparticle states. However, the problem of determining whether a given
quantum state is entangled or separable is known to be an NP-hard problem in
general, and even the task of detecting entanglement breakdown for a given
class of quantum states is difficult. In this work, we develop an approach for
revealing entanglement breakdown using a machine learning technique, which is
known as 'learning by confusion'. We consider a family of quantum states, which
is parameterized such that there is a single critical value dividing states
within this family into separate and entangled. We demonstrate the 'learning by
confusion' scheme allows us to determine the critical value. Specifically, we
study the performance of the method for the two-qubit, two-qutrit, and
two-ququart entangled state. In addition, we investigate the properties of the
local depolarization and the generalized amplitude damping channel in the
framework of the confusion scheme. Within our approach and setting the
parameterization of special trajectories, we obtain an entanglement-breakdown
'phase diagram' of a quantum channel, which indicates regions of entangled
(separable) states and the entanglement-breakdown region. Then we extend the
way of using the 'learning by confusion' scheme for recognizing whether an
arbitrary given state is entangled or separable. We show that the developed
method provides correct answers for a variety of states, including entangled
states with positive partial transpose. We also present a more practical
version of the method, which is suitable for studying entanglement breakdown in
noisy intermediate-scale quantum devices. We demonstrate its performance using
an available cloud-based IBM quantum processor.
M. A. Gavreev A. S. Mastiukova E. O. Kiktenko A. K. Fedorov