This Master Thesis is focused on the study of the fundamental properties that a system must
possess to be able to show synchronization in the quantum regime. In the article “Synchronizing
the Smallest Possible System”  it was claimed that quantum two-level systems are not a good
candidate, as they lack a limit cycle and cannot be seen as self-sustained oscillators, therefore the
smallest system to be a three-level system.
Our intention is to raise objections to this idea using two main arguments. First, we start ques-
tioning the definition of the limit cycle proposed in this article, as well as the premise that only
systems with a limit cycle can be synchronized. And secondly, we point out that the quantum
features observed in the article “Synchronization and Entanglement Generation” , in which the
same authors submit the spontaneous synchronization between two coupled spins s = 1 systems,
can be replicated with a pair of spin s = 1/2 systems, emphasizing the similarity between both systems.
We analyse the evolution of the spin observables using different measures of synchronization.
 Roulet and Bruder, Phys. Rev. Lett., 121, 053601 (2018)
 Roulet and Bruder, Phys. Rev. Lett., 121, 063601 (2018)
Jury: Rosa López, Miguel C. Soriano, Gian Luca Giorgi
Advisors: Gian Luca Giorgi, Roberta Zambrini
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