5 research outputs found
Random unitaries, Robustness, and Complexity of Entanglement
It is widely accepted that the dynamic of entanglement in presence of a
generic circuit can be predicted by the knowledge of the statistical properties
of the entanglement spectrum. We tested this assumption by applying a
Metropolis-like entanglement cooling algorithm generated by different sets of
local gates, on states sharing the same statistic. We employ the ground states
of a unique model, namely the one-dimensional Ising chain with a transverse
field, but belonging to different macroscopic phases such as the paramagnetic,
the magnetically ordered, and the topological frustrated ones. Quite
surprisingly, we observe that the entanglement dynamics are strongly dependent
not just on the different sets of gates but also on the phase, indicating that
different phases can possess different types of entanglement (which we
characterize as purely local, GHZ-like, and W-state-like) with different degree
of resilience against the cooling process. Our work highlights the fact that
the knowledge of the entanglement spectrum alone is not sufficient to determine
its dynamics, thereby demonstrating its incompleteness as a characterization
tool. Moreover, it shows a subtle interplay between locality and non-local
constraints.Comment: 14 pages, 11 figures, 1 tabl
Complexity of frustration: a new source of non-local non-stabilizerness
We advance the characterization of complexity in quantum many-body systems by
examining -states embedded in a spin chain. Such states show an amount of
non-stabilizerness or "magic" (measured as the Stabilizer R\'enyi Entropy
-SRE-) that grows logarithmic with the number of qubits/spins. We focus on
systems whose Hamiltonian admits a classical point with an extensive
degeneracy. Near these points, a Clifford circuit can convert the ground state
into a -state, while in the rest of the phase to which the classic point
belongs, it is dressed with local quantum correlations. Topological frustrated
quantum spin-chains host phases with the desired phenomenology, and we show
that their ground state's SRE is the sum of that of the -states plus an
extensive local contribution. Our work reveals that -states/frustrated
ground states display a non-local degree of complexity that can be harvested as
a quantum resource and has no counterpart in GHZ states/non-frustrated systems.Comment: 8 pages, 3 figure
Devil's staircase and the absence of chaos in the dc- and ac-driven overdamped Frenkel-Kontorova model
The devils staircase structure arising from the complete mode locking of an entirely nonchaotic system, the overdamped dc+ac driven Frenkel-Kontorova model with deformable substrate potential, was observed. Even though no chaos was found, a hierarchical ordering of the Shapiro steps was made possible through the use of a previously introduced continued fraction formula. The absence of chaos, deduced here from Lyapunov exponent analyses, can be attributed to the overdamped character and the Middleton no-passing rule. A comparative analysis of a one-dimensional stack of Josephson junctions confirmed the disappearance of chaos with increasing dissipation. Other common dynamic features were also identified through this comparison. A detailed analysis of the amplitude dependence of the Shapiro steps revealed that only for the case of a purely sinusoidal substrate potential did the relative sizes of the steps follow a Farey sequence. For nonsinusoidal (deformed) potentials, the symmetry of the Stern-Brocot tree, depicting all members of particular Farey sequence, was seen to be increasingly broken, with certain steps being more prominent and their relative sizes not following the Farey rule