arXiv subjects

G. Torre

Publications and source records attributed to G. Torre.

4 recordsLinked to original sources

arXiv2025

Quantum Coherence of Topologically Frustrated Spin Chains

The study of entanglement and magic properties in topologically frustrated systems suggests that, in the thermodynamic limit, these quantities decompose into two distinct contributions. One is determined by the specific nature of the model and its Hamiltonian, and another arises from topological frustration itself, resulting in being independent of the Hamiltonian's parameters. In this work, we test the generality of this picture by investigating an additional quantum resource, namely quantum coherence, in two different models where topological frustration is induced through an appropriate choice of boundary conditions. Our findings reveal a perfect analogy between the behavior of quantum coherence and that of other quantum resources, particularly magic, providing further evidence in support of the universality of this picture and the topological nature of this source of frustration.

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arXiv2024

Magic phase transition and non-local complexity in generalized $W$ State

We employ the Stabilizer Renyi Entropy (SRE) to characterize a quantum phase transition that has so far eluded any standard description and can thus now be explained in terms of the interplay between its non-stabilizer properties and entanglement. The transition under consideration separates a region with a unique ground state from one with a degenerate ground state manifold spanned by states with finite and opposite (intensive) momenta. We show that SRE has a jump at the crossing points, while the entanglement entropy remains continuous. Moreover, by leveraging on a Clifford circuit mapping, we connect the observed jump in SRE to that occurring between standard and generalized $W$-states with finite momenta. This mapping allows us to quantify the SRE discontinuity analytically.

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arXiv2022

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.

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arXiv2022

Complexity of frustration: a new source of non-local non-stabilizerness

We advance the characterization of complexity in quantum many-body systems by examining $W$-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 $W$-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 $W$-states plus an extensive local contribution. Our work reveals that $W$-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.

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