Jovan Odavić

We study quantitatively the interplay between entanglement and non-stabilizer resources in violating the CHSH inequalities. We show that, while non-stabilizer resources are necessary, they must have a specific structure, namely they need to be both asymmetric and (surprisingly) local . We employ stabilizer entropy (SE) to quantify the non-stabilizer resources involved and the probability of violation given the resources. We show how spectral quantities related to the flatness of entanglement spectrum and its relationship with non-local SE affect the CHSH inequality. Finally, we utilize these results – together with tools from representation theory – to construct a systematic way of building ensembles of states with higher probability of violation.

It is well known that the spectral form factor (SFF) of a possibly degenerate many-body Hamiltonian can be identified with a planar random walk taking steps of unequal length. In this paper we push this identification further and propose to study the chaotic content of a Hamiltonian H via its associated random walk seen as a fractal, using the tools of fractal geometry. In particular, we conjecture that for chaotic Hamiltonians the Hausdorff dimension of the frontier of the corresponding random walk approaches the universal value d_{F}=4/3-the same value obtained when the random walk describes a Wiener process. Our numerical simulations for nonintegrable models confirm this expectation while for quasifree integrable models we obtain a value d_{F}=1. Additionally, we numerically show that "Bethe-Ansatz walkers" fall into a category similar to the nonintegrable walkers. To motivate this conjecture we consider many-body Hamiltonians with degenerate but rationally independent eigenvalues. We prove that if the degeneracies satisfy certain Lyapunov conditions, the random walk becomes a Wiener process, d_{F}=4/3, and the distribution of the SFF becomes Gaussian. This is the familiar Gaussian approximation for the SFF which we show to be violated at very low temperature. We also compute the moments of the SFF exactly under milder hypotheses thus solving the classical problem of determining the moments of a random walker taking steps of unequal lengths. Finally, we consider quasifree Fermionic models with possibly degenerate but rationally independent one-particle spectra. We show that in this case the distribution of the SFF becomes lognormal and also give the exact form of the moments under milder hypotheses.

In trajectory surface hopping (TSH) simulations, initial conditions are typically generated using harmonic Wigner distributions, which assume independent harmonic normal modes. While this assumption fails for anharmonic systems, it remains unclear under which conditions harmonic Wigner sampling becomes unreliable in photochemical simulations and whether anharmonicity alone is a sufficient criterion for reconsidering the use of harmonic Wigner sampling. In the present study, we introduce a sampling strategy based on vibrational self-consistent field (VSCF) theory to construct a VSCF Wigner quasiprobability distribution that incorporates anharmonic effects while retaining mode separability. Analytical expressions are derived in both harmonic and distributed Gaussian bases, enabling the implementation in TSH simulations. The method is applied to malonaldehyde and methyl hydroperoxide, which exhibit moderate and strong anharmonicity, respectively. For malonaldehyde, VSCF-based Wigner sampling and harmonic Wigner sampling yield similar results, indicating that harmonic Wigner sampling remains reliable despite the anharmonicity. In methyl hydroperoxide, where torsional motion significantly influences the excited-state character, VSCF Wigner sampling yields results comparable to those of the quantum thermostat approach while offering a computationally efficient and systematically improvable route to initial-condition sampling.

Magic is a non-classical resource whose efficient manipulation is fundamental to advancing efficient and scalable fault-tolerant quantum computing. Quantum advantage is possible only if both magic and entanglement are present. Of particular interest is non-local magic- the fraction of the resource that cannot be distilled (or erased) by local unitary operations - which is a necessary feature for quantum complex behavior. We perform the first experimental demonstration of non-local magic in a superconducting Quantum Processing Unit (QPU). Direct access to the QPU device enables us to identify and characterize the dominant noise mechanisms intrinsic to the quantum hardware. We observe excellent agreement between theory and experiment without the need for any free parameter in the noise modeling of our system and shows the experimental capability of harnessing both local and non-local magic resources separately, thereby offering a promising path towards more reliable pre-fault-tolerant quantum devices and to advance hardware-aware research in quantum information in the near term. Finally, the methods and tools developed in this work are conducive to the experimental realization of efficient purity estimation (featuring exponential speedup) and the decoding of Hawking radiation from a toy-model of a Black Hole.

The harvesting of quantum resources from the vacuum state of a quantum field is a central topic in relativistic quantum information. While several proposals for the harvesting of entanglement from the quantum vacuum exist, less attention has been paid to other quantum resources, such as nonstabilizerness, commonly dubbed magic and quantified by the stabilizer R\'enyi entropy (SRE). In this work, we show how to harvest SRE from the vacuum state of a massless field, using accelerated Unruh-DeWitt detectors in Minkowski spacetime. In particular, one can harvest a particular nonlocal form of SRE that cannot be erased by local unitary operations. This nonlocal SRE is a fundamental quantity to study the interplay between entanglement and nonstabilizer resources. We conclude our work with an analysis of the Clauser-Horne-Shimony-Holt inequalities: when restricting to stabilizer measurements, i.e., Pauli measurements, one cannot extract a violation from the quantum field.

We employ the Stabilizer Rényi 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 a Clifford circuit mapping, we connect the observed jump in SRE to that occurring between standard and generalized W W -states with finite momenta. This mapping allows us to quantify the SRE discontinuity analytically.

Topological order comes in different forms, and its classification and detection is an important field of modern research. In this work, we show that the Disconnected Entanglement Entropy, a measure originally introduced to identify topological phases, is also able to unveil the long-range entanglement (LRE) carried by a single, fractionalized excitation. We show this by considering a quantum, delocalized domain wall excitation that can be introduced into a system by inducing geometric frustration in an antiferromagnetic spin chain. Furthermore, we show that the LRE of such systems is resilient against a quantum quench and the introduction of disorder, as it happens in traditional symmetry-protected topological phases. All these evidences establish the existence of a new phase induced by frustration with topological features despite not being of the usual type.