Isotropic $XX$ models of one-dimensional spin-1/2 chains are investigated with the aim to elucidate the formal structure and the physical properties that allow these systems to act as channels for long-distance, high-fidelity quantum teleportation. We introduce two types of models: (i) open, dimerized $XX$ chains, and (ii) open $XX$ chains with small end bonds. For both models we obtain the exact expressions for the end-to-end correlations and the scaling of the energy gap with the length of the chain. We determine the end-to-end concurrence and show that model (i) supports true long-distance entanglement at zero temperature, while model (ii) supports “quasi-long-distance” entanglement that slowly falls off with the size of the chain. Due to the different scalings of the gaps, respectively exponential for model (i) and algebraic in model (ii), we demonstrate that the latter allows for efficient qubit teleportation with high fidelity in sufficiently long chains even at moderately low temperatures.

Entanglement is usually quantified by von Neumann entropy, but its properties are much more complex than what can be expressed with a single number. We show that the three distinct dynamical phases known as thermalization, Anderson localization, and many-body localization are marked by different patterns of the spectrum of the reduced density matrix for a state evolved after a quantum quench. While the entanglement spectrum displays Poisson statistics for the case of Anderson localization, it displays universal Wigner-Dyson statistics for both the cases of many-body localization and thermalization, albeit the universal distribution is asymptotically reached within very different time scales in these two cases. We further show that the complexity of entanglement, revealed by the possibility of disentangling the state through a Metropolis-like algorithm, is signaled by whether the entanglement spectrum level spacing is Poisson or Wigner-Dyson distributed.

We introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems. The method allows us to determine rigorously the existence, location, and exact form of separable ground states in a large variety of, generally nonexactly solvable, spin models belonging to different universality classes. The theory applies to translationally invariant systems, irrespective of spatial dimensionality, and for spin-spin interactions of arbitrary range.

We advance the characterization of complexity in quantum many-body systems by examining W W -states embedded in a spin chain. Such states show an amount of non-stabilizerness or “magic”, measured as the Stabilizer Rényi Entropy, that grows logarithmically with the number of qubits/spins. We focus on systems whose Hamiltonian admits a classical point with extensive degeneracy. Near these points, a Clifford circuit can convert the ground state into a W W -state, while in the rest of the phase to which the classical 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 Stabilizer Rényi Entropy is the sum of that of the W W -states plus an extensive local contribution. Our work reveals that W 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.

We propose to use a quantum spin chain as a device to store and release energy coherently and we investigate the interplay between its internal correlations and outside decoherence. We employ the quantum Ising chain in a transverse field and our charging protocol consists of a sudden global quantum quench in the external field to take the system out of equilibrium. Interactions with the environment and decoherence phenomena can dissipate part of the work that the chain can supply after being charged, measured by the ergotropy. We find that overall, the system shows remarkably better performance, in terms of resilience, charging time, and energy storage, when topological frustration is introduced by setting antiferromagnetic interactions with an odd number of sites and periodic boundary conditions. Moreover, we show that in a simple discharging protocol to an external spin, only the frustrated chain can transfer work and not just heat. Published by the American Physical Society 2024

We investigate the existence and the properties of fully separable (fully factorized) ground states in quantum spin systems. Exploiting techniques of quantum information and entanglement theory, we extend a recently introduced method and construct a general, self-contained theory of ground state factorization in frustration-free quantum spin models defined on lattices in any spatial dimension and for interactions of arbitrary range. We show that, quite generally, nonexactly solvable translationally invariant models in presence of an external uniform magnetic field can admit exact, fully factorized ground state solutions. Unentangled ground states occur at finite values of the Hamiltonian parameters satisfying well-defined balancing conditions between the applied field and the interaction strengths. These conditions are analytically determined together with the type of magnetic orderings compatible with factorization and the corresponding values of the fundamental observables such as energy and magnetization. The method is applied to a series of examples of increasing complexity, including translationally invariant models with short, long, and infinite ranges of interaction, as well as systems with spatial anisotropies, in lower and higher dimensions. We also illustrate how the general method, besides yielding a large series of exact results for complex models in any dimension, recovers, as particular cases, the results previously achieved on simple models in low dimensions exploiting direct methods based on factorized mean-field ansatz.