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Asymptotic $L_p$-convergence, which resembles convergence in $L_p$, was introduced to address a question in diffusive relaxation. This note aims to compare asymptotic $L_p$-convergence with convergence in measure and in weak $L_p$ spaces. One of the results characterizes convergence in measure on finite measure spaces in terms of asymptotic $L_p$-convergence.

The dynamical behaviour of complex quantum systems can be harnessed for information processing. With this aim, quantum reservoir computing (QRC) with Ising spin networks was recently introduced as a quantum version of classical reservoir computing. In turn, reservoir computing is a neuro-inspired machine learning technique that consists in exploiting dynamical systems to solve nonlinear and temporal tasks. We characterize the performance of the spin-based QRC model with the Information Processing Capacity (IPC), which allows to quantify the computational capabilities of a dynamical system beyond specific tasks. The influence on the IPC of the input injection frequency, time multiplexing, and different measured observables encompassing local spin measurements as well as correlations, is addressed. We find conditions for an optimum input driving and provide different alternatives for the choice of the output variables used for the readout. This work establishes a clear picture of the computational capabilities of a quantum network of spins for reservoir computing. Our results pave the way to future research on QRC both from the theoretical and experimental points of view., Comment: 12 pages, 9 figures. To be published in Cognitive Computation

We study the relationship between the collective phenomena of super and subradiance and spontaneous synchronization of quantum systems. To this aim we revisit the case of two detuned qubits interacting through a pure dissipative bosonic environment, which contains the minimal ingredients for our analysis. By using the Liouville formalism, we are able to find analytically the ultimate connection between these phenomena. We find that dynamical synchronization is due to the presence of long standing coherence between the ground state of the system and the subradiant state. We finally show that, under pure dissipation, the emergence of spontaneous synchronization and of subradiant emission occur on the same time scale. This reciprocity is broken in the presence of dephasing noise., Comment: 12 pages, 6 figures

During the long course of evolution, nature has learnt how to exploit quantum effects. In fact, recent experiments reveal the existence of quantum processes whose coherence extends over unexpectedly long time and space ranges. In particular, photosynthetic processes in light-harvesting complexes display a typical oscillatory dynamics ascribed to quantum coherence. Here, we consider the simple model where a dimer made of two chromophores is strongly coupled with a quasi-resonant vibrational mode. We observe the occurrence of wide oscillations of genuine quantum correlations, between electronic excitations and the environment, represented by vibrational bosonic modes. Such a quantum dynamics has been unveiled through the calculation of the negativity of entanglement and the discord, indicators widely used in quantum information for quantifying the resources needed to realize quantum technologies. We also discuss the possibility of approximating additional weakly-coupled off-resonant vibrational modes, simulating the disturbances induced by the rest of the environment, by a single vibrational mode. Within this approximation, one can show that the off-resonant bath behaves like a classical source of noise.

A resonance theorem providing existence of functions that are counterexamples for all members of a given family of translation invariant differentiation bases is proved. Applications of the theorem to Zygmund problem on a choice of coordinate axes are given.

The transfer of an unknown quantum state, from a sender to a receiver, is one of the main requirements to perform quantum information processing tasks. In this respect, the state transfer of a single qubit by means of spin chains has been widely discussed, and many protocols aiming at performing this task have been proposed. Nevertheless, the state transfer of more than one qubit has not been properly addressed so far. In this paper, we present a modified version of a recently proposed quantum state transfer protocol [Phys. Rev. A 87, 062309 (2013)] to obtain a quantum channel for the transfer of two qubits. This goal is achieved by exploiting Rabi-like oscillations due to excitations induced by means of strong and localized magnetic fields. We derive exact analytical formulae for the fidelity of the quantum state transfer, and obtain a high-quality transfer for general quantum states as well as for specific classes of states relevant for quantum information processing., Comment: 7 pages

We discuss the emergence of spontaneous synchronization for an open spin-pair system interacting only via a common environment. Under suitable conditions, and even in the presence of detuning between the natural precession frequencies of the two spins, they are shown to reach a long-lasting transient behavior where they oscillate in phase. We explore the connection between the emergence of such a behavior and the establishment of robust quantum correlations between the two spins, analyzing differences between dissipative and dephasing effects.

In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it merges a qualitative and a quantitative method to optimize the way of exploiting the a priori information on the background within the inversion procedure, thus improving the quality of the reconstruction and reducing the data amount necessary for a satisfactory result. In the qualitative step, this a priori knowledge is utilized to implement the linear sampling method in its near-field formulation for an inhomogeneous background, in order to identify the region where the scatterer is located. On the other hand, the same a priori information is also encoded in the quantitative step by extending and applying the contrast source inversion method to what we call the `inhomogeneous Lippmann-Schwinger equation': the latter is a generalization of the classical Lippmann-Schwinger equation to the case of an inhomogeneous background, and in our paper is deduced from the differential formulation of the direct scattering problem to provide the reconstruction algorithm with an appropriate theoretical basis. Then, the point values of the refractive index are computed only in the region identified by the linear sampling method at the previous step. The effectiveness of this hybrid approach is supported by numerical simulations presented at the end of the paper., Comment: accepted in SIAM Journal on Applied Mathematics

We study the quantum diffusion of an electron in a quantum chain starting from an initial state localized around a given site. As the wavepacket diffuses, the probability of reconstructing the initial state on another site diminishes drastically with the distance. In order to optimize the state transmission we find that a topological quantum phase can be introduced. The effect of this phase is the reduction of wavepacket spreading together with almost coherent group propagation. In this regime, the electron has a quasi-linear dispersion and high fidelity can be achieved also over large distances in terms of lattice spacing., Comment: 8 pages, 6 figures

We study the possibility of realizing perfect quantum state transfer in mesoscopic devices. We discuss the case of the Fano-Anderson model extended to two impurities. For a channel with an infinite number of degrees of freedom, we obtain coherent behavior in the case of strong coupling or in weak coupling off-resonance. For a finite number of degrees of freedom, coherent behavior is associated to weak coupling and resonance conditions.

We introduce a model of quantum teleportation on a channel built on a quantum dot chain. Quantum dots are coupled through hopping and each dot can accept zero, one or two electrons. Vacuum and double occupation states have the same potential energy, while single occupation states are characterized by a lower potential energy. A single dot initially decoupled from the others is weakly coupled with an external element (Bob), where a pair of electrons has been previously localized. Because of hopping after a suitable time the two dots charge states become maximally entangled. Another chain dot (Alice) is put in an unknown superposition of vacuum and double occupation states, and the other dots are initially empty. The time evolution of the system involves an electron diffusive process. A post selection procedure represented by the detection of charge pairs in a region of the chain equidistant from Alice and Bob, allows, if successful, the reconstruction on the Bob site of the unknown state initially encoded by Alice. The peculiar feature of the model is that the introduction of a trapped magnetic field strongly improves the process efficiency.

We consider an array of N quantum dot pairs interacting via Coulomb interaction between adjacent dots and hopping inside each pair. We show that at the first order in the ratio of hopping and interaction amplitudes, the array maps in an effective two level system with energy separation becoming exponentially small in the macroscopic (large N) limit. Decoherence at zero temperature is studied in the limit of weak coupling with phonons. In this case the macroscopic limit is robust with respect to decoherence. Some possible applications in quantum information processing are discussed., Comment: Phys. Rev. A (in press)

We present a model of quantum teleportation protocol based on a double quantum dot array. The unknown qubit is encoded using a pair of quantum dots, coupled by tunneling, with one excess electron. It is shown how to create maximally entangled states with this kind of qubits using an adiabatically increasing Coulomb repulsion between different pairs. This entangled states are exploited to perform teleportation again using an adiabatic coupling between them and the incoming unknown state. Finally, a sudden separation of Bob's qubit enables a time evolution of Alice's state providing a modified version of standard Bell measurement. Substituting the four quantum dots entangled state with a chain of coupled DQD's, a quantum channel with high fidelity arises from this scheme allowing the transmission over long distances., Comment: 4 pages, 2 figures

A novel single-photon Mach-Zehnder interferometer terminated at two different frequencies realizes the nonlinear frequency conversion of optical quantum superposition states. The information-preserving character of the relevant unitary transformation has been experimentally demonstrated for input qubits and ebits. Besides its own intrinsic fundamental interest, the new scheme will find important applications in modern quantum information technology., Comment: 11 pages, 4 figures