Amplification of quadratic Hamiltonians

We construct a random unitary Gaussian circuit for continuous-variable (CV) systems subject to Gaussian measurements. We show that when the measurement rate is nonzero, the steady state entanglement entropy saturates to an area-law scaling. This is different from a many-body qubit system, where a generic entanglement transition is widely expected. Due to the unbounded local Hilbert space, the time scale to destroy entanglement is always much shorter than the one to build it, while a balance could be achieved for a finite local Hilbert space. By the same reasoning, the absence of transition should also hold for other non-unitary Gaussian CV dynamics.

Quantum correlation provides a promising measure beyond entanglement. Here, we propose a necessary and sufficient condition for nonzero quantum correlation in continuous variable systems, which is simple and easy to perform in terms of a marker Qr. In order to get this condition, we introduce continuous-variable local orthogonal bases of the operator space, which are generalized from the orthogonal basis sets in local operator space for discrete variables. Based on this, we obtain the marker Qr for all bipartite continuous variable states, and provide several examples including two-mode Gaussian and non-Gaussian states. Our result may provide a candidate for quantum correlation measures, and can be measured by designed quantum circuits.

For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for which the question if dynamical decoupling could be applied remained open. Here we first show that not every infinite-dimensional system can be protected from decoherence through dynamical decoupling. Then we develop dynamical decoupling for continuous variable systems which are described by quadratic Hamiltonians. We identify a condition and a set of operations that allow us to map a set of interacting harmonic oscillators onto a set of non-interacting oscillators rotating with an averaged frequency, a procedure we call homogenization. Furthermore we show that every quadratic system-environment interaction can be suppressed with two simple operations acting only on the system. Using a random dynamical decoupling or homogenization scheme, we develop bounds that characterize how fast we have to work in order to achieve the desired uncoupled dynamics. This allows us to identify how well homogenization can be achieved and decoherence can be suppressed in continuous variable systems.

The results of perturbation analysis pertaining to closed queuing networks are reviewed, showing that the basic principles of perturbation analysis can be explained using a dynamic point of view. It is shown that perturbation generation and perturbation propagation rules can be viewed as counterparts of the linearization theory of nonlinear continuous variable dynamic systems; the concept of perturbation realization describes the steady-state effect of a perturbation and reflects the special dynamic feature of a closed queuing network. The realization probability can be used to calculate the sensitivity of steady-state throughputs and some other sensitivities.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Covariance entanglement measure for two-mode continuous variable systems

Steering is a manifestation of quantum correlations that embodies the Einstein-Podolsky-Rosen (EPR) paradox. While there have been recent attempts to quantify steering, continuous variable systems remained elusive. We introduce a steering measure for two-mode continuous variable systems that is valid for arbitrary states. The measure is based on the violation of an optimized variance test for the EPR paradox, and admits a computable and experimentally friendly lower bound only depending on the second moments of the state, which reduces to a recently proposed quantifier of steerability by Gaussian measurements. We further show that Gaussian states are extremal with respect to our measure, minimizing it among all continuous variable states with fixed second moments. As a byproduct of our analysis, we generalize and relate well-known EPR-steering criteria. Finally an operational interpretation is provided, as the proposed measure is shown to quantify the optimal guaranteed key rate in semi-device independent quantum key distribution.

The authors analyze two simple deterministic flow models for multiple buffer servers which are examples of the supervision of continuous variable systems by a discrete controller. These systems exhibit what may be regarded as the two extremes of complexity of closed loop behavior: one is eventually periodic, the other is chaotic. The first example exhibits chaotic behavior that could be characterized statistically. The dual system, the switched server system, exhibits very predictable behavior, which is modeled by a finite state automaton. This research has application to multimodal discrete time systems where the controller can choose from a set of transition maps to implement.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

While commonly used entanglement criteria for continuous variable systems are based on quadrature measurements, here we study entanglement detection from measurements of the Wigner function. These are routinely performed in platforms such as trapped ions and circuit QED, where homodyne measurements are difficult to be implemented. We provide complementary criteria which we show to be tight for a variety of experimentally relevant Gaussian and non-Gaussian states. Our results show novel approaches to detect entanglement in continuous variable systems and shed light on interesting connections between known criteria and the Wigner function.

In this paper, we investigated measurement of quantum correlation for two mode continuous variable systems, and constructed two operators to measure quantum correlation of continuous variable systems. These operators not only can be criteria for quantum correlation, but also can be measurement for quantum correlation.

In the present study, the effect of ‘red’, ‘white’ and ‘blue’ environmental noise on population dynamics in a simple three‐species food chain system was analyzed. The ‘colored’ noise was superimposed on the three‐species food chain model first put forth by Rosenzweig in different ways and the resulting power spectra were investigated. We showed that the amplitude of environmental noise, the trophic level at which a population is positioned and whether a population is directly affected by environmental noise, are all important with respect to the way in which a population responds to noise with different colors. For the deterministic case, all population dynamics are ‘red’ irrespective of the system dynamics. When all species are sensitive to environmental noise, the top predator's dynamics always remain ‘red’ regardless of the color of the noise and its amplitude, whereas the dynamics of the intermediate species turn ‘blue’ under disturbances of any color with high amplitude, and those of the basal species may become ‘blue’ only under ‘blue’ noise. If only one species is sensitive to environmental noise, the dynamics of the insensitive species are always ‘red’, irrespective of the color of the noise and its amplitude. Unlike previous results obtained by studying single‐species models, our results have almost nothing to do with deterministic system dynamics. In other words, changing the deterministic system dynamics from stable via periodic to chaotic does not qualitatively change the outcome. Our results are of importance in determining how we interpret the ubiquitous ‘red’ power spectrum of natural ecological time series.

Continuous-variable entanglement dynamics in Lorentzian environment

Recently, a class of adaptive schemes has been developed for rejecting sinusoidal output disturbances with unknown frequencies, phases, and amplitudes. These adaptive schemes require an accurate model of the affected system's dynamics to function, and the controller performance degrades as the modeling error increases. While linear time-invariant (LTI) dynamics can adequately model the dynamics of some systems, a time-varying model of the system dynamics is more appropriate in certain scenarios. This paper proposes a robust adaptive scheme for rejecting disturbances that affect the output of a system described by a known linear time-varying model. The disturbances are described by an unknown number of sinusoidal terms with unknown time-varying frequencies. Analysis is done in ideal case where the disturbance frequencies are perfectly known to provide conditions guaranteeing the existence of a controller and a corresponding set of parameters which reject the disturbance. Analysis is then done in the more realistic adaptive scenario where the disturbance frequencies are unknown, and a robust adaptive scheme for selecting controller parameters which reject the disturbance is proposed. Performance of the controller with respect to the speed of variation in the plant model parameters is assessed via simulation.

We study a coherent superposition $t\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}+r{\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}}^{\ifmmode\dagger\else\textdagger\fi{}}$ of field annihilation and creation operators acting on continuous variable systems and propose its application for quantum state engineering. Specifically, it is investigated how the superposed operation transforms a classical state to a nonclassical one, together with emerging nonclassical effects. We also propose an experimental scheme to implement this elementary coherent operation and discuss its usefulness to produce an arbitrary superposition of number states involving up to two photons.

Non-Gaussian quantum states are a known necessary resource for reaching a quantum advantage and for violating Bell inequalities in continuous variable systems. As one kind of manifestation of quantum correlations, Einstein–Podolsky–Rosen steering enables verification of shared entanglement even when one of the subsystems is not characterized. However, how to detect and classify such an effect for non-Gaussian states is far from being well understood. Here, we present an efficient non-Gaussian steering criterion based on the high-order observables and conduct a systematic investigation into the hierarchy of non-Gaussian steering criteria. Moreover, we apply our criterion to three experimentally-relevant non-Gaussian states under realistic conditions and, in particular, propose a feasible scheme to create multi-component cat states with tunable size by performing a suitable high-order quadrature measurement on the steering party. Our work reveals the fundamental characteristics of non-Gaussianity and quantum correlations, and offers new insights to explore their applications in quantum information processing.

Quantum state engineering and state characterization is a key task in quantum information processing in both discrete and continuous variable systems in the optical domain. In particular, quantum states with non-Gaussian (i.e., non-positive) Wigner quasiprobability distribution functions are crucial to universal, fault-tolerant quantum computing with continuous variables. In this talk, we present our recent results on single-photon Fock state tomography using Photon-Number-Resolving (PNR) measurements. We generated a highly pure narrow-band single-photon Fock state by heralding cavity-enhanced spontaneous-parametric-downconversion from a PPKTP optical parametric oscillator. The Wigner function was reconstructed with photon statistics obtained using superconducting transition-edge sensors with an overall system efficiency of 58(2)%. We then discuss quantum state engineering for pure displaced single-photon Fock states, optical cat states, and approximate GKP states using coherent states and single-photon states along with linear optics and PNR measurements. We report our experimental progress for the same.