Aspects of quantum work.

Gaussian states of quantum oscillators are fully characterized by the mean values and the covariance matrix of their quadrature observables. We consider the dynamics of a system of oscillators subject to interactions, damping, and continuous probing which maintain their Gaussian state property. Such dynamics is found in many physical systems that can therefore be efficiently described by the ensuing effective representation of the density matrix $\rho(t)$. Our probabilistic knowledge about the outcome of measurements on a quantum system at time $t$ is not only governed by $\rho(t)$ conditioned on the evolution and measurement outcomes obtained until time $t$, but is also modified by any information acquired after $t$. It was shown in [Phys. Rev. Lett. 111, 160401 (2013)] that this information is represented by a supplementary matrix, $E(t)$. We show here that the restriction of the dynamics of $\rho(t)$ to Gaussian states implies that the matrix $E(t)$ is also fully characterized by a vector of mean values and a covariance matrix. We derive the dynamical equations for these quantities and we illustrate their use in the retrodiction of measurements on Gaussian systems.

We derive a hierarchy of separability criteria for multi-mode continuous variable systems. They permit to study in a unified way the k-partite entanglement of broad classes of Gaussian and non- Gaussian states. With specific examples we demonstrate the strength of the criteria, and, we discuss their assessment based on data obtained from Gaussian measurements.

Classical Hamiltonian description of a two-level quantum system: The quantum Zeno effect

Something for Nothing: Universal Basic Income and the Value of Work Beyond Incentives

While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as "Heisenberg's uncertainty principle," Heisenberg originally formulated his ideas in terms of a relationship between the precision of a measurement and the disturbance it must create. Although this latter relationship is not rigorously proven, it is commonly believed (and taught) as an aspect of the broader uncertainty principle. Here, we experimentally observe a violation of Heisenberg's "measurement-disturbance relationship", using weak measurements to characterize a quantum system before and after it interacts with a measurement apparatus. Our experiment implements a 2010 proposal of Lund and Wiseman to confirm a revised measurement-disturbance relationship derived by Ozawa in 2003. Its results have broad implications for the foundations of quantum mechanics and for practical issues in quantum measurement.

Consider two bosonic modes which are prepared in one of two possible Gaussian states with the same local energy: either a tensor-product thermal state (with zero correlations) or a separable Gaussian state with maximal correlations (with both classical and quantum correlations, the latter being quantified by quantum discord). For the discrimination of these states, we compare the optimal joint coherent measurement with the best local measurement based on single-mode Gaussian detections. We show how the coherent measurement always strictly outperforms the local detection strategy for both single- and multi-copy discrimination. This means that using local Gaussian measurements (assisted by classical communication) is strictly suboptimal in detecting discord. A better performance may only be achieved by either using non Gaussian measurements (non linear optics) or coherent non-local measurements.

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.

Beam splitters are important components in numerous tasks of quantum information protocols used either in simple or in an interferometric arrangement or together with other quantum systems. This report shows interesting aspects of the quantum correlations of two-mode Gaussian state (TMGS) for the photons retrieved via a linear beam splitter when they are initially employed at the input of either pure or mixed two single-mode Gaussian states (TSMGSs). The quantum correlations obey the boundaries of quantum non-locality, steering, entanglement and discord for pure input states. Though Bell inequality does not violate, quantum steering, entanglement and discord exist in the quantum state evolved by the beam splitter when input states become mixed. Specifically, the quantum steering, entanglement and discord persist to some degrees against the thermal photon number, the Bell inequality is, nonetheless, obeyed by the quantum state except in a very sharp regime.

The dynamics of Markovian open quantum systems are described by Lindblad master equations. For fermionic and bosonic systems that are quasi-free, i.e. with Hamiltonians that are quadratic in the ladder operators and Lindblad operators that are linear in the ladder operators, we derive the equation of motion for the covariance matrix. This determines the evolution of Gaussian initial states and the steady states, which are also Gaussian. Using ladder super-operators (a.k.a. third quantization), we show how the Liouvillian can be transformed to a many-body Jordan normal form which also reveals the full many-body spectrum. Extending previous work by Prosen and Seligman, we treat fermionic and bosonic systems on equal footing with Majorana operators, shorten and complete some derivations, also address the odd-parity sector for fermions, give a criterion for the existence of bosonic steady states, cover non-diagonalizable Liouvillians also for bosons, and include quadratic systems. In extension of the quasi-free open systems, quadratic open systems comprise additional Hermitian Lindblad operators that are quadratic in the ladder operators. While Gaussian states may then evolve into non-Gaussian states, the Liouvillian can still be transformed to a useful block-triangular form, and the equations of motion for k-point Green’s functions form a closed hierarchy. Based on this formalism, results on criticality and dissipative phase transitions in such models are discussed in a companion paper.

State variable and parameter estimations are important for signal sensing and feedback control in both traditional engineering systems and quantum systems. The Kalman filter, which is one of the most popular signal recovery techniques in classical systems for decades, has now been connected to the stochastic master equations of linear quantum mechanical systems. Various studies have invested effort on mapping the state evolution of a quantum system into a set of classical filtering equations. However, establishing proper evolution models with symmetry to classical filter equation for quantum systems is not easy. Here, we review works that have successfully built a Kalman filter model for quantum systems and provide an improved method for optimal estimations. We also discuss a practical scenario involving magnetic field estimations in quantum systems, where non-linear Kalman filters could be considered an estimation solution.

Understanding how quantum resources can be quantified and distributed over many parties has profound applications in quantum communication. As one of the most intriguing features of quantum mechanics, Einstein-Podolsky-Rosen (EPR) steering is a useful resource for secure quantum networks. By reconstructing the covariance matrix of a continuous variable four-mode square Gaussian cluster state subject to asymmetric loss, we quantify the amount of bipartite steering with a variable number of modes per party, and verify recently introduced monogamy relations for Gaussian steerability, which establish quantitative constraints on the security of information shared among different parties. We observe a very rich structure for the steering distribution, and demonstrate one-way EPR steering of the cluster state under Gaussian measurements, as well as one-to-multimode steering. Our experiment paves the way for exploiting EPR steering in Gaussian cluster states as a valuable resource for multiparty quantum information tasks.

Generation of high fidelity photonic non-Gaussian states is a crucial\ningredient for universal quantum computation using continous-variable\nplatforms, yet it remains a challenge to do so efficiently. We present a\ngeneral framework for a probabilistic production of multimode non-Gaussian\nstates by measuring few modes of multimode Gaussian states via\nphoton-number-resolving detectors. We use Gaussian elements consisting of\nsqueezed displaced vacuum states and interferometers, the only non-Gaussian\nelements consisting of photon-number-resolving detectors. We derive analytic\nexpressions for the output Wigner function, and the probability of generating\nthe states in terms of the mean and the covariance matrix of the Gaussian state\nand the photon detection pattern. We find that the output states can be written\nas a Fock basis superposition state followed by a Gaussian gate, and we derive\nexplicit expressions for these parameters. These analytic expressions show\nexactly what non-Gaussian states can be generated by this probabilistic scheme.\nFurther, it provides a method to search for the Gaussian circuit and\nmeasurement pattern that produces a target non-Gaussian state with optimal\nfidelity and success probability. We present specific examples such as the\ngeneration of cat states, ON states, Gottesman-Kitaev-Preskill states, NOON\nstates and bosonic code states. The proposed framework has potential\nfar-reaching implications for the generation of bosonic error-correction codes\nthat require non-Gaussian states, resource states for the implementation of\nnon-Gaussian gates needed for universal quantum computation, among other\napplications requiring non-Gaussianity. The tools developed here could also\nprove useful for the quantum resource theory of non-Gaussianity.\n

Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cramér–Rao bound (CRB) is not well defined. In particular, it applies when no initial information about the parameter value is available, e.g., when few measurements are performed. Here, we consider three paradigmatic estimation schemes in continuous-variable (CV) quantum metrology (estimation of displacements, phases, and squeezing strengths) and analyse them from the Bayesian perspective. For each of these scenarios, we investigate the precision achievable with single-mode Gaussian states under homodyne and heterodyne detection. This allows us to identify Bayesian estimation strategies that combine good performance with the potential for straightforward experimental realization in terms of Gaussian states and measurements. Our results provide practical solutions for reaching uncertainties where local estimation techniques apply, thus bridging the gap to regimes where asymptotically optimal strategies can be employed.

We investigate the atom–photon entanglement between a four-level double V-type quantum system and a linearly polarized field near a plasmonic nanostructure in the presence of a static magnetic field. It is demonstrated that the magneto-optical effect can affect the atom–photon entanglement only when the atom is near the plasmonic nanostructure. We show that atom–photon entanglement increases when the quantum system is placed near the plasmonic nanostructure in order to modification of the spontaneous decays of the quantum system. It is demonstrated that the degree of entanglement (DEM) increases by increasing the intensity of the linearly polarized field when the quantum system is close to the surface of the plasmons. Moreover, we find that near the plasmonic nanostructure, the static magnetic field has a major role in increasing the steady-state DEM so that the DEM is completely demolished in the absence of the static magnetic field. Finally, it is shown that the atom–photon entanglement near a plasmonic nanostructure is destroyed by free space decay rate.

Approaches for improving students' understanding of quantum mechanics