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Although ecological networks are typically constructed based on a single type of interaction, e.g. trophic interactions in a food web, a more complete picture of ecosystem composition and functioning arises from merging networks of multiple interaction types. In this work, we consider tripartite networks constructed by merging two bipartite networks, one mutualistic and one antagonistic. Taking the interactions within each sub-network to be distributed randomly, we consider the stability of the dynamics of the network based on the spectrum of its community matrix. In the asymptotic limit of a large number of species, we show that the spectrum undergoes an eigenvalue phase transition, which leads to an abrupt destabilisation of the network as the ratio of mutualists to antagonists is increased. We also derive results that show how this transition is manifest in networks of finite size, as well as when disorder is introduced in the segregation of the two interaction types. Our random-matrix results will serve as a baseline for understanding the behaviour of merged networks with more realistic structures and/or more detailed dynamics.

We consider theoretically an electronic Mach-Zehnder interferometer constructed from quantum Hall edge channels and quantum point contacts, fed with single electrons from a dynamic quantum dot source. By considering the energy dependence of the edge-channel guide centres, we give an account of the phase averaging in this set up that is particularly relevant for the short, high-energy wavepackets injected by this type of electron source. We present both analytic and numerical results for the energy-dependent arrival time distributions of the electrons and also give an analysis of the delay times associated with the quantum point contacts and their effects on the interference patterns. A key finding is that, contrary to expectation, maximum visibility requires the interferometer arms to be different in length, with an offset of up to a micron for typical parameters. By designing interferometers that incorporate this asymmetry in their geometry, phase-averaging effects can be overcome such that visibility is only limited by other incoherent mechanisms., Comment: 12 pages; 6 figures

Financial markets are paradigmatic examples of complex systems and have been compared to ecological networks in which different species (firms) interact and co-evolve. A central object governing species dynamics in ecology is the community matrix, whose elements are closely related to pairwise interspecific interaction coefficients. Using this ecological analogy we propose a method, based on the Maximum Entropy (MaxEnt) principle, that allows us to infer candidates for an economic community matrix from time series data of market values. To assess the usefulness of this picture, we construct community matrices for a set of companies belonging to the Fortune 500 list and perform a community analysis on the resultant networks. This analysis shows these networks to strongly reflect the known industry groupings of the firms. We conclude therefore that our community matrices capture non-trivial information about the interaction of firms, not immediately apparent from the covariance of market values. We anticipate our approach being useful in elucidating further aspects of market structure, as well as forming the basis of forecasting market dynamics.

This paper explores two circuit approaches for quantum walks: The first consists of generalized controlled inversions, whereas the second one effectively replaces them with rotation operations around the basis states. We show the theoretical foundation of the rotational implementation. The rotational approach nullifies the large amount of ancilla qubits required to carry out the computation when using the inverter implementation. Our results concentrate around the comparison of the two architectures in terms of structure, benefits, and detriments, as well as the computational resources needed for each approach. We show that the inverter approach requires exponentially fewer gates than the rotations but almost half the number of qubits in the system. Finally, we execute a number of experiments using an IBM quantum computer. The experiments show the effects of noise in our circuits. Small two-qubit quantum walks evolve closer to our expectations, whereas for a larger number of steps or state space the evolution is severely affected by noise.

Noise dominates every aspect of near-term quantum computers, rendering it exceedingly difficult to carry out even small computations. In this paper we are concerned with the modelling of noise in Noisy Intermediate-Scale Quantum (NISQ) computers. We focus on three error groups that represent the main sources of noise during a computation and present quantum channels that model each source. We engineer a noise model that combines all three noise channels and simulates the evolution of the quantum computer using its calibrated error rates. We run various experiments of our model, showcasing its behaviour compared to other noise models and an IBM quantum computer. We find that our model provides a better approximation of the quantum computer's behaviour than the other models. Following this, we use a genetic algorithm to optimize the parameters used by our noise model, bringing the behaviour of the model even closer to the quantum computer. Finally, a comparison between the pre and postoptimization parameters reveals that, according to our model, certain operations can be more or less erroneous than the hardware-calibrated parameters show., Comment: 16 pages; 7 figures; changes for journal publication

In a recent experiment [A. Donarini et al., Nat Comms 10, 381 (2019)], electronic transport through a carbon nanotube quantum dot was observed to be suppressed by the formation of a quantum-coherent ``dark state''. In this paper we consider theoretically the counting statistics and waiting-time distribution of this dark-state-limited transport. We show that the statistics are characterised by giant super-Poissonian Fano factors and long-tailed waiting-time distributions, both of which are signatures of the bistability and extreme electron bunching caused by the dark state., 9 pages; 10 figures. Updated version with new section on experimental signatures

We investigate the interplay of superradiant phase transition (SPT) and energy band physics in an extended Dicke-Hubbard lattice whose unit cell consists of a Dicke model coupled to an atomless cavity. We found in such a periodic lattice the critical point that occurs in a single Dicke model becomes a critical region that is periodically changing with the wavenumber $k$. In the weak-coupling normal phase of the system we observed a flat band and its corresponding localization that can be controlled by the ground-state SPT. Our work builds the connection between flat band physics and SPT, which may fundamentally broaden the regimes of many-body theory and quantum optics., 9 pages, 5 figures, published version

The Leggett–Garg inequality attempts to classify experimental outcomes as arising from one of two possible classes of physical theories: those described by macrorealism (which obey our intuition about how the macroscopic classical world behaves) and those that are not (e.g., quantum theory). The development of cloud-based quantum computing devices enables us to explore the limits of macrorealism. In particular, here we take advantage of the properties of the programmable nature of the IBM quantum experience to observe the violation of the Leggett–Garg inequality (in the form of a ‘quantum witness’) as a function of the number of constituent systems (qubits), while simultaneously maximizing the ‘disconnectivity’, a potential measure of macroscopicity, between constituents. Our results show that two- and four-qubit ‘cat states’ (which have large disconnectivity) are seen to violate the inequality, and hence can be classified as non-macrorealistic. In contrast, a six-qubit cat state does not violate the ‘quantum witness’ beyond a so-called clumsy invasive-measurement bound, and thus is compatible with ‘clumsy macrorealism’. As a comparison, we also consider un-entangled product states with n = 2, 3, 4 and 6 qubits, in which the disconnectivity is low.

Due to their high energy, hot electrons in quantum Hall edge states can be considered as single particles that have the potential to be used for quantum optics-like experiments. Unlike photons, however, electrons typically undergo scattering processes in transport, which results in a loss of coherence and limits their ability to show quantum-coherent behaviour. Here we study theoretically the decoherence mechanisms of hot electrons in a Mach-Zehnder interferometer, and highlight the role played by both acoustic and optical phonon emission. We discuss optimal choices of experimental parameters and show that high visibilities of $\gtrsim 85\%$ are achievable in hot-electron devices over relatively long distances of 10 $\mu$m. We also discuss energy filtration techniques to remove decoherent electrons and show that this can increase visibilities to over $95\%$. This represents an improvement over Fermi-level electron quantum optics, and suggests hot-electron charge pumps as a platform for realising quantum-coherent nanoelectronic devices., Comment: 23 pages, 7 figures

We study theoretically the relaxation of hot quantum-Hall edge-channel electrons under the emission of both acoustic and optical phonons. Aiming to model recent experiments with single-electron sources, we describe simulations that provide the distribution of electron energies and arrival times at a detector a fixed distance from the source. From these simulations we extract an effective rate of emission of optical phonons that contains contributions from both a direct emission process as well as one involving inter-edge-channel transitions that are driven by the sequential emission of first an acoustic -- and then an optical -- phonon. Furthermore, we consider the mean energy loss due to acoustic phonon emission and resultant broadening of the electron energy distribution and derive an effective drift-diffusion model for this process., 11 pages; 8 figures

Elitzur and Vaidman have proposed a measurement scheme that, based on the quantum superposition principle, allows one to detect the presence of an object—in a dramatic scenario, a bomb—without interacting with it. It was pointed out by Ghirardi that this interaction-free measurement scheme can be put in direct relation with falsification tests of the macro-realistic worldview. Here we have implemented the “bomb test” with a single atom trapped in a spin-dependent optical lattice to show explicitly a violation of the Leggett–Garg inequality—a quantitative criterion fulfilled by macro-realistic physical theories. To perform interaction-free measurements, we have implemented a novel measurement method that correlates spin and position of the atom. This method, which quantum mechanically entangles spin and position, finds general application for spin measurements, thereby avoiding the shortcomings inherent in the widely used push-out technique. Allowing decoherence to dominate the evolution of our system causes a transition from quantum to classical behavior in fulfillment of the Leggett–Garg inequality.

Using a recently-developed time-of-flight measurement technique with 1 ps time resolution and electron-energy spectroscopy, we developed a method to measure the longitudinal-optical-phonon emission rate of hot electrons travelling along a depleted edge of a quantum Hall bar. A comparison of the experimental results to a single-particle model implies that the main scattering mechanism involves a two-step process via intra-Landau-level transition. We show this scattering can be suppressed by controlling the edge potential profile, and a scattering length > 1 mm can be achieved, allowing the use of this system for scalable single-electron device applications., 5 pages and supplementary

We realise a quantum three-level system with photons distributed among three different spatial and polarization modes. Ambiguous measurement of the state of the qutrit are realised by blocking one out for the three modes at any one time. Using these measurements we construct a test of a Leggett-Garg inequality as well as tests of no-signalling-in-time for the measurements. We observe violations of the Leggett-Garg inequality that can not be accounted for in terms of signalling. Moreover, we tailor the qutrit dynamics such that both ambiguous and unambiguous measurements are simultaneously non-signalling, which is an essential step for the justification of the use of ambiguous measurements in Leggett-Garg tests., Comment: 7 pages, 4 figures

Ambiguous measurements do not reveal complete information about the system under test. Their quantum-mechanical counterparts are semi-weak (or in the limit, weak-) measurements and here we discuss their role in tests of the Leggett-Garg inequalities. We show that, whilst ambiguous measurements allow one to forgo the usual non-invasive measureability assumption, to derive an LGI that may be violated, we are forced to introduce another assumption that equates the invasive influence of ambiguous and unambiguous detectors. Based on this assumption, we derive signalling conditions that should be fulfilled for the plausibility of the Leggett-Garg test. We then propose an experiment on a three-level system with a direct quantum-optics realisation that satisfies all signalling constraints and violates a Leggett-Garg inequality., Comment: 9 pages; 4 figures

Quantum transport is the study of the motion of electrons through nano-scale structures small enough that quantum effects are important. In this contribution I review recent theoretical proposals to use the techniques of quantum feedback control to manipulate the properties of electron flows and states in quantum-transport devices. Quantum control strategies can be grouped into two broad classes: measurement-based control and coherent control, and both are covered here. I discuss how measurement-based techniques are capable of producing a range of effects, such as noise suppression, stabilisation of nonequillibrium quantum states and the realisation of a nano-electronic Maxwell’s demon. I also describe recent results on coherent transport control and its relation to quantum networks.

We investigate the ground-state properties of the Anderson single impurity model (finite Coulomb impurity repulsion) with the Coupled Cluster Method. We consider different CCM reference states and approximation schemes and make comparison with exact Green's function results for the non-interacting model and with Brillouin–Wigner perturbation theory for the full interacting model. Our results show that coupled cluster techniques are well suited to quantum impurity problems.

We describe a technique to emulate the dynamics of two-level P T -symmetric spin Hamiltonians, replete with gain and loss, using the unitary dynamics of a larger quantum system. The two-level system in question is embedded in a subspace of a four-level Hamiltonian, with the exterior levels acting as reservoirs. The emulation time is normally finite, limited by the depletion of the reservoirs. We show that it is possible to emulate the desired behaviour of the P T -symmetric Hamiltonian without depleting the reservoir levels, by including an additional coupling between them. This extends the emulation time indefinitely, when in the unbroken symmetry phase of the non-unitary P T dynamics. We propose a realistic experimental implementation using dynamically decoupled magnetic sublevels of ultracold atoms.

Leggett-Garg inequalities are tests of macroscopic realism that can be violated by quantum mechanics. In this letter, we realise photonic Leggett-Garg tests on a three-level system and implement measurements that admit three distinct measurement outcomes, rather than the usual two. In this way we obtain violations of three- and four-time Leggett-Garg inequalities that are significantly in excess of those obtainable in standard Leggett-Garg tests. We also report violations the quantum-witness equality up to the maximum permitted for a three-outcome measurement. Our results highlight differences between spatial and temporal correlations in quantum mechanics., Comment: 9 pages, 3 figures

In recent charge-pump experiments, single electrons are injected into quantum Hall edge channels at energies significantly above the Fermi level. We consider here the relaxation of these hot edge-channel electrons through longitudinal-optical phonon emission. Our results show that the probability for an electron in the outermost edge channel to emit one or more phonons en route to a detector some microns distant along the edge channel suffers a double-exponential suppression with increasing magnetic field. This explains recent experimental observations. We also describe how the shape of the arrival-time distribution of electrons at the detector reflects the velocities of the electronic states post phonon emission. We show how this can give rise to pronounced oscillations in the arrival-time-distribution width as a function of magnetic field or electron energy., 11 pages; 6 figs

The waiting time distribution (WTD) is a common tool for analyzing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete, or where it is favourable to discuss the dynamics on a discretized and a continuous level in parallel. An example is the hindered motion of particles through potential landscapes with barriers. In the present paper we propose a consistent generalization of the WTD from the discrete case to situations where the particles perform continuous barrier crossing characterized by a finite duration. To this end, we introduce a recipe to calculate the WTD from the Fokker-Planck (Smoluchowski) equation. In contrast to the closely related first passage time distribution (FPTD), which is frequently used to describe continuous processes, the WTD contains information about the direction of motion. As an application, we consider the paradigmatic example of an overdamped particle diffusing through a washboard potential. To verify the approach and to elucidate its numerical implications, we compare the WTD defined via the Smoluchowski equation with data from direct simulation of the underlying Langevin equation and find full consistency provided that the jumps in the Langevin approach are defined properly. Moreover, for sufficiently large energy barriers, the WTD defined via the Smoluchowski equation becomes consistent with that resulting from the analytical solution of a (two-state) master equation model for the short-time dynamics developed previously by us [Phys. Rev. E 86, 061135 (2012)]. Thus, our approach ``interpolates'' between these two types of stochastic motion. We illustrate our approach for both symmetric systems and systems under constant force.

We consider coherent feedback control of quantum transport and focus on the application of simple controllers and the effects of a finite bias voltage. We show that simple single-parameter controllers can give rise to a range of useful effects such as amplification of changes in plant transmission, increased resolution of energy filtration, and the detection of differences between otherwise indistinguishable plants. We explore how these effects are impacted by the phase-averaging effects associated with the application of a finite bias and identify important voltage scales for the maintenance of the functionalities achieved through feedback control., Comment: 18 pages; 6 figs

We discuss control of the quantum-transport properties of a mesoscopic device by connecting it in a coherent feedback loop with a quantum-mechanical controller. We work in a scattering approach and derive results for the combined scattering matrix of the device-controller system and determine the conditions under which the controller can exert ideal control on the output characteristics. As concrete example we consider the use of feedback to optimise the conductance of a chaotic quantum dot and investigate effects of controller dimension and decoherence. In both respects we find that the performance of the feedback geometry is well in excess of that offered by a simple series configuration., 8 pages; 7 figures

We define a quantum witness for high-mass matter-wave interferometers that allows us to test fundamental assumptions of macroscopic realism. We propose an experimental realisation using absorptive laser gratings and show that such systems can strongly violate a macrorealistic quantum-witness equality. The measurement of the witness can therefore provide clear evidence of physics beyond macrorealism for macromolecules and nanoparticles., 5 pages; 4 figs

We report on a stringent test of the non-classicality of the motion of a massive quantum particle, which propagates on a discrete lattice. Measuring temporal correlations of the position of single atoms performing a quantum walk, we observe a $6\sigma$ violation of the Leggett-Garg inequality. Our results rigorously excludes (i.e. falsifies) any explanation of quantum transport based on classical, well-defined trajectories. We use so-called ideal negative measurements -- an essential requisite for any genuine Leggett-Garg test -- to acquire information about the atom's position, yet avoiding any direct interaction with it. The interaction-free measurement is based on a novel atom transport system, which allows us to directly probe the absence rather than the presence of atoms at a chosen lattice site. Beyond the fundamental aspect of this test, we demonstrate the application of the Leggett-Garg correlation function as a witness of quantum superposition. We here employ the witness to discriminate different types of walks spanning from merely classical to wholly quantum dynamics., Comment: 10 pages, 4 figures

We study the full-counting statistics of current of large open systems through the application of random-matrix theory to transition-rate matrices. We develop a method for calculating the ensemble-averaged current-cumulant generating functions based on an expansion in terms of the inverse system size. We investigate how different symmetry properties and different counting schemes affect the results.

We show that the quantum bound for temporal correlations in a Leggett-Garg test, analogous to the Tsirelson bound for spatial correlations in a Bell test, strongly depends on the number of levels $N$ that can be accessed by the measurement apparatus via projective measurements. We provide exact bounds for small $N$, that exceed the known bound for the Leggett-Garg inequality, and show that in the limit $N\rightarrow \infty$ the Leggett-Garg inequality can be violated up to its algebraic maximum., 6 pages, 2 figures

We consider a driven single mode Dicke-Hamiltonian coupled to a dissipative zero-temperature bath. We derive the cumulant generating function for emitted photons of this quantum-critical system by using a $P$-representation of the master equation in the thermodynamic limit. This cumulant generating function is shown to consist of two parts: a macroscopic component, which is Poissonian in nature with characteristic rate proportional to the order parameter of the system; and a part describing fluctuations which is non-trivial in form and divergent around the quantum phase transition., Comment: 9 pages, 5 figures

We study an atom-cavity system in which the cavity has several degenerate transverse modes. Mode-resolved cavity transmission spectroscopy reveals well-resolved atom-cavity resonances for several cavity modes, a signature of collective strong coupling for the different modes. Furthermore, the experiment shows that the cavity modes are coupled via the atomic ensemble contained in the cavity. The experimental observations are supported by a detailed theoretical analysis. The work paves the way to the use of interacting degenerate modes in cavity-based quantum information processing, where qubits corresponding to different cavity modes interact via an atom shared by the two modes. Our results are also relevant to the experimental realization of quantum spin glasses with ultracold atoms., Comment: Published in April 2013 in Physical Review A

We present a transport setup of coupled quantum dots that enables the creation of spatially separated spin-entangled two-electron dark states. We prove the existence of an entangled transport dark state by investigating the system Hamiltonian without coupling to the electronic reservoirs. In the transport regime the entangled dark state which corresponds to a singlet has a strongly enhanced Fano factor compared to the dark state which corresponds to a mixture of the triplet states. Furthermore we calculate the concurrence of the occupying electrons to show the degree of entanglement in the transport regime., Comment: 9 pages and 3 figures

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence., We present a theoretical study of a hybrid circuit-quantum electrodynamics system composed of two semiconducting charge-qubits confined in a microwave resonator. The qubits are defined in terms of the charge states of two spatially separated double quantum dots (DQDs) which are coupled to the same photon mode in the microwave resonator. We analyse a transport setup where each DQD is attached to electronic reservoirs and biased out-of-equilibrium by a large voltage, and study how electron transport across each DQD is modified by the coupling to the common resonator. In particular, we show that the inelastic current through each DQD reflects an indirect qubit-qubit interaction mediated by off-resonant photons in the microwave resonator. As a result of this interaction, both charge qubits stay entangled in the steady (dissipative) state. Finite shot noise cross-correlations between currents across distant DQDs are another manifestation of this nontrivial steady-state entanglement. © IOP Publishing and Deutsche Physikalische Gesellschaft., This work was supported by the European Commission (STREP PICC), the Alexander von Humboldt Foundation, the DAAD and DFG grant numbers BR 1528/7-1, 1528/8-1, SFB 910 and GRK 1558 and the Spanish MINECO through grant numbers FIS2009-08744 and FIS2012-33521.

We establish a set of nonequilibrium quantum phase transitions in the Ising model driven under monochromatic nonadiabatic modulation of the transverse field. We show that besides the Ising-like critical behavior, the system exhibits an anisotropic transition which is absent in equilibrium. The nonequilibrium quantum phases correspond to states which are synchronized with the external control in the long-time dynamics., Comment: 10 pages, 5 figures. Published in Physical Review A

We consider an ensemble of three-level particles in lambda-configuration interacting with two bosonic modes. The Hamiltonian has the form of a generalized Dicke-model. We show that in the thermodynamic limit this model supports a superradiant quantum phase transition. Remarkably, this can be both a first and a second order phase transition. A connection of the phase diagram to the symmetries of the Hamiltonian is also given. In addition, we show that this model can describe atoms interacting with an electromagnetic field in which the microscopic Hamiltonian includes a diamagnetic contribution. Even though the parameters of the atomic system respect the Thomas--Reiche--Kuhn sum rule, the system still shows a superradiant phase transition., Comment: 9 pages, 3 figures

We consider maximal violations of the Leggett-Garg inequality, obtained by maximising over all possible measurement operators, in relation to non-unitary aspects of the system dynamics. We model the action of an environment on a qubit in terms of generic quantum channels and relate the maximal value of the Leggett-Garg correlator to the channel parameters. We focus on unital channels, and hence on decoherence. In certain important cases, exact relations between the channel parameters and maximal violations can be found. Moreover, we demonstrate the existence of distinct thresholds for the channel parameters, below which no violation of the Leggett-Garg inequality can occur., 7 pages; 3 figures

We establish a set of nonequilibrium quantum phase transitions in the Lipkin-Meshkov-Glick model under monochromatic modulation of the inter-particle interaction. We show that the external driving induces a rich phase diagram that characterizes the multistability in the system. Interestingly, the number of stable configurations can be tuned by increasing the amplitude of the driving field. Furthermore, by studying the quantum evolution, we demonstrate that the system exhibits a set of quantum phases that correspond to dynamically stabilized states., 9 pages, 4 figures. This version contains corrected typos, new references, new figures, and a new appendix. Comments are welcome

We consider the violation of the Leggett-Garg inequality in electronic Mach-Zehnder inteferometers. This set-up has two distinct advantages over earlier quantum-transport proposals: firstly, the required correlation functions can be obtained without time-resolved measurements. Secondly, the geometry of an interferometer allows one to construct the correlation functions from ideal negative measurements, which addresses the non-invasiveness requirement of the Leggett-Garg inequality. We discuss two concrete realisations of these ideas: the first in quantum Hall edge-channels, the second in a double quantum dot interferometer., 11 pages, 5 figures

We investigate the dynamics of a single, overdamped colloidal particle, which is driven by a constant force through a one-dimensional periodic potential. We focus on systems with large barrier heights where the lowest-order cumulants of the density field, that is, average position and the mean-squared displacement, show nontrivial (non-diffusive) short-time behavior characterized by the appearance of plateaus. We demonstrate that this "cage-like" dynamics can be well described by a discretized master equation model involving two states (related to two positions) within each potential valley. Non-trivial predictions of our approach include analytic expressions for the plateau heights and an estimate of the "de-caging time" obtained from the study of deviations from Gaussian behaviour. The simplicity of our approach means that it offers a minimal model to describe the short-time behavior of systems with hindered dynamics., Comment: 8 pages, 6 figures

Made available in DSpace on 2022-04-29T04:22:53Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-07-18 We consider the Dicke model in the ultrastrong-coupling limit to investigate thermal phase transitions and their precursors at finite particle numbers N for bosonic and fermionic systems. We derive partition functions with degeneracy factors that account for the number of configurations and derive explicit expressions for the Landau free energy. This allows us to discuss the difference between the original Dicke (fermionic) and the bosonic case. We find a crossover between these two cases that shows up, for example, in the specific heat. © 2012 American Physical Society. Instituto de Física Teórica UNESP-São Paulo State University, Caixa Postal 70532-2, 01156-970 São Paulo, SP Institut für Theoretische Physik TU Berlin, Hardenbergstr. 36, D-10623 Berlin Instituto de Física Teórica UNESP-São Paulo State University, Caixa Postal 70532-2, 01156-970 São Paulo, SP

In quantum optics the $g^{(2)}$-function is a standard tool to investigate photon emission statistics. We define a $g^{(2)}$-function for electronic transport and use it to investigate the bunching and anti-bunching of electron currents. Importantly, we show that super-Poissonian electron statistics do not necessarily imply electron bunching, and that sub-Poissonian statistics do not imply anti-bunching. We discuss the information contained in $g^{(2)}(\tau)$ for several typical examples of transport through nano-structures such as few-level quantum dots., Comment: 8 pages, 5 figures

We derive a set of Leggett-Garg inequalities (temporal Bell's inequalities) for the moment generating function of charge transferred through a conductor. Violation of these inequalities demonstrates the absence of a macroscopic-real description of the transport process. We show how these inequalities can be violated by quantum-mechanical systems and consider transport through normal and superconducting single-electron transistors as examples., Comment: 5 pages; 3 figures

We extend the second-order von Neumann approach within the generalized master equation formalism for quantum electronic transport to include the counting field. The resulting non-Markovian evolution equation for the reduced density matrix of the system resolved with respect to the number of transported charges enables the evaluation of the noise and higher-order cumulants of the full counting statistics. We apply this formalism to an analytically solvable model of a single-level quantum dot coupled to highly biased leads with Lorentzian energy-dependent tunnel coupling and demonstrate that, although reproducing exactly the mean current, the resonant tunneling approximation is not exact for the noise and higher order cumulants. Even if it may fail in the regime of strongly non-Markovian dynamics, this approach generically improves results of lower-order and/or Markovian approaches., Comment: 5 pages, 1 figure; little changes; very similar to the published version