Using Qubits to Measure Fidelity in Mesoscopic Systems

We point out the similarities in the definition of the `fidelity' of a quantum system and the generating function determining the full counting statistics of charge transport through a quantum wire and suggest to use flux- or charge qubits for their measurement. As an application we use the notion of fidelity within a first-quantized formalism in order to derive new results and insights on the generating function of the full counting statistics.Comment: 5 pages, 1 figur

Full counting statistics for noninteracting fermions: Exact finite temperature results and generalized long time approximation

Exact numerical results for the full counting statistics (FCS) of a one-dimensional tight-binding model of noninteracting electrons are presented at finite temperatures using an identity recently presented by Abanov and Ivanov. A similar idea is used to derive a new expression for the cumulant generating function for a system consisting of two quasi-one-dimensional leads connected by a quantum dot in the long time limit. This provides a generalization of the Levitov-Lesovik formula for such systems.Comment: 17 pages, 6 figures, extended introduction, additional comment

Full counting statistics for noninteracting fermions: Joint probability distributions

The joint probability distribution in the full counting statistics (FCS) for noninteracting electrons is discussed for an arbitrary number of initially separate subsystems which are connected at t=0 and separated at a later time. A simple method to obtain the leading order long time contribution to the logarithm of the characteristic function is presented which simplifies earlier approaches. New explicit results for the determinant involving the scattering matrices are found. The joint probability distribution for two leads is discussed for Y-junctions and dots connected to four leads.Comment: 17 pages, 3 figure

Wave-packet Formalism of Full Counting Statistics

We make use of the first-quantized wave-packet formulation of the full counting statistics to describe charge transport of noninteracting electrons in a mesoscopic device. We derive various expressions for the characteristic function generating the full counting statistics, accounting for both energy and time dependence in the scattering process and including exchange effects due to finite overlap of the incoming wave packets. We apply our results to describe the generic statistical properties of a two-fermion scattering event and find, among other features, sub-binomial statistics for nonentangled incoming states (Slater rank 1), while entangled states (Slater rank 2) may generate super-binomial (and even super-Poissonian) noise, a feature that can be used as a spin singlet-triplet detector. Another application is concerned with the constant-voltage case, where we generalize the original result of Levitov-Lesovik to account for energy-dependent scattering and finite measurement time, including short time measurements, where Pauli blocking becomes important.Comment: 20 pages, 5 figures; major update, new figures and explanations included as well as a discussion about finite temperatures and subleading logarithmic term

Partitioning of on-demand electron pairs

We demonstrate the high fidelity splitting of electron pairs emitted on demand from a dynamic quantum dot by an electronic beam splitter. The fidelity of pair splitting is inferred from the coincidence of arrival in two detector paths probed by a measurement of the partitioning noise. The emission characteristic of the on-demand electron source is tunable from electrons being partitioned equally and independently to electron pairs being split with a fidelity of 90%. For low beam splitter transmittance we further find evidence of pair bunching violating statistical expectations for independent fermions

Prolonged NCX activation prevents SOD1 accumulation, reduces neuroinflammation, ameliorates motor behavior and prolongs survival in a ALS mouse model

Imbalance in cellular ionic homeostasis is a hallmark of several neurodegenerative diseases including Amyotrophic Lateral Sclerosis (ALS). Sodium-calcium exchanger (NCX) is a membrane antiporter that, operating in a bidirectional way, couples the exchange of Ca2+ and Na + ions in neurons and glial cells, thus controlling the intracellular homeostasis of these ions. Among the three NCX genes, NCX1 and NCX2 are widely expressed within the CNS, while NCX3 is present only in skeletal muscles and at lower levels of expression in selected brain regions. ALS mice showed a reduction in the expression and activity of NCX1 and NCX2 consistent with disease progression, therefore we aimed to investigate their role in ALS pathophysiology. Notably, we demonstrated that the pharmacological activation of NCX1 and NCX2 by the prolonged treatment of SOD1G93A mice with the newly synthesized compound neurounina: (1) prevented the reduction in NCX activity observed in spinal cord; (2) preserved motor neurons survival in the ventral spinal horn of SOD1G93A mice; (3) prevented the spinal cord accumulation of misfolded SOD1; (4) reduced astroglia and microglia activation and spared the resident microglia cells in the spinal cord; (5) improved the lifespan and mitigated motor symptoms of ALS mice. The present study highlights the significant role of NCX1 and NCX2 in the pathophysiology of this neurodegenerative disorder and paves the way for the design of a new pharmacological approach for ALS

Time ordering and counting statistics

The basic quantum mechanical relation between fluctuations of transported charge and current correlators is discussed. It is found that, as a rule, the correlators are to be time-ordered in an unusual way. Instances where the difference with the conventional ordering matters are illustrated by means of a simple scattering model. We apply the results to resolve a discrepancy concerning the third cumulant of charge transport across a quantum point contact.Comment: 19 pages, 1 figure; inconsequential mistake and typos correcte

Iron biogeochemistry across marine systems progress from the past decade

Based on an international workshop (Gothenburg, 14–16 May 2008), this review article aims to combine interdisciplinary knowledge from coastal and open ocean research on iron biogeochemistry. The major scientific findings of the past decade are structured into sections on natural and artificial iron fertilization, iron inputs into coastal and estuarine systems, colloidal iron and organic matter, and biological processes. Potential effects of global climate change, particularly ocean acidification, on iron biogeochemistry are discussed. The findings are synthesized into recommendations for future research areas

Non-Abelian statistics and topological quantum information processing in 1D wire networks

Topological quantum computation provides an elegant way around decoherence, as one encodes quantum information in a non-local fashion that the environment finds difficult to corrupt. Here we establish that one of the key operations---braiding of non-Abelian anyons---can be implemented in one-dimensional semiconductor wire networks. Previous work [Lutchyn et al., arXiv:1002.4033 and Oreg et al., arXiv:1003.1145] provided a recipe for driving semiconducting wires into a topological phase supporting long-sought particles known as Majorana fermions that can store topologically protected quantum information. Majorana fermions in this setting can be transported, created, and fused by applying locally tunable gates to the wire. More importantly, we show that networks of such wires allow braiding of Majorana fermions and that they exhibit non-Abelian statistics like vortices in a p+ip superconductor. We propose experimental setups that enable the Majorana fusion rules to be probed, along with networks that allow for efficient exchange of arbitrary numbers of Majorana fermions. This work paves a new path forward in topological quantum computation that benefits from physical transparency and experimental realism.Comment: 6 pages + 17 pages of Supp. Mat.; 10 figures. Supp. Mat. has doubled in size to establish results more rigorously; many other improvements as wel

Introduction to topological superconductivity and Majorana fermions

This short review article provides a pedagogical introduction to the rapidly growing research field of Majorana fermions in topological superconductors. We first discuss in some details the simplest "toy model" in which Majoranas appear, namely a one-dimensional tight-binding representation of a p-wave superconductor, introduced more than ten years ago by Kitaev. We then give a general introduction to the remarkable properties of Majorana fermions in condensed matter systems, such as their intrinsically non-local nature and exotic exchange statistics, and explain why these quasiparticles are suspected to be especially well suited for low-decoherence quantum information processing. We also discuss the experimentally promising (and perhaps already successfully realized) possibility of creating topological superconductors using semiconductors with strong spin-orbit coupling, proximity-coupled to standard s-wave superconductors and exposed to a magnetic field. The goal is to provide an introduction to the subject for experimentalists or theorists who are new to the field, focusing on the aspects which are most important for understanding the basic physics. The text should be accessible for readers with a basic understanding of quantum mechanics and second quantization, and does not require knowledge of quantum field theory or topological states of matter.Comment: 21 pages, 5 figure