Four Equivalent Versions of Non-Abelian Gerbes

We recall and partially improve four versions of smooth, non-abelian gerbes: Cech cocycles, classifying maps, bundle gerbes, and principal 2-bundles. We prove that all these four versions are equivalent, and so establish new relations between interesting recent developments. Prominent partial results we prove are a bijection between continuous and smooth non-abelian cohomology, and an explicit equivalence between bundle gerbes and principal 2-bundles as 2-stacks.Comment: 65 pages, v2: minor corrections, new Corollary 7.2 about equivariant gerbes; v3: again minor corrections; v3 is the final and published versio

Electron Waiting Times in Non-Markovian Quantum Transport

We formulate a quantum theory of electron waiting time distributions for charge transport in nano-structures described by non-Markovian generalized master equations. We illustrate our method by calculating the waiting time distribution of electron transport through a dissipative double quantum dot, where memory effects are present due to a strongly coupled heat bath. We consider the influence of non-Markovian dephasing on the distribution of electron waiting times and discuss how spectral properties of the heat bath may be detected through measurements of the electron waiting time.Comment: 4+ pages, 3 figure

Waiting time distributions of noninteracting fermions on a tight-binding chain

We consider the distribution of waiting times between non-interacting fermions on a tight-binding chain. We calculate the waiting time distribution for a quantum point contact and find a cross-over from Wigner-Dyson statistics at full transmission to Poisson statistics close to pinch-off as predicted by scattering theory. In addition, we consider several quantum dot structures for which we can associate oscillations in the waiting time distributions to internal energy scales of the scatterers. A detailed comparison with scattering theory and generalized master equations is provided. We focus on mesoscopic conductors, but our tight-binding models may also be realized in cold atomic gases.Comment: 13 pages, 10 figure

Teleporting photonic qudits using multimode quantum scissors

Teleportation plays an important role in the communication of quantum information between the nodes of a quantum network and is viewed as an essential ingredient for long-distance Quantum Cryptography. We describe a method to teleport the quantum information carried by a photon in a superposition of a number $d$ of light modes (a "qudit") by the help of $d$ additional photons based on transcription. A qudit encoded into a single excitation of $d$ light modes (in our case Laguerre-Gauss modes which carry orbital angular momentum) is transcribed to $d$ single-rail photonic qubits, which are spatially separated. Each single-rail qubit consists of a superposition of vacuum and a single photon in each one of the modes. After successful teleportation of each of the $d$ single-rail qubits by means of "quantum scissors" they are converted back into a qudit carried by a single photon which completes the teleportation scheme.Comment: Published in Nature Scientific Report

Quantum optical weak measurements can visualize photon dynamics in real time

An experiment is proposed to visualize stroboscopically in real time the dynamics of a photon oscillating between two cavities. The visualization is implemented by a sequence of weak measurements (POVM), which are carried out by probing one of the cavities with a Rydberg atom and detecting a resulting phase shift by Ramsey interferometry. This way to measure the number of photons in a cavity was experimentally realized by Brune et al.. We suggest a feedback mechanism which minimizes the disturbance due to the measurement and enables a detection of the original evolution of the radiation field. PACS numbers: 03.65.Ta, 32.80.-t, 03.67.-aComment: 4 pages revtex, replacement with revised version to appear in Phys. Rev. A. We now take into account the finite lifetime of the cavity and limited efficiencies to detect the energy of the meter atom

Measuring the non-separability of classically entangled vector vortex beams

Given the multitude of applications of vector vortex beams there is a need for robust tools to measure them. Here we exploit the non-separability of such beams, akin to entanglement of quantum states, to apply tools traditionally associated with quantum measurements to these classical fields. We apply three measures of non-separability: a Bell inequality, a concurrence, and an entanglement entropy to define the "vectorness" of such beams. In addition to providing novel tools for the analysis of vector beams, we also introduce the concept of classical entanglement to explain why these tools are appropriate in the first place

Security and entanglement in differential-phase-shift quantum key distribution

The differential-phase-shift quantum key distribution protocol is formalised as a prepare-and-measure scheme and translated into an equivalent entanglement-based protocol. A necessary condition for security is that Bob's measurement can detect the entanglement of the distributed state in the entanglement-based translation, which implies that his measurement is described by non-commuting POVM elements. This condition is shown to be met.Comment: 11 pages, 1 figur

Monitoring Quantum Oscillations with very small Disturbance

We present a new scheme to detect and visualize oscillations of a single quantum system in real time. The scheme is based upon a sequence of very weak generalized measurements, distinguished by their low disturbance and low information gain. Accumulating the information from the single measurements by means of an appropriate Bayesian Estimator, the actual oscillations can be monitored nevertheless with high accuracy and low disturbance. For this purpose only the minimum and the maximum expected oscillation frequency need to be known. The accumulation of information is based on a general derivation of the optimal estimator of the expectation value of a hermitian observable for a sequence of measurements. At any time it takes into account all the preceding measurement results.Comment: 6 pages, 1 figure, submitted to PR

Unitary Equivalence of Quantum Walks

A simple coined quantum walk in one dimension can be characterized by a $SU(2)$ operator with three parameters which represents the coin toss. However, different such coin toss operators lead to equivalent dynamics of the quantum walker. In this manuscript we present the unitary equivalence classes of quantum walks and show that all the nonequivalent quantum walks can be distinguished by a single parameter. Moreover, we argue that the electric quantum walks are equivalent to quantum walks with time dependent coin toss operator

Non-Markovian Toy Quantum Chain

We propose a simple structure for stationary non-Markovian quantum chains in the framework of collisional dynamics of open quantum systems. To this end, we modify the microscopic Markovian system--reservoir model, consider multiple collisions with each of the molecules with an overlap between the collisional time intervals. We show how the equivalent Markovian quantum chain can be constructed with the addition of satellite quantum memory to the system. We distinguish quantum from classical non-Markovianity. Moreover, we define the counts of non-Markovianity by the required number of satellite qubits and bits, respectively. As the particular measure of quantum non-Markovianity the discord of the satellite w.r.t. the system is suggested. Simplest qubit realizations are discussed, and the significance for real system--environment dynamics is also pointed out.Comment: 10 pages, 10 figure