Quantum Walks of SU(2)_k Anyons on a Ladder

We study the effects of braiding interactions on single anyon dynamics using a quantum walk model on a quasi-1-dimensional ladder filled with stationary anyons. The model includes loss of information of the coin and nonlocal fusion degrees of freedom on every second time step, such that the entanglement between the position states and the exponentially growing auxiliary degrees of freedom is lost. The computational complexity of numerical calculations reduces drastically from the fully coherent anyonic quantum walk model, allowing for relatively long simulations for anyons which are spin-1/2 irreps of SU(2)_k Chern-Simons theory. We find that for Abelian anyons, the walk retains the ballistic spreading velocity just like particles with trivial braiding statistics. For non-Abelian anyons, the numerical results indicate that the spreading velocity is linearly dependent on the number of time steps. By approximating the Kraus generators of the time evolution map by circulant matrices, it is shown that the spatial probability distribution for the k=2 walk, corresponding to Ising model anyons, is equal to the classical unbiased random walk distribution.Comment: 12 pages, 4 figure

Anyonic Quantum Walks

The one dimensional quantum walk of anyonic systems is presented. The anyonic walker performs braiding operations with stationary anyons of the same type ordered canonically on the line of the walk. Abelian as well as non-Abelian anyons are studied and it is shown that they have very different properties. Abelian anyonic walks demonstrate the expected quadratic quantum speedup. Non-Abelian anyonic walks are much more subtle. The exponential increase of the system's Hilbert space and the particular statistical evolution of non-Abelian anyons give a variety of new behaviors. The position distribution of the walker is related to Jones polynomials, topological invariants of the links created by the anyonic world-lines during the walk. Several examples such as the SU(2) level k and the quantum double models are considered that provide insight to the rich diffusion properties of anyons.Comment: 17 pages, 10 figure

Deterministic generation of an on-demand Fock state

We theoretically study the deterministic generation of photon Fock states on-demand using a protocol based on a Jaynes Cummings quantum random walk which includes damping. We then show how each of the steps of this protocol can be implemented in a low temperature solid-state quantum system with a Nitrogen-Vacancy centre in a nano-diamond coupled to a nearby high-Q optical cavity. By controlling the coupling duration between the NV and the cavity via the application of a time dependent Stark shift, and by increasing the decay rate of the NV via stimulated emission depletion (STED) a Fock state with high photon number can be generated on-demand. Our setup can be integrated on a chip and can be accurately controlled.Comment: 13 pages, 9 figure

Realization of Arbitrary Gates in Holonomic Quantum Computation

Among the many proposals for the realization of a quantum computer, holonomic quantum computation (HQC) is distinguished from the rest in that it is geometrical in nature and thus expected to be robust against decoherence. Here we analyze the realization of various quantum gates by solving the inverse problem: Given a unitary matrix, we develop a formalism by which we find loops in the parameter space generating this matrix as a holonomy. We demonstrate for the first time that such a one-qubit gate as the Hadamard gate and such two-qubit gates as the CNOT gate, the SWAP gate and the discrete Fourier transformation can be obtained with a single loop.Comment: 8 pages, 6 figure

Geometric phase in open systems

We calculate the geometric phase associated to the evolution of a system subjected to decoherence through a quantum-jump approach. The method is general and can be applied to many different physical systems. As examples, two main source of decoherence are considered: dephasing and spontaneous decay. We show that the geometric phase is completely insensitive to the former, i.e. it is independent of the number of jumps determined by the dephasing operator.Comment: 4 pages, 2 figures, RevTe

An expectation value expansion of Hermitian operators in a discrete Hilbert space

We discuss a real-valued expansion of any Hermitian operator defined in a Hilbert space of finite dimension N, where N is a prime number, or an integer power of a prime. The expansion has a direct interpretation in terms of the operator expectation values for a set of complementary bases. The expansion can be said to be the complement of the discrete Wigner function. We expect the expansion to be of use in quantum information applications since qubits typically are represented by a discrete, and finite-dimensional physical system of dimension N=2^p, where p is the number of qubits involved. As a particular example we use the expansion to prove that an intermediate measurement basis (a Breidbart basis) cannot be found if the Hilbert space dimension is 3 or 4.Comment: A mild update. In particular, I. D. Ivanovic's earlier derivation of the expansion is properly acknowledged. 16 pages, one PS figure, 1 table, written in RevTe

SafeDrones: Real-Time Reliability Evaluation of UAVs using Executable Digital Dependable Identities

The use of Unmanned Arial Vehicles (UAVs) offers many advantages across a variety of applications. However, safety assurance is a key barrier to widespread usage, especially given the unpredictable operational and environmental factors experienced by UAVs, which are hard to capture solely at design-time. This paper proposes a new reliability modeling approach called SafeDrones to help address this issue by enabling runtime reliability and risk assessment of UAVs. It is a prototype instantiation of the Executable Digital Dependable Identity (EDDI) concept, which aims to create a model-based solution for real-time, data-driven dependability assurance for multi-robot systems. By providing real-time reliability estimates, SafeDrones allows UAVs to update their missions accordingly in an adaptive manner

Quantum Computation and Information: Multi-Particle Aspects

This editorial explains the scope of the special issue and provides a thematic introduction to the contributed papers

Factorizations and Physical Representations

A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (J. Zak, Phys. Today, {\bf 23} (2), 51 (1970)), and related representations termed $q_{1}q_{2}$ representations (together with their conjugates) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M