arXiv subjects

Igor Jex

Publications and source records attributed to Igor Jex.

At least 55 records · Page 3Linked to original sources

arXiv2015

Strongly trapped two-dimensional quantum walks

Discrete time quantum walks (DTQWs) are nontrivial generalizations of random walks with a broad scope of applications. In particular, they can be used as computational primitives, and they are suitable tools for simulating other quantum systems. DTQWs usually spread ballistically due to their quantumness. In some cases, however, they can remain localized at their initial state (trapping). The trapping and other fundamental properties of DTQWs are determined by the choice of the coin operator. We introduce and analyze an up to now uncharted type of walks driven by a coin class leading to strong trapping, complementing the known list of walks. This class of walks exhibit a number of exciting properties with the possible applications ranging from light pulse trapping in a medium to topological effects and quantum search.

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arXiv2014

Selective dynamical decoupling for quantum state transfer

State transfer across discrete quantum networks is one of the elementary tasks of quantum information processing. Its aim is the faithful placement of information into a specific position in the network. However, all physical systems suffer from imperfections, which can severely limit the transfer fidelity. We present selective dynamical decoupling schemes which are capable of stabilizing imperfect quantum state transfer protocols on the model of a bent linear qubit chain. The efficiency of the schemes is tested and verified in numerical simulations on a number of realistic cases. The simulations demonstrate that these selective dynamical decoupling schemes are capable of suppressing unwanted errors in quantum state transfer protocols efficiently.

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arXiv2014

N00N states from a single non-linear directional coupler

In the quest for applicable quantum information technology miniaturised, compact and scalable sources are of paramount importance. Here, we present the concept for the generation of 2-photon N00N states without further post-processing in a single non-linear optical element. Based upon a periodically poled waveguide coupler, we present the principle of state generation via type-0 parametric down-conversion inside this type of devices. With the eigenmode description of the linear optical element, we utilise the delocalised photon pair generation to generate a N00N state in the measurement basis. We show, that we are able to eliminate the need for narrow-band spectral filtering, as well as for phase-stabilisation of the pump light, making this approach an elegant way to produce 2-photon N00N states.

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arXiv2014

Limit distributions of three-state quantum walks: the role of coin eigenstates

We analyze two families of three-state quantum walks which show the localization effect. We focus on the role of the initial coin state and its coherence in controlling the properties of the quantum walk. In particular, we show that the description of the walk simplifies considerably when the initial coin state is decomposed in the basis formed by the eigenvectors of the coin operator. This allows us to express the limit distributions in a much more convenient form. Consequently, striking features which are hidden in the standard basis description are easily identified. Moreover, the dependence of moments of the position distribution on the initial coin state can be analyzed in full detail. In particular, we find that in the eigenvector basis the even moments and the localization probability at the origin depend only on incoherent combination of probabilities. In contrast, odd moments and localization outside the origin are affected by the coherence of the initial coin state.

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arXiv2014

Driven Quantum Walks

In this letter we introduce the concept of a driven quantum walk. This work is motivated by recent theoretical and experimental progress that combines quantum walks and parametric down- conversion, leading to fundamentally different phenomena. We compare these striking differences by relating the driven quantum walks to the original quantum walk. Next, we illustrate typical dynamics of such systems and show these walks can be controlled by various pump configurations and phase matchings. Finally, we end by proposing an application of this process based on a quantum search algorithm that performs faster than a classical search.

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arXiv2014

Discrete time quantum walks on percolation graphs

Randomly breaking connections in a graph alters its transport properties, a model used to describe percolation. In the case of quantum walks, dynamic percolation graphs represent a special type of imperfections, where the connections appear and disappear randomly in each step during the time evolution. The resulting open system dynamics is hard to treat numerically in general. We shortly review the literature on this problem. We then present our method to solve the evolution on finite percolation graphs in the long time limit, applying the asymptotic methods concerning random unitary maps. We work out the case of one dimensional chains in detail and provide a concrete, step by step numerical example in order to give more insight into the possible asymptotic behavior. The results about the case of the two-dimensional integer lattice are summarized, focusing on the Grover type coin operator.

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arXiv2014

Controlling quantum walks with coin eigenstates

The control of quantum walk is made particularly transparent when the initial state is expressed in terms of the eigenstates of the coin operator. We show that the group-velocity density acquires a much simpler form when expressed in this basis. This allows us to obtain a much deeper understanding of the role of the initial coin state on the dynamics of quantum walks and control it. We find that the eigenvectors of the coin result in an extremal regime of a quantum walk. The approach is illustrated on two examples of quantum walks on a line.

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arXiv2014

Percolation induced effects in 2D coined quantum walks: analytic asymptotic solutions

Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the long-time behaviour appears untreatable with direct numerical methods. We develop novel analytic methods based on the theory of random unitary operations which help us to determine explicitly the asymptotic dynamics of quantum walks on 2D finite integer lattices with percolation. Based on this theory we find new unexpected features of percolated walks like asymptotic position inhomogeneity or special directional symmetry breaking.

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arXiv2013

Spatio-spectral characteristics of parametric down-conversion in waveguide arrays

High dimensional quantum states are of fundamental interest for quantum information processing. They give access to large Hilbert spaces and, in turn, enable the encoding of quantum information on multiple modes. One method to create such quantum states is parametric down-conversion (PDC) in waveguide arrays (WGAs) which allows for the creation of highly entangled photon-pairs in controlled, easily accessible spatial modes, with unique spectral properties. In this paper we examine both theoretically and experimentally the PDC process in a lithium niobate WGA. We measure the spatial and spectral properties of the emitted photon-pairs, revealing strong correlations between spectral and spatial degrees of freedom of the created photons. Our measurements show that, in contrast to prior theoretical approaches, spectrally dependent coupling effects have to be taken into account in the theory of PDC in WGAs. To interpret the results, we developed a theoretical model specifically taking into account spectrally dependent coupling effects, which further enables us to explore the capabilities and limitations for engineering the spatial correlations of the generated quantum states.

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arXiv2012

Asymptotic properties of quantum Markov chains

The asymptotic dynamics of quantum Markov chains generated by the most general physically relevant quantum operations is investigated. It is shown that it is confined to an attractor space on which the resulting quantum Markov chain is diagonalizable. A construction procedure of a basis of this attractor space and its associated dual basis is presented. It applies whenever a strictly positive quantum state exists which is contracted or left invariant by the generating quantum operation. Moreover, algebraic relations between the attractor space and Kraus operators involved in the definition of a quantum Markov chain are derived. This construction is not only expected to offer significant computational advantages in cases in which the dimension of the Hilbert space is large and the dimension of the attractor space is small but it also sheds new light onto the relation between the asymptotic dynamics of quantum Markov chains and fixed points of their generating quantum operations.

math-ph↗

arXiv2012

Asymptotic dynamics of coined quantum walks on percolation graphs

Quantum walks obey unitary dynamics: they form closed quantum systems. The system becomes open if the walk suffers from imperfections represented as missing links on the underlying basic graph structure, described by dynamical percolation. Openness of the system's dynamics creates decoherence, leading to strong mixing. We present a method to analytically solve the asymptotic dynamics of coined, percolated quantum walks for a general graph structure. For the case of a circle and a linear graph we derive the explicit form of the asymptotic states. We find that a rich variety of asymptotic evolutions occur: not only the fully mixed state, but other stationary states; stable periodic and quasiperiodic oscillations can emerge, depending on the coin operator, the initial state, and the topology of the underlying graph.

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arXiv2012

Continuous deformations of the Grover walk preserving localization

The three-state Grover walk on a line exhibits the localization effect characterized by a non-vanishing probability of the particle to stay at the origin. We present two continuous deformations of the Grover walk which preserve its localization nature. The resulting quantum walks differ in the rate at which they spread through the lattice. The velocities of the left and right-traveling probability peaks are given by the maximum of the group velocity. We find the explicit form of peak velocities in dependence on the coin parameter. Our results show that localization of the quantum walk is not a singular property of an isolated coin operator but can be found for entire families of coins.

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arXiv2012

Increasing the dimensionality of quantum walks using multiple walkers

We show that with the addition of multiple walkers, quantum walks on a line can be transformed into lattice graphs of higher dimension. Thus, multi-walker walks can simulate single-walker walks on higher dimensional graphs and vice versa. This exponential complexity opens up new applications for present-day quantum walk experiments. We discuss the applications of such higher-dimensional structures and how they relate to linear optics quantum computing. In particular we show that multi-walker quantum walks are equivalent to the BosonSampling model for linear optics quantum computation proposed by Aaronson & Arkhipov. With the addition of control over phase-defects in the lattice, which can be simulated with entangling gates, asymmetric lattice structures can be constructed which are universal for quantum computation.

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arXiv2012

A 2D Quantum Walk Simulation of Two-Particle Dynamics

Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a lattice, demonstrating a scalable quantum walk on a non-trivial graph structure. We realized a coherent quantum walk over 12 steps and 169 positions using an optical fiber network. With our broad spectrum of quantum coins we were able to simulate the creation of entanglement in bipartite systems with conditioned interactions. Introducing dynamic control allowed for the investigation of effects such as strong non-linearities or two-particle scattering. Our results illustrate the potential of quantum walks as a route for simulating and understanding complex quantum systems.

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arXiv2011

Entanglement and decoherence: fragile and robust entanglement

The destruction of entanglement of open quantum systems by decoherence is investigated in the asymptotic long-time limit. Starting from a general and analytically solvable decoherence model which does not involve any weak-coupling or Markovian assumption it is shown that two fundamentally different classes of entangled states can be distinguished. Quantum states of the first class are fragile against decoherence so that they can be disentangled asymptotically even if coherences between pointer states are still present. Quantum states of the second type are robust against decoherence. Asymptotically they can be disentangled only if also decoherence is perfect. A simple criterion for identifying these two classes on the basis of two-qubit entanglement is presented.

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arXiv2011

Quantum Walk with a four-dimensional coin

We examine the physical implementation of a discrete time quantum walk with a four-dimensional coin. Our quantum walker is a photon moving repeatedly through a time delay loop, with time being our position space. The quantum coin is implemented using the internal states of the photon: the polarization and two of the orbital angular momentum states. We demonstrate how to implement this physically and what components would be needed. We then illustrate some of the results that could be obtained by performing the experiment.

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arXiv2011

Multi-walker discrete time quantum walks on arbitrary graphs, their properties, and their photonic implementation

Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more naturally to some physical implementations, such as linear optics. Numerous authors have considered walks with one or two walkers, on one dimensional graphs, and several experimental demonstrations have been performed. In this paper we discuss generalizing the model of discrete time quantum walks to the case of an arbitrary number of walkers acting on arbitrary graph structures. We present a formalism which allows for analysis of such situations, and several example scenarios for how our techniques can be applied. We consider the most important features of quantum walks -- measurement, distinguishability, characterization, and the distinction between classical and quantum interference. We also discuss the potential for physical implementation in the context of linear optics, which is of relevance to present day experiments.

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arXiv2010

General U(4) gate for photon polarization and orbital angular momentum

We examine the implementation of an arbitrary U(4) gate consisting of CNOT gates and single qubit unitary gates for the Hilbert space of photon spin polarization and two states of photon orbital angular momentum. Our scheme improves over a recently proposed one that uses q-plates because the fidelity is limited only by losses thus in principle it could be used to achieve a perfect transformation.

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