Decoherence and Disorder in Quantum Walks: From Ballistic Spread to Localization

Schreiber, Andreas; Cassemiro, K. N.; Potoček, Václav; Gábris, Aurél; Jex, Igor; Silberhorn, Christine

doi:10.1103/physrevlett.106.180403

Cited by 381 publications

(410 citation statements)

References 31 publications

(31 reference statements)

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“…Besides theoretical [18,19] and numerical [20] studies, this effect has also been observed experimentally [21].…”

Section: Introductionmentioning

confidence: 62%

Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk

Rakovszky

Asbóth

2015

Phys. Rev. A

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Quantum walks are promising for information processing tasks because in regular graphs they spread quadratically more rapidly than random walks. Static disorder, however, can turn the tables: unlike random walks, quantum walks can suffer Anderson localization, with their wave function staying within a finite region even in the infinite time limit, with a probability exponentially close to 1. It is thus important to understand when a quantum walk will be Anderson localized and when we can expect it to spread to infinity even in the presence of disorder. In this work we analyze the response of a one-dimensional quantum walk-the split-step walk-to different forms of static disorder. We find that introducing static, symmetry-preserving disorder in the parameters of the walk leads to Anderson localization. In the completely disordered limit, however, a delocalization transition occurs, and the walk spreads subdiffusively to infinity. Using an efficient numerical algorithm, we calculate the bulk topological invariants of the disordered walk and find that the disorder-induced Anderson localization and delocalization transitions are governed by the topological phases of the quantum walk.

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“…Besides theoretical [18,19] and numerical [20] studies, this effect has also been observed experimentally [21].…”

Section: Introductionmentioning

confidence: 62%

Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk

Rakovszky

Asbóth

2015

Phys. Rev. A

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“…Depending on the types of disorder and symmetries, experiments and theory on DTQWs have already seen both Anderson localization, 39 and delocalization. 40 Our generalized scattering matrix formalism allows a continuation of this research to more general multistep DTQWs.…”

Section: Discussionmentioning

confidence: 99%

Scattering theory of topological phases in discrete-time quantum walks

2014

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One-dimensional discrete-time quantum walks show a rich spectrum of topological phases that have so far been exclusively analysed based on the Floquet operator in momentum space. In this work we introduce an alternative approach to topology which is based on the scattering matrix of a quantum walk, adapting concepts from time-independent systems. For quantum walks with gaps in the quasienergy spectrum at 0 and π, we find three different types of topological invariants, which apply dependent on the symmetries of the system. These determine the number of protected boundary states at an interface between two quantum walk regions. Unbalanced quantum walks on the other hand are characterised by the number of perfectly transmitting unidirectional modes they support, which is equal to their non-trivial quasienergy winding. Our classification provides a unified framework that includes all known types of topology in one dimensional discrete-time quantum walks and is very well suited for the analysis of finite size and disorder effects. We provide a simple scheme to directly measure the topological invariants in an optical quantum walk experiment.

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“…Such configurations have been systematically employed to investigate a number of issues ranging from discrete quantum walks [44][45][46][47] to Bloch oscillations and fractal patterns [43,48]. While spatial realizations of such mesh lattices have also been reported [47,49], time-multiplexed fiber loop schemes have so far demonstrated a high degree of flexibility [43,45].…”

Section: Optical Mesh Lattices In the Time Domainmentioning

confidence: 99%

Optical mesh lattices withPTsymmetry

Miri

Regensburger

Peschel³

et al. 2012

Phys. Rev. A

111

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We investigate a new class of optical mesh periodic structures that are discretized in both the transverse and longitudinal directions. These networks are composed of waveguide arrays that are discretely coupled while phase elements are also inserted to discretely control their effective potentials and can be realized both in the temporal and the spatial domain. Their band structure and impulse response is studied in both the passive and parity-time (PT ) symmetric regime. The possibility of band merging and the emergence of exceptional points along with the associated optical dynamics are considered in detail both above and below the PT -symmetry breaking point. Finally unidirectional invisibility in PT -synthetic mesh lattices is also examined along with possible superluminal light transport dynamics.

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Decoherence and Disorder in Quantum Walks: From Ballistic Spread to Localization

Cited by 381 publications

References 31 publications

Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk

Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk

Scattering theory of topological phases in discrete-time quantum walks

Optical mesh lattices withPTsymmetry

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