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Sep 19, 2013
09/13

by
A. H. Werner; T. Franz; R. F. Werner

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We propose a quantum key distribution protocol based on a quantum retrodiction protocol, known as the Mean King problem. The protocol uses a two way quantum channel. We show security against coherent attacks in a transmission error free scenario, even if Eve is allowed to attack both transmissions. This establishes a connection between retrodiction and key distribution.

Source: http://arxiv.org/abs/0909.3375v1

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1.0

Jun 29, 2018
06/18

by
H. Wilming; M. J. Kastoryano; A. H. Werner; J. Eisert

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A cornerstone of the theory of phase transitions is the observation that many-body systems exhibiting a spontaneous symmetry breaking in the thermodynamic limit generally show extensive fluctuations of an order parameter in large but finite systems. In this work, we introduce the dynamical analogue of such a theory. Specifically, we consider local dissipative dynamics preparing a steady-state of quantum spins on a lattice exhibiting a discrete or continuous symmetry but with extensive...

Topics: Quantum Physics, Other Condensed Matter, Statistical Mechanics, Condensed Matter, Mathematics,...

Source: http://arxiv.org/abs/1602.01108

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1.0

Jun 29, 2018
06/18

by
M. Goihl; M. Friesdorf; A. H. Werner; W. Brown; J. Eisert

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The phenomenon of many-body localised (MBL) systems has attracted significant interest in recent years, for its intriguing implications from a perspective of both condensed-matter and statistical physics: they are insulators even at non-zero temperature and fail to thermalise, violating expectations from quantum statistical mechanics. What is more, recent seminal experimental developments with ultra-cold atoms in optical lattices constituting analog quantum simulators have pushed many-body...

Topics: Statistical Mechanics, Condensed Matter, Quantum Gases, Quantum Physics

Source: http://arxiv.org/abs/1601.02666

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26

Sep 23, 2013
09/13

by
F. A. Grünbaum; L. Velázquez; A. H. Werner; R. F. Werner

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We consider quantum dynamical systems specified by a unitary operator U and an initial state vector \phi. In each step the unitary is followed by a projective measurement checking whether the system has returned to the initial state. We call the system recurrent if this eventually happens with probability one. We show that recurrence is equivalent to the absence of an absolutely continuous part from the spectral measure of U with respect to \phi. We also show that in the recurrent case the...

Source: http://arxiv.org/abs/1202.3903v3

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2.0

Jun 30, 2018
06/18

by
M. Friesdorf; A. H. Werner; W. Brown; V. B. Scholz; J. Eisert

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The phenomenon of many-body localisation received a lot of attention recently, both for its implications in condensed-matter physics of allowing systems to be an insulator even at non-zero temperature as well as in the context of the foundations of quantum statistical mechanics, providing examples of systems showing the absence of thermalisation following out-of-equilibrium dynamics. In this work, we establish a novel link between dynamical properties - the absence of a group velocity and...

Topics: Quantum Physics, Mathematics, Mathematical Physics, Disordered Systems and Neural Networks,...

Source: http://arxiv.org/abs/1409.1252

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0.0

Jun 30, 2018
06/18

by
C. Cedzich; F. A. Grünbaum; L. Velázquez; A. H. Werner; R. F. Werner

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Khrushchev's formula is the cornerstone of the so called Khrushchev theory, a body of results which has revolutionized the theory of orthogonal polynomials on the unit circle. This formula can be understood as a factorization of the Schur function for an orthogonal polynomial modification of a measure on the unit circle. No such formula is known in the case of matrix-valued measures. This constitutes the main obstacle to generalize Khrushchev theory to the matrix-valued setting which we...

Topics: Mathematics, Functional Analysis, Mathematical Physics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1405.0985

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0.0

Jun 30, 2018
06/18

by
A. H. Werner; D. Jaschke; P. Silvi; M. Kliesch; T. Calarco; J. Eisert; S. Montangero

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Open many-body quantum systems play an important role in quantum optics and condensed-matter physics, and capture phenomena like transport, interplay between Hamiltonian and incoherent dynamics, and topological order generated by dissipation. We introduce a versatile and practical method to numerically simulate one-dimensional open quantum many-body dynamics using tensor networks. It is based on representing mixed quantum states in a locally purified form, which guarantees that positivity is...

Topics: Quantum Physics, Strongly Correlated Electrons, Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1412.5746

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Jun 26, 2018
06/18

by
C. Cedzich; F. A. Grünbaum; C. Stahl; L. Velázquez; A. H. Werner; R. F. Werner

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We outline a theory of symmetry protected topological phases of one-dimensional quantum walks. We assume spectral gaps around the symmetry-distinguished points +1 and -1, in which only discrete eigenvalues are allowed. The phase classification by integer or binary indices extends the classification known for translation invariant systems in terms of their band structure. However, our theory requires no translation invariance whatsoever, and the indices we define in this general setting are...

Topics: Other Condensed Matter, Mathematics, Quantum Physics, Mathematical Physics, Condensed Matter

Source: http://arxiv.org/abs/1502.02592

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1.0

Jun 30, 2018
06/18

by
M. Friesdorf; A. H. Werner; M. Goihl; J. Eisert; W. Brown

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Interacting quantum many-body systems are usually expected to thermalise, in the sense that the evolution of local expectation values approach a stationary value resembling a thermal ensemble. This intuition is notably contradicted in systems exhibiting many-body localisation, a phenomenon receiving significant recent attention. One of its most intriguing features is that, in stark contrast to the non-interacting case, entanglement of states grows without limit over time, albeit slowly. In this...

Topics: Quantum Physics, Mathematics, Mathematical Physics, Disordered Systems and Neural Networks,...

Source: http://arxiv.org/abs/1412.5605

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Sep 22, 2013
09/13

by
C. Cedzich; T. Rybár; A. H. Werner; A. Alberti; M. Genske; R. F. Werner

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We study one-dimensional quantum walks in a homogeneous electric field. The field is given by a phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion and Anderson localization, depend very sensitively on the value of the electric field $\Phi$, e.g., on whether $\Phi/(2\pi)$ is rational or irrational. We relate these properties to the continued fraction expansion of the field. When the...

Source: http://arxiv.org/abs/1302.2081v1

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0.0

Jun 29, 2018
06/18

by
C. Cedzich; T. Geib; F. A. Grünbaum; C. Stahl; L. Velázquez; A. H. Werner; R. F. Werner

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We give a topological classification of quantum walks on an infinite 1D lattice, which obey one of the discrete symmetry groups of the tenfold way, have a gap around some eigenvalues at symmetry protected points, and satisfy a mild locality condition. No translation invariance is assumed. The classification is parameterized by three indices, taking values in a group, which is either trivial, the group of integers, or the group of integers modulo 2, depending on the type of symmetry. The...

Topics: Mathematics, Quantum Physics, Condensed Matter, Mathematical Physics, Other Condensed Matter

Source: http://arxiv.org/abs/1611.04439