New method of quantum dynamics simulation based on the quantum tomography

Arkhipov, A. S.; Lozovik, Yu. E.

doi:10.1016/j.physleta.2003.09.084

Cited by 20 publications

(16 citation statements)

References 31 publications

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“…Such a description seems promising in view of an effective MC sampling of the trajectories during the propagation. The quantum tomogram [2,3],…”

Section: Semiclassical Methodsmentioning

confidence: 99%

“…Such a description seems promising in view of an effective MC sampling of the trajectories during the propagation. The quantum tomogram [2,3], w(X, µ, ν, t) = dk dq dp 2π W (q, p, t)e −ik(X−µq−νp) , (12) relates to the Wigner function by a class of Radon transforms [6] which are characterised by µ and ν. Each tomogram contains a density information, and tuning (µ, ν) appropriately, we may continuously switch between coordinate and momentum representation.…”

Section: Semiclassical Methodsmentioning

confidence: 99%

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Numerical approaches to time evolution of complex quantum systems

et al. 2009

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We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev polynomials. The Chebyshev approach benefits from two advantages over the standard time-integration Crank-Nicholson scheme: speedup and efficiency. Potential competitors are semiclassical methods such as the Wigner-Moyal or quantum tomographic approaches. We outline the basic concepts of these techniques and benchmark their performance against the Chebyshev approach by monitoring the time evolution of a Gaussian wave packet in restricted one-dimensional (1D) geometries. Thereby the focus is on tunnelling processes and the motion in anharmonic potentials. Finally we apply the prominent Chebyshev technique to two highly non-trivial problems of current interest: (i) the injection of a particle in a disordered 2D graphene nanoribbon and (ii) the spatiotemporal evolution of polaron states in finite quantum systems. Here, depending on the disorder/electron-phonon coupling strength and the device dimensions, we observe transmission or localisation of the matter wave.Comment: 8 pages, 3 figure

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“…Such a description seems promising in view of an effective MC sampling of the trajectories during the propagation. The quantum tomogram [2,3],…”

Section: Semiclassical Methodsmentioning

confidence: 99%

Section: Semiclassical Methodsmentioning

confidence: 99%

Numerical approaches to time evolution of complex quantum systems

et al. 2009

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“…This map has been used to provide a formulation of quantum mechanics, in which quantum states are described by a parametrized family of probability distributions [17,18], alternative to the description of the states by wave functions or density operators. The tomographic map has been used to reconstruct the quantum state, to obtain the Wigner function by measuring the state tomogram, to define quantum characteristic exponents [23], and for the simulation of nonstationary quantum systems [24].…”

Section: The Tomographic Operator Symbolsmentioning

confidence: 99%

A probabilistic operator symbol framework for quantum information

2006

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Hilbert space operators may be mapped onto a space of ordinary functions (operator symbols) equipped with an associative (but noncommutative) star-product. A unified framework for such maps is reviewed. Because of its clear probabilistic interpretation, a particular class of operator symbols (tomograms) is proposed as a framework for quantum information problems. Qudit states are identified with maps of the unitary group into the simplex. The image of the unitary group on the simplex provides a geometrical characterization of the nature of the quantum states. Generalized measurements, typical quantum channels, entropies, and entropy inequalities are discussed in this setting.

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“…In another line of studies, simulation of quantum systems have been performed using tomography. For example, tomograms were used for simulation of tunneling [25][26][27] and multimode quantum states [28]. Attempts have also been made to understand the tomogram via path integrals [29,30].…”

Section: Introductionmentioning

confidence: 99%

Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

2016

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Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them.

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New method of quantum dynamics simulation based on the quantum tomography

Cited by 20 publications

References 31 publications

Numerical approaches to time evolution of complex quantum systems

Numerical approaches to time evolution of complex quantum systems

A probabilistic operator symbol framework for quantum information

Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

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