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Sungwoo Hwang - One of the best experts on this subject based on the ideXlab platform.

  • lorentz covariant Reduced Density Operator theory for relativistic quantum information processing
    Physical Review A, 2003
    Co-Authors: Doyeol Ahn, Hyukjae Lee, Sungwoo Hwang
    Abstract:

    In this paper, we derived a Lorentz-covariant quantum Liouville equation for the Density Operator which describes the relativistic-quantum-information processing from Tomonaga-Schwinger equation and an exact formal solution for the Reduced Density Operator is obtained using the projector Operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of the nonrelativistic case, which is valid only in some specified reference frame. To show that our formulation can be applied to practical problems, we derived the polarization of the vacuum in quantum electrodynamics up to the second order. The formulation presented in this work is general and could be applied to related fields such as quantum electrodynamics and relativistic statistical mechanics.

  • time convolutionless Reduced Density Operator theory of a noisy quantum channel two bit quantum gate for quantum information processing
    Physical Review A, 2000
    Co-Authors: Doyeol Ahn, K Kimm, Sungwoo Hwang
    Abstract:

    An exact Reduced-Density-Operator for the output quantum states in time-convolutionless form was derived by solving the quantum Liouville equation which governs the dynamics of a noisy quantum channel by using a projection Operator method and both advanced and retarded propagators in time. The formalism developed in this work is general enough to model a noisy quantum channel provided specific forms of the Hamiltonians for the system, reservoir, and the mutual interaction between the system and the reservoir are given. Then we apply the formulation to model a two-bit quantum gate composed of coupled spin systems in which the Heisenberg coupling is controlled by the tunneling barrier between neighboring quantum dots. Gate characteristics, including the entropy, fidelity, and the purity, are calculated numerically for both mixed and entangled initial states.

Nikesh S Dattani - One of the best experts on this subject based on the ideXlab platform.

  • feyndyn a matlab program for fast numerical feynman integral calculations for open quantum system dynamics on gpus
    Computer Physics Communications, 2013
    Co-Authors: Nikesh S Dattani
    Abstract:

    Abstract This MATLAB program calculates the dynamics of the Reduced Density matrix of an open quantum system modeled either by the Feynman–Vernon model or the Caldeira–Leggett model. The user gives the program a Hamiltonian matrix that describes the open quantum system as if it were in isolation, a matrix of the same size that describes how that system couples to its environment, and a spectral distribution function and temperature describing the environment’s influence on it, in addition to the open quantum system’s initial Density matrix and a grid of times. With this, the program returns the Reduced Density matrix of the open quantum system at all moments specified by that grid of times (or just the last moment specified by the grid of times if the user makes this choice). This overall calculation can be divided into two stages: the setup of the Feynman integral, and the actual calculation of the Feynman integral for time propagation of the Density matrix. When this program calculates this propagation on a multi-core CPU, it is this propagation that is usually the rate-limiting step of the calculation, but when it is calculated on a GPU, the propagation is calculated so quickly that the setup of the Feynman integral can actually become the rate-limiting step. The overhead of transferring information from the CPU to the GPU and back seems to have a negligible effect on the overall runtime of the program. When the required information cannot fit on the GPU, the user can choose to run the entire program on a CPU. Program summary Program title: FeynDyn. Catalogue identifier: AEPX_v1_0. Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEPX_v1_0.html . Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland. Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html . No. of lines in distributed program, including test data, etc.: 703. No. of bytes in distributed program, including test data, etc.: 11026. Distribution format: tar.gz. Programming language: MATLAB R2012a. Computer: See “Operating system”. Operating system: Any operating system that can run MATLAB R2007a or above. Classification: 4.4. Nature of problem: Calculating the dynamics of the Reduced Density Operator of an open quantum system. Solution method: Numerical Feynman integral. Running time: Depends on the input parameters. See the main text for examples.

  • feyndyn a matlab program for fast numerical feynman integral calculations for open quantum system dynamics on gpus
    Computer Physics Communications, 2013
    Co-Authors: Nikesh S Dattani
    Abstract:

    Abstract This MATLAB program calculates the dynamics of the Reduced Density matrix of an open quantum system modeled either by the Feynman–Vernon model or the Caldeira–Leggett model. The user gives the program a Hamiltonian matrix that describes the open quantum system as if it were in isolation, a matrix of the same size that describes how that system couples to its environment, and a spectral distribution function and temperature describing the environment’s influence on it, in addition to the open quantum system’s initial Density matrix and a grid of times. With this, the program returns the Reduced Density matrix of the open quantum system at all moments specified by that grid of times (or just the last moment specified by the grid of times if the user makes this choice). This overall calculation can be divided into two stages: the setup of the Feynman integral, and the actual calculation of the Feynman integral for time propagation of the Density matrix. When this program calculates this propagation on a multi-core CPU, it is this propagation that is usually the rate-limiting step of the calculation, but when it is calculated on a GPU, the propagation is calculated so quickly that the setup of the Feynman integral can actually become the rate-limiting step. The overhead of transferring information from the CPU to the GPU and back seems to have a negligible effect on the overall runtime of the program. When the required information cannot fit on the GPU, the user can choose to run the entire program on a CPU. Program summary Program title: FeynDyn. Catalogue identifier: AEPX_v1_0. Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEPX_v1_0.html . Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland. Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html . No. of lines in distributed program, including test data, etc.: 703. No. of bytes in distributed program, including test data, etc.: 11026. Distribution format: tar.gz. Programming language: MATLAB R2012a. Computer: See “Operating system”. Operating system: Any operating system that can run MATLAB R2007a or above. Classification: 4.4. Nature of problem: Calculating the dynamics of the Reduced Density Operator of an open quantum system. Solution method: Numerical Feynman integral. Running time: Depends on the input parameters. See the main text for examples.

  • numerical feynman integrals with physically inspired interpolation faster convergence and significant reduction of computational cost
    AIP Advances, 2012
    Co-Authors: Nikesh S Dattani
    Abstract:

    One of the most successful methods for calculating Reduced Density Operator dynamics in open quantum systems, that can give numerically exact results, uses Feynman integrals. However, when simulating the dynamics for a given amount of time, the number of time steps that can realistically be used with this method is always limited, therefore one often obtains an approximation of the Reduced Density Operator at a sparse grid of points in time. Instead of relying only on ad hoc interpolation methods (such as splines) to estimate the system Density Operator in between these points, I propose a method that uses physical information to assist with this interpolation. This method is tested on a physically significant system, on which its use allows important qualitative features of the Density Operator dynamics to be captured with as little as two time steps in the Feynman integral. This method allows for an enormous reduction in the amount of memory and CPU time required for approximating Density Operator dynam...

Doyeol Ahn - One of the best experts on this subject based on the ideXlab platform.

  • lorentz covariant Reduced Density Operator theory for relativistic quantum information processing
    Physical Review A, 2003
    Co-Authors: Doyeol Ahn, Hyukjae Lee, Sungwoo Hwang
    Abstract:

    In this paper, we derived a Lorentz-covariant quantum Liouville equation for the Density Operator which describes the relativistic-quantum-information processing from Tomonaga-Schwinger equation and an exact formal solution for the Reduced Density Operator is obtained using the projector Operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of the nonrelativistic case, which is valid only in some specified reference frame. To show that our formulation can be applied to practical problems, we derived the polarization of the vacuum in quantum electrodynamics up to the second order. The formulation presented in this work is general and could be applied to related fields such as quantum electrodynamics and relativistic statistical mechanics.

  • time convolutionless Reduced Density Operator theory of a noisy quantum channel two bit quantum gate for quantum information processing
    Physical Review A, 2000
    Co-Authors: Doyeol Ahn, K Kimm, Sungwoo Hwang
    Abstract:

    An exact Reduced-Density-Operator for the output quantum states in time-convolutionless form was derived by solving the quantum Liouville equation which governs the dynamics of a noisy quantum channel by using a projection Operator method and both advanced and retarded propagators in time. The formalism developed in this work is general enough to model a noisy quantum channel provided specific forms of the Hamiltonians for the system, reservoir, and the mutual interaction between the system and the reservoir are given. Then we apply the formulation to model a two-bit quantum gate composed of coupled spin systems in which the Heisenberg coupling is controlled by the tunneling barrier between neighboring quantum dots. Gate characteristics, including the entropy, fidelity, and the purity, are calculated numerically for both mixed and entangled initial states.

  • time convolutionless Reduced Density Operator theory of an arbitrary driven system coupled to a stochastic reservoir ii optical gain and line shape function of a driven semiconductor
    Physical Review B, 1995
    Co-Authors: Doyeol Ahn
    Abstract:

    In this paper, recently developed time-convolutionless quantum-kinetic equations for electron-hole pairs near the band edge are used to derive the optical gain and the line-shape function of a driven semiconductor taking into account excitonic effects. The equation of motion for the interband pair amplitude is integrated directly assuming the quasiequilibrium or adiabatic approximation. It is shown that the line shape of the optical-gain spectra is Gaussian for the simplest non-Markovian quantum kinetics. On the other hand, the line-shape function becomes Lorentzian, which has been assumed in most practical calculations, in the Markovian limit. It is also shown that the optical gain is enhanced by (1) excitonic effects caused by the attractive electron-hole Coulomb interaction and (2) interference effects (or renormalized memory effects) between the external driving field and the stochastic reservoir of the system. Gain enhancement by the memory effects can be interpreted as the result of the violation of energy conservation on the time scale shorter than the correlation time.

Runyao Duan - One of the best experts on this subject based on the ideXlab platform.

  • tripartite to bipartite entanglement transformation by stochastic local operations and classical communication and the structure of matrix spaces
    Communications in Mathematical Physics, 2018
    Co-Authors: Youming Qiao, Xin Wang, Runyao Duan
    Abstract:

    We study the problem of transforming a tripartite pure state to a bipartite one using stochastic local operations and classical communication (SLOCC). It is known that the tripartite-to-bipartite SLOCC convertibility is characterized by the maximal Schmidt rank of the given tripartite state, i.e. the largest Schmidt rank over those bipartite states lying in the support of the Reduced Density Operator. In this paper, we further study this problem and exhibit novel results in both multi-copy and asymptotic settings, utilizing powerful results from the structure of matrix spaces. In the multi-copy regime, we observe that the maximal Schmidt rank is strictly super-multiplicative, i.e. the maximal Schmidt rank of the tensor product of two tripartite pure states can be strictly larger than the product of their maximal Schmidt ranks. We then provide a full characterization of those tripartite states whose maximal Schmidt rank is strictly super-multiplicative when taking tensor product with itself. Notice that such tripartite states admit strict advantages in tripartite-to-bipartite SLOCC transformation when multiple copies are provided. In the asymptotic setting, we focus on determining the tripartite-to-bipartite SLOCC entanglement transformation rate. Computing this rate turns out to be equivalent to computing the asymptotic maximal Schmidt rank of the tripartite state, defined as the regularization of its maximal Schmidt rank. Despite the difficulty caused by the super-multiplicative property, we provide explicit formulas for evaluating the asymptotic maximal Schmidt ranks of two important families of tripartite pure states by resorting to certain results of the structure of matrix spaces, including the study of matrix semi-invariants. These formulas turn out to be powerful enough to give a sufficient and necessary condition to determine whether a given tripartite pure state can be transformed to the bipartite maximally entangled state under SLOCC, in the asymptotic setting. Applying the recent progress on the non-commutative rank problem, we can verify this condition in deterministic polynomial time.

  • tripartite to bipartite entanglement transformation by stochastic local operations and classical communication and the structure of matrix spaces
    arXiv: Quantum Physics, 2016
    Co-Authors: Youming Qiao, Xin Wang, Runyao Duan
    Abstract:

    We study the problem of transforming a tripartite pure state to a bipartite one using stochastic local operations and classical communication (SLOCC). It is known that the tripartite-to-bipartite SLOCC convertibility is characterized by the maximal Schmidt rank of the given tripartite state, i.e. the largest Schmidt rank over those bipartite states lying in the support of the Reduced Density Operator. In this paper, we further study this problem and exhibit novel results in both multi-copy and asymptotic settings. In the multi-copy regime, we observe that the maximal Schmidt rank is strictly super-multiplicative, i.e. the maximal Schmidt rank of the tensor product of two tripartite pure states can be strictly larger than the product of their maximal Schmidt ranks. We then provide a full characterization of those tripartite states whose maximal Schmidt rank is strictly super-multiplicative when taking tensor product with itself. In the asymptotic setting, we focus on determining the tripartite-to-bipartite SLOCC entanglement transformation rate, which turns out to be equivalent to computing the asymptotic maximal Schmidt rank of the tripartite state, defined as the regularization of its maximal Schmidt rank. Despite the difficulty caused by the super-multiplicative property, we provide explicit formulas for evaluating the asymptotic maximal Schmidt ranks of two important families of tripartite pure states, by resorting to certain results of the structure of matrix spaces, including the study of matrix semi-invariants. These formulas give a sufficient and necessary condition to determine whether a given tripartite pure state can be transformed to the bipartite maximally entangled state under SLOCC, in the asymptotic setting. Applying the recent progress on the non-commutative rank problem, we can verify this condition in deterministic polynomial time.

Walter T Strunz - One of the best experts on this subject based on the ideXlab platform.

  • hierarchy of stochastic pure states for open quantum system dynamics
    Physical Review Letters, 2014
    Co-Authors: Daniel Suess, Alexander Eisfeld, Walter T Strunz
    Abstract:

    We derive a hierarchy of stochastic evolution equations for pure states (quantum trajectories) for open quantum system dynamics with non-Markovian structured environments. This hierarchy of pure states (HOPS) is generally applicable and provides the exact Reduced Density Operator as an ensemble average over normalized states. The corresponding nonlinear equations are presented. We demonstrate that HOPS provides an efficient theoretical tool and apply it to the spin-boson model, the calculation of absorption spectra of molecular aggregates, and energy transfer in a photosynthetic pigment-protein complex.