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Philipp Krammer - One of the best experts on this subject based on the ideXlab platform.

  • Bloch vectors for qudits
    Journal of Physics A, 2008
    Co-Authors: Reinhold A. Bertlmann, Philipp Krammer
    Abstract:

    We present three different Matrix bases that can be used to decompose density matrices of d-dimensional quantum systems, so-called qudits: the generalized Gell–Mann Matrix basis, the polarization operator basis and the Weyl operator basis. Such a decomposition can be identified with a vector—the Bloch vector, i.e. a generalization of the well-known qubit case—and is a convenient expression for comparison with measurable quantities and for explicit calculations avoiding the handling of large matrices. We present a new method to decompose density matrices via so-called standard matrices, consider the important case of an isotropic two-qudit state and decompose it according to each basis. In the case of qutrits we show a representation of an entanglement witness in terms of expectation values of spin-1 measurements, which is appropriate for an experimental realization.

  • Bloch vectors for qudits and geometry of entanglement
    arXiv: Quantum Physics, 2007
    Co-Authors: Reinhold A. Bertlmann, Philipp Krammer
    Abstract:

    We present three different Matrix bases that can be used to decompose density matrices of d--dimensional quantum systems, so-called qudits: the generalized Gell-Mann Matrix basis, the polarization operator basis, and the Weyl operator basis. Such a decomposition can be identified with a vector --the Bloch vector, i.e. a generalization of the well known qubit case-- and is a convenient expression for comparison with measurable quantities and for explicit calculations avoiding the handling of large matrices. We consider the important case of an isotropic two--qudit state and decompose it according to each basis. Investigating the geometry of entanglement of special parameterized two--qubit and two--qutrit states, in particular we calculate the Hilbert--Schmidt measure of entanglement, we find that the Weyl operator basis is the optimal choice since it is closely connected to the entanglement of the considered states.

Reinhold A. Bertlmann - One of the best experts on this subject based on the ideXlab platform.

  • Bloch vectors for qudits
    Journal of Physics A, 2008
    Co-Authors: Reinhold A. Bertlmann, Philipp Krammer
    Abstract:

    We present three different Matrix bases that can be used to decompose density matrices of d-dimensional quantum systems, so-called qudits: the generalized Gell–Mann Matrix basis, the polarization operator basis and the Weyl operator basis. Such a decomposition can be identified with a vector—the Bloch vector, i.e. a generalization of the well-known qubit case—and is a convenient expression for comparison with measurable quantities and for explicit calculations avoiding the handling of large matrices. We present a new method to decompose density matrices via so-called standard matrices, consider the important case of an isotropic two-qudit state and decompose it according to each basis. In the case of qutrits we show a representation of an entanglement witness in terms of expectation values of spin-1 measurements, which is appropriate for an experimental realization.

  • Bloch vectors for qudits and geometry of entanglement
    arXiv: Quantum Physics, 2007
    Co-Authors: Reinhold A. Bertlmann, Philipp Krammer
    Abstract:

    We present three different Matrix bases that can be used to decompose density matrices of d--dimensional quantum systems, so-called qudits: the generalized Gell-Mann Matrix basis, the polarization operator basis, and the Weyl operator basis. Such a decomposition can be identified with a vector --the Bloch vector, i.e. a generalization of the well known qubit case-- and is a convenient expression for comparison with measurable quantities and for explicit calculations avoiding the handling of large matrices. We consider the important case of an isotropic two--qudit state and decompose it according to each basis. Investigating the geometry of entanglement of special parameterized two--qubit and two--qutrit states, in particular we calculate the Hilbert--Schmidt measure of entanglement, we find that the Weyl operator basis is the optimal choice since it is closely connected to the entanglement of the considered states.

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

  • Majorana representation, qutrit Hilbert space and NMR implementation of qutrit gates
    Journal of Physics B: Atomic Molecular and Optical Physics, 2018
    Co-Authors: Shruti Dogra, Kavita Dorai, Arvind
    Abstract:

    We report a study of the Majorana geometrical representation of a qutrit, where a pair of points on a unit sphere represents its quantum states. A canonical form for qutrit states is presented, where every state can be obtained from a one-parameter family of states via $SO(3)$ action. The notion of spin-1 magnetization which is invariant under $SO(3)$ is geometrically interpreted on the Majorana sphere. Furthermore, we describe the action of several quantum gates in the Majorana picture and experimentally implement these gates on a spin-1 system (an NMR qutrit) oriented in a liquid crystalline environment. We study the dynamics of the pair of points representing a qutrit state under various useful quantum operations and connect them to different NMR operations. Finally, using the Gell Mann Matrix picture we experimentally implement a scheme for complete qutrit state tomography.

Shruti Dogra - One of the best experts on this subject based on the ideXlab platform.

  • Majorana representation, qutrit Hilbert space and NMR implementation of qutrit gates
    Journal of Physics B: Atomic Molecular and Optical Physics, 2018
    Co-Authors: Shruti Dogra, Kavita Dorai, Arvind
    Abstract:

    We report a study of the Majorana geometrical representation of a qutrit, where a pair of points on a unit sphere represents its quantum states. A canonical form for qutrit states is presented, where every state can be obtained from a one-parameter family of states via $SO(3)$ action. The notion of spin-1 magnetization which is invariant under $SO(3)$ is geometrically interpreted on the Majorana sphere. Furthermore, we describe the action of several quantum gates in the Majorana picture and experimentally implement these gates on a spin-1 system (an NMR qutrit) oriented in a liquid crystalline environment. We study the dynamics of the pair of points representing a qutrit state under various useful quantum operations and connect them to different NMR operations. Finally, using the Gell Mann Matrix picture we experimentally implement a scheme for complete qutrit state tomography.

Kavita Dorai - One of the best experts on this subject based on the ideXlab platform.

  • Majorana representation, qutrit Hilbert space and NMR implementation of qutrit gates
    Journal of Physics B: Atomic Molecular and Optical Physics, 2018
    Co-Authors: Shruti Dogra, Kavita Dorai, Arvind
    Abstract:

    We report a study of the Majorana geometrical representation of a qutrit, where a pair of points on a unit sphere represents its quantum states. A canonical form for qutrit states is presented, where every state can be obtained from a one-parameter family of states via $SO(3)$ action. The notion of spin-1 magnetization which is invariant under $SO(3)$ is geometrically interpreted on the Majorana sphere. Furthermore, we describe the action of several quantum gates in the Majorana picture and experimentally implement these gates on a spin-1 system (an NMR qutrit) oriented in a liquid crystalline environment. We study the dynamics of the pair of points representing a qutrit state under various useful quantum operations and connect them to different NMR operations. Finally, using the Gell Mann Matrix picture we experimentally implement a scheme for complete qutrit state tomography.