An extended Weyl-Wigner transformation for special finite spaces

Galetti, D.; Piza, A. F. R. de Toledo

doi:10.1016/0378-4371(88)90219-1

Cited by 140 publications

(142 citation statements)

References 22 publications

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“…Discrete Wigner functions have been constructed using both the Schwinger bases [20] and more general mutually unbiased bases [19]. For the Schwinger basis, the inversion formula (28) simplifies to…”

Section: Informational Completenessmentioning

confidence: 99%

Quantum theory of successive projective measurements

2007

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We show that a quantum state may be represented as the sum of a joint probability and a complex quantum modification term. The joint probability and the modification term can both be observed in successive projective measurements. The complex modification term is a measure of measurement disturbance. A selective phase rotation is needed to obtain the imaginary part. This leads to a complex quasiprobability, the Kirkwood distribution. We show that the Kirkwood distribution contains full information about the state if the two observables are maximal and complementary. The Kirkwood distribution gives a new picture of state reduction. In a nonselective measurement, the modification term vanishes. A selective measurement leads to a quantum state as a nonnegative conditional probability. We demonstrate the special significance of the Schwinger basis.

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Section: Informational Completenessmentioning

confidence: 99%

Quantum theory of successive projective measurements

2007

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“…Weyl pairs were introduced at the begining of quantum mechanics 15 . They were extensively used for factorizing the secular equation in connection with a study of alternating hydrocarbons 16 and for constructing analogues of the usual Pauli matrices 14,17,18,19 .…”

Section: Generalized Pauli Matricesmentioning

confidence: 99%

Generalized Spin Bases for Quantum Chemistry and Quantum Information

Kibler

2008

Collect. Czech. Chem. Commun.

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Symmetry adapted bases in quantum chemistry and bases adapted to quantum information share a common characteristics: both of them are constructed from subspaces of the representation space of the group SO(3) or its double group (i.e., spinor group) SU(2).We exploit this fact for generating spin bases of relevance for quantum systems with cyclic symmetry and equally well for quantum information and quantum computation.Our approach is based on the use of generalized Pauli matrices arising from a polar decomposition of SU(2). This approach leads to a complete solution for the construction of mutually unbiased bases in the case where the dimension d of the considered Hilbert subspace is a prime number. We also give the starting point for studying the case where d is the power of a prime number. A connection of this work with the unitary group U(d) and the Pauli group is brielly underlined.

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“…The flow of information in the quantum distributor, as described by the unitary operator (3.1), is governed by the preparation of the distributor itself, i.e., by the choice of the program state |Θ 23 . In other words, we imagine the transformation (3.1) as a universal "processor" or distributor and the state |Θ 23 as "program" through which the information flow is controlled.…”

Section: Quantum Information Distributormentioning

confidence: 99%

“…A simple way to see how the accuracy of the approximations in the different outputs is constrained, is to define the fidelities 23) and to note that F 1 + F 2 + F 3 = 2. Each of the fidelities lies between 1/2 and 1.…”

Section: The Case Of Qubitsmentioning

confidence: 99%

Generalized measurements via a programmable quantum processor

et al. 2003

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We show that it is possible to control the trade-off between information gain and disturbance in generalized measurements of qudits by utilizing the programmable quantum processor. This universal quantum machine allows us to perform a generalized measurement on the initial state of the input qudit to construct a Husimi function of this state. The trade-off between the gain and the disturbance of the qudit is controlled by the initial state of ancillary system that acts as a program register for the quantum-information distributor. The trade-off fidelity does not depend on the initial state of the qudit.

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An extended Weyl-Wigner transformation for special finite spaces

Cited by 140 publications

References 22 publications

Quantum theory of successive projective measurements

Quantum theory of successive projective measurements

Generalized Spin Bases for Quantum Chemistry and Quantum Information

Generalized measurements via a programmable quantum processor

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