Method for calculating<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Tr</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>in solid-state theory

Buot, F. A.

doi:10.1103/physrevb.10.3700

Cited by 75 publications

(81 citation statements)

References 22 publications

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“…Two lines 12) are parallel if they have no common points, which implies that ηζ ′ = ζη ′ . If the lines (2.12) are not parallel they cross each other.…”

Section: Mutually Unbiased Bases For N Qubitsmentioning

confidence: 99%

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Discrete phase-space structure of n-qubit mutually unbiased bases

et al. 2009

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We work out the phase-space structure for a system of n qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field GF(2 n ) and investigate the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We provide a simple classification of such curves and study in detail the four-and eight-dimensional cases, analyzing also the effect of local transformations. In this way, we provide a comprehensive phase-space approach to the construction of mutually unbiased bases for n qubits.

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“…Two lines 12) are parallel if they have no common points, which implies that ηζ ′ = ζη ′ . If the lines (2.12) are not parallel they cross each other.…”

Section: Mutually Unbiased Bases For N Qubitsmentioning

confidence: 99%

“…This line was started by Buot [12], who introduced a discrete Weyl transform that generates a Wigner function on the toroidal lattice Z d (with d odd). More recently, these ideas have been developed further by other authors [13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Discrete phase-space structure of n-qubit mutually unbiased bases

et al. 2009

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“…One possible form for the kernel (α,β) that guarantees the above properties are satisfied is [6,11] (α,β)…”

Section: Spin Amplitudes On the Latticementioning

confidence: 99%

“…The treatments of deGroot and Suttorp [4] and O'Connell and Wigner [5] combined the continuous phase space picture with the finite spin degrees of freedom into a single WW transform. Buot [6] formulated a discrete WW transform on a periodic lattice phase space; Chumakov et al [7] defined a WW-type quasiprobability function as a linear combination of spherical harmonics on the phase space of the sphere S 2 ; and Berezin [8,9] introduced a general method of quantization by representing functions on S 2 in terms of covariant Q symbols and contravariant P symbols.…”

Section: Introductionmentioning

confidence: 99%

Phase-space spinor amplitudes for spin-1/2systems

Watson

Bracken

2011

Phys. Rev. A

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The concept of phase-space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more fundamental description of pure spin states than that previously given by Wigner functions. In each case the Wigner function can be expressed as the star product of the amplitude and its conjugate, so providing a generalized Born interpretation of amplitudes that emphasizes their more fundamental status. The ordinary product of the amplitude and its conjugate produces a (generalized) spin Husimi function. The case of spin -1 2 is treated in detail, and it is shown that phase-space amplitudes on the sphere transform correctly as spinors under rotations, despite their expression in terms of spherical harmonics. Spin amplitudes on a lattice are also found to transform as spinors. Applications are given to the phase space description of state superposition, and to the evolution in phase space of the state of a spin-1 2 magnetic dipole in a time-dependent magnetic field.

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“…This can be traced back to the elegant approach proposed by Schwinger [15,16,17], who clearly recognized that the expansion of arbitrary operators in terms of certain operator basis was the crucial mathematical concept in setting such a grid. These ideas have been rediscovered and developed further by several authors [18,19,20,21,22,23,24], although the contributions of Wootters [25,26,27,28] and Galetti and coworkers [29,30,31] are worth stressing.…”

Section: Introductionmentioning

confidence: 99%

Discrete coherent and squeezed states of many-qudit systems

2009

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We consider the phase space for a system of n identical qudits (each one of dimension d, with d a primer number) as a grid of d n × d n points and use the finite field GF(d n ) to label the corresponding axes. The associated displacement operators permit to define s-parametrized quasidistribution functions in this grid, with properties analogous to their continuous counterparts. These displacements allow also for the construction of finite coherent states, once a fiducial state is fixed. We take this reference as one eigenstate of the discrete Fourier transform and study the factorization properties of the resulting coherent states. We extend these ideas to include discrete squeezed states, and show their intriguing relation with entangled states between different qudits.

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Method for calculatingTrHnin solid-state theory

Cited by 75 publications

References 22 publications

Discrete phase-space structure of n-qubit mutually unbiased bases

Discrete phase-space structure of n-qubit mutually unbiased bases

Phase-space spinor amplitudes for spin-1/2systems

Discrete coherent and squeezed states of many-qudit systems

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