Quasidistributions and coherent states for finite-dimensional quantum systems

Marchiolli, Marcelo A.; Ruzzi, M.

doi:10.1007/s10946-011-9226-y

Cited by 5 publications

(2 citation statements)

References 17 publications

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“…on the equator of the Bloch sphere. In particular, the eigenstates of the discrete Fourier transform (15), frequently selected as the fiducial state [38][39][40], do not lead to a good set of DCS in the qubit case, since they correspond to ξ = √ 2 ± 1. An alternative choice of the fiducial state was proposed in [46] and corresponds to…”

Section: Discrete Coherent States For a Single Qubitsmentioning

confidence: 99%

“…Nevertheless, the framework valid for the continuous case cannot be directly applied to the selection of the fiducial state. There are several proposals on how to fix the reference state [37][38][39]. Probably the most popular candidate is an eigenstate of the discrete Fourier transform operator [41,42], which possesses several remarkable properties and can be used to define a discrete squeezing [40,44,45].…”

Section: Introductionmentioning

confidence: 99%

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Coherent, isotropic and squeezed states in anN-qubit system

Klimov

Muñoz

2013

Phys. Scr.

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We discuss how to construct a sensible set of discrete coherent states for an N -qubit system and how to use them as a tool for the analysis and representation of states in the discrete phase space. Considering N qubits as a single system of dimension 2 N , we analyze the concept of squeezing as a reduction of isotropic fluctuations below the minimum achievable level for factorized (but non-necessary symmetric under permutations) qubit states.

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Section: Discrete Coherent States For a Single Qubitsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Coherent, isotropic and squeezed states in anN-qubit system

Klimov

Muñoz

2013

Phys. Scr.

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Theoretical formulation of finite-dimensional discrete phase spaces: I. Algebraic structures and uncertainty principles

Marchiolli¹,

Ruzzi²

2012

Annals of Physics

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Theoretical formulation of finite-dimensional discrete phase spaces: II. On the uncertainty principle for Schwinger unitary operators

Marchiolli¹,

Mendonça

2013

Annals of Physics

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We introduce a self-consistent theoretical framework associated with the Schwinger unitary operators whose basic mathematical rules embrace a new uncertainty principle that generalizes and strengthens the Massar-Spindel inequality. Among other remarkable virtues, this quantum-algebraic approach exhibits a sound connection with the Wiener-Kinchin theorem for signal processing, which permits us to determine an effective tighter bound that not only imposes a new subtle set of restrictions upon the selective process of signals and wavelets bases, but also represents an important complement for property testing of unitary operators. Moreover, we establish a hierarchy of tighter bounds, which interpolates between the tightest bound and the Massar-Spindel inequality, as well as its respective link with the discrete Weyl function and tomographic reconstructions of finite quantum states. We also show how the Harper Hamiltonian and discrete Fourier operators can be combined to construct finite ground states which yield the tightest bound of a given finite-dimensional state vector space. Such results touch on some fundamental questions inherent to quantum mechanics and their implications in quantum information theory.

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Quasidistributions and coherent states for finite-dimensional quantum systems

Cited by 5 publications

References 17 publications

Coherent, isotropic and squeezed states in anN-qubit system

Coherent, isotropic and squeezed states in anN-qubit system

Theoretical formulation of finite-dimensional discrete phase spaces: I. Algebraic structures and uncertainty principles

Theoretical formulation of finite-dimensional discrete phase spaces: II. On the uncertainty principle for Schwinger unitary operators

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