Finite Quantum Tomography and Semidefinite Programming

Mirzaee, M.; Rezaee, Mousa; Jafarizadeh, M. A.

doi:10.1007/s10773-006-9287-9

Cited by 7 publications

(10 citation statements)

References 29 publications

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“…We only mention the concepts that will be needed in the sequel, a more detailed treatment may be found in 1 [22][23][24], for example. Let G be a locally compact group with the left Haar measure µ and H be a closed subgroup of G. Letπ be a continuous representation of a group and X = G/H a homogeneous space.…”

Section: Wavelet Transform On Homogeneous Spacementioning

confidence: 99%

“…(22). Now, the positivity of the partial transpose of density matrix (22) implies that: (25) Comparing the characteristic function (25) with separable characteristic function (7), one can see that the function (25) cannot be represented as a convex mixture of products of positive definite functions K ( 1 ) and η ( 2 ), depending on parameters (λ ) and (λ ) respectively.…”

Section: Moyal-type Representations For a Spinmentioning

confidence: 99%

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Separability criteria via wavelet transform on homogenous spaces and projective representations

Karamati¹,

Rezapour

2010

Open Physics

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Abstract:The intimate connection between the Banach space wavelet reconstruction method for each unitary representation of a given group and homogenous space, and the quantum entanglement description using group theory were both studied in our previous articles. Here, we present a universal description of quantum entanglement using group theory and non-commutative characteristic functions for homogenous space and projective representation of compact groups on Banach spaces for some well known examples, such as: Moyal representation for a spin; Dihedral and Permutation groups.PACS (

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Section: Wavelet Transform On Homogeneous Spacementioning

confidence: 99%

Section: Moyal-type Representations For a Spinmentioning

confidence: 99%

Separability criteria via wavelet transform on homogenous spaces and projective representations

Karamati¹,

Rezapour

2010

Open Physics

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“…By use of quantum state tomography 6–29 on the 5-qubit quantum computers ibmq_lima, 30 ibmq_manila, 31 and ibmq_belem, 32 we have found non-zero values of the von Neumann entropy for cat states with n = 2 to 5. The entropy is reduced by the error-mitigation method suggested in the qiskit documentation.…”

Section: Introductionmentioning

confidence: 97%

Shannon and von Neumann entropies of multi-qubit Schrödinger's cat states

Jansen

Loucks

Gilbert

et al. 2022

Phys. Chem. Chem. Phys.

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“…Here we study qudit coherent states (QCS), i.e., finitedimensional analogs of the conventional infinite-dimensional Glauber CS [8][9][10][11][12][13][14][15][16] (for a review see [17]). QCS were studied since the 1990s in the context of quantum phase problem (especially for the Pegg-Barnett formalism, for reviews see [18,19]), and quantum information and engineering (reviewed in, e.g., Refs.…”

Section: Introductionmentioning

confidence: 99%

Phase-space interference of states optically truncated by quantum scissors: Generation of distinct superpositions of qudit coherent states by displacement of vacuum

et al. 2014

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Conventional Glauber coherent states (CS) can be defined in several equivalent ways, e.g., by displacing the vacuum or, explicitly, by their infinite Poissonian expansion in Fock states. It is well known that these definitions become inequivalent if applied to finite d-level systems (qudits). We present a comparative Wigner-function description of the qudit CS defined (i) by the action of the truncated displacement operator on the vacuum and (ii) by the Poissonian expansion in Fock states of the Glauber CS truncated at (d − 1)-photon Fock state. These states can be generated from a classical light by its optical truncation using nonlinear and linear quantum scissors devices, respectively. We show a surprising effect that a macroscopically distinguishable superposition of two qudit CS (according to both definitions) can be generated with high fidelity by displacing the vacuum in the qudit Hilbert space. If the qudit dimension d is even (odd) then the superposition state contains Fock states with only odd (even) photon numbers, which can be referred to as the odd (even) qudit CS or the female (male) Schrödinger cat state. This phenomenon can be interpreted as an interference of a single CS with its reflection from the highest-energy Fock state of the Hilbert space, as clearly seen via phase-space interference of the Wigner function. We also analyze nonclassical properties of the qudit CS including their photon-number statistics and nonclassical volume of the Wigner function, which is a quantitative parameter of nonclassicality (quantumness) of states. Finally, we study optical tomograms, which can be directly measured in the homodyne detection of the analyzed qudit cat states and enable the complete reconstructions of their Wigner functions.

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Finite Quantum Tomography and Semidefinite Programming

Cited by 7 publications

References 29 publications

Separability criteria via wavelet transform on homogenous spaces and projective representations

Separability criteria via wavelet transform on homogenous spaces and projective representations

Shannon and von Neumann entropies of multi-qubit Schrödinger's cat states

Phase-space interference of states optically truncated by quantum scissors: Generation of distinct superpositions of qudit coherent states by displacement of vacuum

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