Four-mode entangled states in coupled nonlinear optical processes and teleportation of two-mode entangled CV state

Chirkin, A. S.; Saigin, Mikhail Yu.

doi:10.1088/0031-8949/2009/t135/014029

Cited by 13 publications

(14 citation statements)

References 23 publications

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“…The solution of Eqs. (14), (15), (16) could be expressed in terms of the solution of Eq. (14) without inhomogeneity by the following proposition.…”

Section: Dynamics Of Moments and Gaussian Solutionsmentioning

confidence: 99%

“…Eqs. (15), (16) could be considered as linear differential equations in (2n) 2 × (2n) 2 variables. The following proposition allows one to represent their solution in terms of solutions of a linear differential equation in 4n variables.…”

Section: Dynamics Of Moments and Gaussian Solutionsmentioning

confidence: 99%

“…[13]. Modern applications could be found in works by A. S. Chirkin et al [14,15,16,17,18,19]. Also quadratic Hamiltonians arise in opto-mechanical problems [20,21].…”

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confidence: 99%

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Irreversible quantum evolution with quadratic generator: Review

Teretenkov

2019

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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We review results on GKSL-type equations with multi-modal generators which are quadratic in bosonic or fermionic creation and annihilation operators. General forms of such equations are presented. The Gaussian solutions are obtained in terms of equations for the first and the second moments. Different approaches for their solutions are discussed.was developed in the works by I. A. Malkin, V. I. Man'ko and V. V. Dodonov [3,4,5]. Some modern studies on unitary dynamics with quadratic Hamiltonians could be found in works by A. M. Chebotraev and T. V. Tlyachov [7,8,9]. One of the main areas of application of quadratic multi-modal Hamiltonians is quantum optics, especially in case of parametric approximation (see Ref.[10], Ch. II, Ref. [11], Ch. 16, or Ref. [12], Sec. 7.1.2). Coherent states for multi-modal parametric systems were considered in Ref. [13]. Modern applications could be found in works by A. S. Chirkin et al [14,15,16,17,18,19]. Also quadratic Hamiltonians arise in opto-mechanical problems [20,21]. Another source of such Hamiltonians is the approximate quantization method by N. N. Bogolyubov [22]. (See also Ref. 80 for contemporary discussion.) Discussion of the unitary dynamics with non-stationary (time-dependent) Hamiltonians could be found in Refs.[24]- [26]. Physical applications of such Hamiltonians were discussed in Ref. [27]. Quantum evolution with a quadratic generator is also closely related to the classical one, which was studied in the general case by J. Williamson [28,29,30]. The quasi-classical approximation for squeezed states was discussed in Ref. [31]. More detailed bibliography for bosonic unitary evolution could be found in Refs. [5] and [32]. The fermionic case without dissipation was considered in Ref.[2] by F. A. Berezin. The unified approach both for the bosonic reversible dynamics and the fermionic one was considered by V. I. Man'ko and V. V. Dodonov.[33] We consider reversible (non-unitary) evolution with quadratic generators. From the historical point of view one should mention Ref.[34] by L. D. Landau, which is famous for the first appearance of the concept of the density matrix. What is interesting for this review is that equations for irreversible quantum evolution of the density matrix were also introduced there. As it was mentioned on p. 183 in Ref.[5] and in Sec. 23.1 of Ref. [35] in the harmonic oscillator case one has (in modern notation)ρ

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“…The solution of Eqs. (14), (15), (16) could be expressed in terms of the solution of Eq. (14) without inhomogeneity by the following proposition.…”

Section: Dynamics Of Moments and Gaussian Solutionsmentioning

confidence: 99%

Section: Dynamics Of Moments and Gaussian Solutionsmentioning

confidence: 99%

See 1 more Smart Citation

Irreversible quantum evolution with quadratic generator: Review

Teretenkov

2019

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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“…Our analysis uses some previous results obtained for this kind of process [19]. Applications of the fields generated in these types of interactions, for teleportation of spatially single-mode two-color entangled states was discussed in [20]. Detailed analysis of the spatially multimode fields generated in coupled parametric processes was carried out in [24,25].…”

Section: Coupled Parametric Interactionsmentioning

confidence: 99%

“…Our scheme represents a unification of the teleportation scheme for coherent optical images [10], with that for teleportation of entangled two-mode states [20]. The original feature of our scheme is that the spatially multimode quantum fields, used to set up a quantum channel, are obtained in a single specifically tailored nonlinear crystal.…”

Section: Introductionmentioning

confidence: 99%

Quantum holographic teleportation of entangled two-color optical images

2012

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We introduce and theoretically investigate a scheme for teleportation of two-frequency entangled optical images in which the quantum channel is formed by four-frequency multimode states, generated in a single nonlinear photonic crystal by coupled parametric interactions. We study in detail the performance of the scheme. Namely, we evaluate its fidelity and the spatial-frequency spectra of the quadrature components characterizing the deterioration of the entanglement in the initial images due to the teleportation process. We analyze the influence of the spatial bandwidth of entanglement on the fidelity of teleportation. We investigate the performance of the scheme both in the near and the far diffraction field. Our analysis suggests that bandwidth matching of the quantum channel field with that of the images is generally necessary for high-quality teleportation. We show that entangled images are more fragile and more difficult to teleport than their coherent counterparts.

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Statistical properties of four-mode quantum states in coupled optical parametric down-conversions

Belyaeva

Chirkin

2009

J Russ Laser Res

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Four-mode entangled states in coupled nonlinear optical processes and teleportation of two-mode entangled CV state

Cited by 13 publications

References 23 publications

Irreversible quantum evolution with quadratic generator: Review

Irreversible quantum evolution with quadratic generator: Review

Quantum holographic teleportation of entangled two-color optical images

Statistical properties of four-mode quantum states in coupled optical parametric down-conversions

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