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Journal of Optics

Quantum-optical input–output relations and entanglement distillation by anisotropic planar multilayers

Yunxia Dong, Xiangdong Zhang

Published Jan 20, 2011• 6 citations
Publisher

Abstract

By using the Green-function approach to the problem of quantization of the electromagnetic field, the propagation of quantized radiation through dispersive and absorptive anisotropic multilayer structures is studied. Input–output relations are derived. Based on these relations, an efficient method to perform procrustean distillation and concentration for quantum entanglement has been proposed. The Clauser–Horne–Shimony–Holt parameter for an entangled pure state, the quantum relative entropy and linear entropy for a mixed state have been calculated theoretically. It is shown that the efficiency of such a method is not only much higher for the distillation of non-maximally entangled pure states than those using partial polarizers, but it is also good for the concentration for the mixed states. Both the purity and the degree of entanglement of the mixed states can be improved simultaneously several times by using such a method. Another advantage of the scheme is that it can be widely adjusted by a proper choice of the structural parameters and the external field.

DOI
10.1088/2040-8978/13/3/035401

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By using the Green-function approach to the problem of quantization of the electromagnetic field, the propagation of quantized radiation through dispersive and absorptive anisotropic multilayer structures is studied. Input–output relations are derived. Based on these relations, an efficient method to perform procrustean distillation and concentration for quantum entanglement has been proposed. The Clauser–Horne–Shimony–Holt parameter for an entangled pure state, the quantum relative entropy and linear entropy for a mixed state have been calculated theoretically. It is shown that the efficiency of such a method is not only much higher for the distillation of non-maximally entangled pure states than those using partial polarizers, but it is also good for the concentration for the mixed states. Both the purity and the degree of entanglement of the mixed states can be improved simultaneously several times by using such a method. Another advantage of the scheme is that it can be widely adjusted by a proper choice of the structural parameters and the external field.
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Using the Green-function approach to the problem of quantization of the phenomenological Maxwell theory, the propagation of quantized radiation through dispersive and absorptive multilayer dielectric plates is studied. Input-output relations are derived, with special emphasis on the determination of the quantum noise generators associated with the absorption of radiation inside the dielectric matter. The input-output relations are used to express arbitrary correlation functions of the outgoing field in terms of correlation functions of the incoming field and those of the noise generators. To illustrate the theory, photons at dielectric tunneling barriers are considered. It is shown that inclusion in the calculations of losses in the photonic band gaps may substantially change the barrier traversal times. \textcopyright{} 1996 The American Physical Society.
Using the Green function approach to the problem of quantization of the phenomenological Maxwell theory, the propagation of quantized radiation through dispersive and absorptive multilayer dielectric plates is studied. Input--output relations are derived, with special emphasis on the determination of the quantum noise generators associated with the absorption of radiation inside the dielectric matter. The input--output relations are used to express arbitrary correlation functions of the outgoing field in terms of correlation functions of the incoming field and those of the noise generators. To illustrate the theory, the effect of a single-slab plate on the mean photon-number densities in the frequency domain is discussed in more detail.
The theory developed by Gruner and Welsch [Phys. Rev. A 54, 1661 (1996)] for calculating the 1D input-output relations of the quantized electromagnetic field at dispersing and absorbing dielectric (multilayer) plates is generalized to the three-dimensional case. First a general recipe for the derivation of the reflection and transmission coefficients at an arbitrary body that separates two half spaces from each other is presented. The general theory is then applied to the case of planar multilayer structures, for which the Green tensor is well-known.
We devise and examine two procrustean entanglement concentration schemes using quantum nondemolition (QND) interaction Hamiltonians in the continuous variable regime, applicable for light, for atomic ensembles or in a hybrid setting. We thus expand the standard entanglement distillation toolbox for use of a much more general, versatile, and experimentally feasible interaction class. The first protocol uses Gaussian ancillary modes and a non-Gaussian postmeasurement, the second a non-Gaussian ancillary mode and a Gaussian postmeasurement. We explicitly calculate the density matrix elements of the non-Gaussian mixed states resulting from these protocols using an elegant Wigner-function-based method in a numerically efficient manner. We then quantify the entanglement increase calculating the logarithmic negativity of the output state and discuss and compare the performance of the protocols.
We devise and examine two procrustean entanglement concentration schemes using Quantum Non- Demolition (QND) interaction Hamiltonians in the continuous variable regime, applicable for light, for atomic ensembles or in a hybrid setting. We thus expand the standard entanglement distillation toolbox to the use of a much more general, versatile and experimentally feasible interaction class. The first protocol uses Gaussian ancillary modes and a non-Gaussian post-measurement, the second a non-Gaussian ancillary mode and a Gaussian post-measurement. We explicitly calculate the density matrix elements of the non-Gaussian mixed states resulting from these protocols using an elegant Wigner-function based method in a numerically efficient manner. We then quantify the entanglement increase calculating the Logarithmic Negativity of the output state and discuss and compare the performance of the protocols.