Evolution and Entanglement of Gaussian States in the Parametric Amplifier

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• 作者：Julio A. López-Saldívar ; Armando Figueroa…
• 关键词：parametric amplifier ; quantum entanglement ; Gaussian states ; Bell inequalities ; probability Representation
• 刊名：Journal of Russian Laser Research
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：37
• 期：1
• 页码：23-44
• 全文大小：659 KB
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• 作者单位：Julio A. López-Saldívar (1)
  Armando Figueroa (1)
  Octavio Castaños (1)
  Ramón López-Peña (1)
  Margarita A. Man’ko (2)
  Vladimir I. Man’ko (2) (3)
  
  1. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, México, 04510, D.F., Mexico City
  2. Lebedev Physical Institute, Leninskii Prospect 53, Moscow, 119991, Russia
  3. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow Region, 141700, Russia
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Applied Optics, Optoelectronics and Optical Devices
  Laser Technology and Physics and Photonics
  Microwaves, RF and Optical Engineering
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-8760

文摘

We obtain the linear time-dependent constants of motion of the parametric amplifier and use them to determine the evolution of a general two-mode Gaussian state in the tomographic-probability representation. By means of the discretization of the continuous variable density matrix, we calculate the von Neumann and linear entropies to measure the entanglement properties between the modes of the amplifier. We compare the obtained results for the nonlocal correlations with those associated to a linear map of discretized symplectic Gaussian-state tomogram onto a qubit tomogram. We use this qubit portrait procedure to establish Bell-type inequalities, which provide a necessary condition to determine the separability of quantum states, which can be evaluated through homodyne detection. We define the other no-signaling nonlocal correlations through the portrait procedure for noncomposite systems.