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Journal of Physics A Mathematical and General

Continuous teleportation of the photon statistics of squeezed states

Miguel Orszag, Douglas F. Mundarain

Published Jul 6, 2005• 1 citation
Publisher

Abstract

In this work, we study the oscillations that appear in the photon statistics of a squeezed state in a process that allows teleportation of continuous spectrum variables. In some cases, comparisons are made with the theory of photodetection. The most remarkable result is observed when the fidelity of teleportation is optimized, in that case the teleported statistics is equal to the counting statistics of photoelectrons in non-ideal photocount measurements. We also determine the effect of one-photon subtraction from each arm of the Einstein?Podolsky?Rosen source to enhance the quality of the teleportation process.

DOI
10.1088/0305-4470/38/29/011

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In this work, we study the oscillations that appear in the photon statistics of a squeezed state in a process that allows teleportation of continuous spectrum variables. In some cases, comparisons are made with the theory of photodetection. The most remarkable result is observed when the fidelity of teleportation is optimized, in that case the teleported statistics is equal to the counting statistics of photoelectrons in non-ideal photocount measurements. We also determine the effect of one-photon subtraction from each arm of the Einstein?Podolsky?Rosen source to enhance the quality of the teleportation process.
The properties of continuous-variable teleportation of single-photon states are investigated. The output state is different from the input state due to the nonmaximal entanglement in the Einstein–Podolsky–Rosen beams. The photon statistics of the teleportation output are determined, the correlation between the field information is obtained in the teleportation process, and the change in photon number is discussed. The results of the output photon statistics are applied to the transmission of a qubit encoded in the polarization of a single photon
The properties of continuous-variable teleportation of single-photon states are investigated. The output state is different from the input state due to the nonmaximal entanglement in the Einstein-Podolsky-Rosen beams. The photon statistics of the teleportation output are determined and the correlation between the field information \ensuremath{\beta} obtained in the teleportation process and the change in photon number is discussed. The results of the output photon statistics are applied to the transmission of a qubit encoded in the polarization of a single photon.
We study the continuous-variable quantum teleportation of states, statistical moments of observables, and scale parameters such as squeezing. We investigate the problem both in ideal and imperfect Vaidman-Braunstein-Kimble protocol setups. We show how the teleportation fidelity is maximized and the difference between output and input variances is minimized by using suitably optimized entangled resources. Specifically, we consider the teleportation of coherent squeezed states, exploiting squeezed Bell states as entangled resources. This class of non-Gaussian states, introduced by Illuminati and co-workers [F. Dell'Anno, S. De Siena, L. Albano, and F. Illuminati, Phys. Rev. A 76, 022301 (2007); F. Dell'Anno, S. De Siena, and F. Illuminati, Phys. Rev. A 81, 012333 (2010)], includes photon-added and photon-subtracted squeezed states as special cases. At variance with the case of entangled Gaussian resources, the use of entangled non-Gaussian squeezed Bell resources allows one to choose different optimization procedures that lead to inequivalent results. Performing two independent optimization procedures, one can either maximize the state teleportation fidelity, or minimize the difference between input and output quadrature variances. The two different procedures are compared depending on the degrees of displacement and squeezing of the input states and on the working conditions in ideal and nonideal setups.
The fidelity of quantum teleportation of a single-mode squeezed state of light is calculated based on the general theory of quantum-mechanical measurement in the Schrödinger picture. It is shown that the criterion for the nonclassical state teleportation is different from that for coherent state. F = 1/2 is no longer the rigorous boundary between classical and quantum teleportation for a squeezed state of light. When the quantum entanglement of an Einstein–Podolsky–Rosen (EPR) beam used for teleportation and the parameters of the system are given, the fidelity depends on the squeezing of the input squeezed state. The higher the squeezing is, the smaller the fidelity is, and the lower the classical limitation of fidelity is. The dependence of the optimum gain for teleporting a squeezed vacuum state upon the EPR entanglement is also calculated. The results obtained provide important references for designing experimental systems of teleporting a non-classical state and judging the quality of the teleported quantum state.
Quantum teleportation using continuous-variable cluster states is a promising method for quantum state transmission. Experiments show photon subtraction improves the fidelity of two-mode-entangled state-based teleportation, but its effect on universal quantum teleportation with cluster states is unclear. This study clarifies this issue. We create a characteristic function-based representation for universal teleportation, combining it with the Hermite polynomial representation to analyze the impact of photon subtraction. Our analysis finds that the enhancement depends on the photon subtraction modes and the initial squeezing parameter of cluster states. Contrary to the two-mode case, subtracting photons from all cluster state modes does not improve fidelity. By analyzing the equivalent squeezing of initial states after photon subtraction, we determine that squeezing improvement decides teleportation quality. A remarkable finding reveals that performing photon subtraction on two modes of a multirail cluster state can enhance equivalent squeezing of all modes, offering new possibilities for quantum information processing tasks.
We theoretically analyze the Einstein-Podolsky-Rosen (EPR) correlation, the quadrature squeezing, and the continuous-variable quantum teleportation when considering non-Gaussian entangled states generated by applying multiple-photon subtraction and multiple-photon addition to a two-mode squeezed vacuum state (TMSVs). Our results indicate that in the case of the multiple-photon-subtracted TMSVs with symmetric operations, the corresponding EPR correlation, the two-mode squeezing degree, the sum squeezing, and the fidelity of teleporting a coherent state or a squeezed vacuum state can be enhanced for any squeezing parameter rrr and these enhancements increase with the number of subtracted photons in the low-squeezing regime, while asymmetric multiple-photon subtractions will generally reduce these quantities. For the multiple-photon-added TMSVs, although it holds stronger entanglement, its EPR correlation, two-mode squeezing, sum squeezing, and the fidelity of a coherent state are always smaller than that of the TMSVs. Only when considering the case of teleporting a squeezed vacuum state does the symmetric photon addition make somewhat of an improvement in the fidelity for large-squeezing parameters. In addition, we analytically prove that a one-mode multiple-photon-subtracted TMSVs is equivalent to that of the one-mode multiple-photon-added one. And one-mode multiple-photon operations will diminish the above four quantities for any squeezing parameter rrr.