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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Teleportation of continuous quantum variables using squeezed-state entanglement

Kok Win Goh, C. W. Chou, Tiancai Zhang, Peter Lodahl, Harry J. Kimble

Published Feb 3, 2004• 0 citations
Publisher

Abstract

We report recent developments in our experiment to teleport light beams by utilizing Einstein-Podolsky-Rosen (EPR) entanglement for continuous quantum variables. We describe details of our experimental apparatus, including the generation of EPR entanglement from squeezed states of light. In addition, we have developed an explicit model for the teleportation of coherent states that includes the effect of diverse loss factors and limited degrees of entanglement, and that enables us to project the possibilities for achieving yet higher fidelities beyond the currently achieved value of 62% with our apparatus. Propects for other teleportation schemes will also be discussed.

DOI
10.1117/12.508566

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We report recent developments in our experiment to teleport light beams by utilizing Einstein-Podolsky-Rosen (EPR) entanglement for continuous quantum variables. We describe details of our experimental apparatus, including the generation of EPR entanglement from squeezed states of light. In addition, we have developed an explicit model for the teleportation of coherent states that includes the effect of diverse loss factors and limited degrees of entanglement, and that enables us to project the possibilities for achieving yet higher fidelities beyond the currently achieved value of 62% with our apparatus. Propects for other teleportation schemes will also be discussed.
We experimentally demonstrate quantum teleportation for continuous variables using squeezed-state entanglement. The teleportation fidelity for a real experimental system is calculated explicitly, including relevant imperfection factors such as propagation losses, detection inefficiencies, and phase fluctuations. The inferred fidelity for input coherent states is $F=0.61\ifmmode\pm\else\textpm\fi{}0.02,$ which when corrected for the efficiency of detection by the output observer, gives a fidelity of 0.62.0.62.0.62. By contrast, the projected result based on the independently measured entanglement and efficiencies is 0.69.0.69.0.69. The teleportation protocol is explained in detail, including a discussion on discrepancy between experiment and theory, as well as on the limitations of the current apparatus.
Results of experiments recently performed are reported, in which two optical parametric amplifiers were set up to generate two independently quadrature squeezed continuous wave laser beams. The transformation of quadrature squeezed states into polarization squeezed states and into states with spatial quantum correlations is demonstrated. By utilizing two squeezed laser beams, a polarization squeezed state exhibiting three simultaneously squeezed Stokes operator variances was generated. Continuous variable polarization entanglement was generated and the Einstein-Podolsky-Rosen paradox was observed. A pair of Stokes operators satisfied both the inseparability criterion and the conditional variance criterion. Values of 0.49 and 0.77, respectively, were observed, with entanglement requiring values below unity. The inseparability measure of the observed quadrature entanglement was 0.44. This value is sufficient for a demonstration of quantum teleportation, which is the next experimental goal of the authors.
We experimentally demonstrate quantum teleportation for continuous variables by using squeezed-state entanglement. A fidelity expression for a real experimental system is presented, where all the imperfection factors are considered, including losses and phase fluctuations. The measured fidelity for input coherent states is 0.62 and the prospective result with our measured entanglement and efficiencies is 0.69. We will show the details of the quantum teleportation for continuous variable and discuss the problems for further improvement in this experiment.
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.
Summary form only given. Quantum teleportation, first proposed as a method for teleporting an unknown spin-1/2 quantum state from a sender, "Alice", to a receiver, "Bob", has been extended to continuous-variable quantum teleportation (CVQT). In this variant of quantum teleportation, Bob and Alice share a nonlocal entangled two-mode field which, ideally, should have perfect correlations between in-phase quadrature ('position' x) and out-of-phase quadrature ('momentum' p), although the requirement of perfect correlations can be relaxed somewhat. The experimental success of CVQT has recently been reported, with two-mode squeezed light providing the nonlocal, entangled source shared between Alice and Bob. The objective here is to consider whether CVQT has indeed been achieved, or could ever be achieved, in optical experiments employing conventional laser sources. In particular we show that, in the context of this experiment, Alice and Bob may not employ independent laser sources for their operations if the state is to be teleported, yet this requires them to share more than just the Einstein-Podolsky-Rosen (EPR) resource.
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.