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Physical Review A

Nonclassical properties of teleported optical fields in quantum teleportation of continuous variables

Fuli Li, Hongrong Li, Junxiang Zhang, Shi‐Yao Zhu

Published Aug 5, 2002• 15 citations
Publisher

Abstract

When sending a quantum state which originally has nonclassical properties such as various kinds of squeezing and photon antibunching effects according to the protocol for teleportation of continuous variables [S. L. Braunstein and H. J. Kimble, Phys. Rev. Lett. 80, 869 (1998)], we investigate to what extent those nonclassical properties can be preserved in the teleported field. Explicit conditions of the squeezing parameter for the second- and fourth-order quadrature-phase squeezings, the squared amplitude squeezing, and the photon antibunching effect to survive in the teleported field are obtained.

DOI
10.1103/physreva.66.024302

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When sending a quantum state which originally has nonclassical properties such as various kinds of squeezing and photon antibunching effects according to the protocol for teleportation of continuous variables [S. L. Braunstein and H. J. Kimble, Phys. Rev. Lett. 80, 869 (1998)], we investigate to what extent those nonclassical properties can be preserved in the teleported field. Explicit conditions of the squeezing parameter for the second- and fourth-order quadrature-phase squeezings, the squared amplitude squeezing, and the photon antibunching effect to survive in the teleported field are obtained.
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.
Quantum teleportation of an unknown broadband electromagnetic field is investigated. The continuous-variable teleportation protocol by Braunstein and Kimble [Phys. Rev. Lett. 80, 869 (1998)] for teleporting the quantum state of a single mode of the electromagnetic field is generalized for the case of a multimode field with finite bandwith. We discuss criteria for continuous-variable teleportation with various sets of input states and apply them to the teleportation of broadband fields. We first consider as a set of input fields (from which an independent state preparer draws the inputs to be teleported) arbitrary pure Gaussian states with unknown coherent amplitude (squeezed or coherent states). This set of input states, further restricted to an alphabet of coherent states, was used in the experiment by Furusawa et al. [Science 282, 706 (1998)]. It requires unit-gain teleportation for optimizing the teleportation fidelity. In our broadband scheme, the excess noise added through unit-gain teleportation due to the finite degree of the squeezed-state entanglement is just twice the (entanglement) source's squeezing spectrum for its ``quiet quadrature.'' The teleportation of one half of an entangled state (two-mode squeezed vacuum state), i.e., ``entanglement swapping,'' and its verification are optimized under a certain nonunit gain condition. We will also give a broadband description of this continuous-variable entanglement swapping based on the single-mode scheme by van Loock and Braunstein [Phys. Rev. A 61, 10 302 (2000)].
ABSTRACT We propose a setup for teleportation of continuous quantum variables which is optimized for teleportation ofsqueezed coherent states. Our scheme is a modified version of the original setup proposed by Braunstein andKimble [Phys. Rev. Lett. 80, 869, 1998] and it involves an unbalanced beam splitter on the sender's side and asingle mode squeezer on receiver's side. We show that the quality of the teleportation can be evaluated by meansof a fidelity of entanglement swapping and we prove that our modified setup and the original Braunstein-Kimblesetup are equivalent with respect to this fidelity measure.Keywords: Quantum teleportation, squeezed states, completely positive maps, fidelity 1. INTRODUCTION Quantum teleportation, a disembodied transfer of a quantum state between two distant parties, is perhaps themost remarkable and exciting development in the rapidly growing field of quantum information processing. Intheir seminal paper, Bennett et al.1 proposed a protocol for teleportation of a single qubit from the sender Aliceto the receiver Bob. The information about the teleported state is sent to Bob via dual classical and quantumEPR channels. The latter is established by a maximally entangled state shared by Alice and Bob.Recently, there has been much interest in quantum information processing with continuous quantum van-ables. Here, the focus is on systems with infinite dimensional Hubert spaces such as quantized electromagneticfield. Teleportation of continuous quantum variables was first considered by Vaidman,2 and an experimentallyfeasible setup was suggested by Braunstein and Kimble.3 Subsequent experiment4 demonstrated that theteleportation of a single mode of optical field is fully within the reach of current technology. Since then, manyauthors discussed various aspects of the teleportation,5'° including fidelity of teleportation of various quantumstates and influence of losses on the degradation of the quantum channel.Besides teleportation, many other protocols developed originally in the framework of discrete quantum van-ables, have been successfully formulated also for continuous variables. These include quantum cloning,11'3quantum
Summary form only given. An unknown continuous-variable state can he teleported by use of the two-mode squeezed state as the quantum channel. If the quantum channel is maximally squeezed (100% squeezing), the unknown state will be perfectly reproduced at a remote place. However the assumption of the maximally squeezed quantum channel is unphysical as it means the infinite average photon number of the channel state. Moreover, the interaction of the channel state with the environment degrades the entanglement and purity of the channel. We are interested in how the nonclassical features of the unknown state is revived by quantum teleportation in the real world. It is obvious that a nonclassical nature in the unknown state can be lost during the teleportation even when the channel is entangled unless it is maximally entangled Is it also obvious that any nonclassical feature, cannot be teleported by a classical correlated channel? We find the relation between the entanglement of the channel and teleportation of nonclassical nature in the unknown state.