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Fortschritte der Physik

Two‐mode Schrödinger cats, entanglement and teleportation

József Janszky, János K. Asbóth, A. Gábris, András Vukics, Mátyás Koniorczyk, T. Kobayashi

Published Feb 26, 2003• 7 citations
Publisher

Abstract

Abstract Two‐mode Schrödinger cats consisting of two and four coherent‐state terms are considered. It is shown that they are closely related to the quadrature entangled EPR pair. The properties of their wave functions are investigated from their aspects of entanglement. It is shown that at certain parameters the entangled properties of the two‐mode Schrödinger cats allow for good teleportation fidelity. A theoretical generalization to the teleportation of two qubits is also discussed.

DOI
10.1002/prop.200310020

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Abstract Two‐mode Schrödinger cats consisting of two and four coherent‐state terms are considered. It is shown that they are closely related to the quadrature entangled EPR pair. The properties of their wave functions are investigated from their aspects of entanglement. It is shown that at certain parameters the entangled properties of the two‐mode Schrödinger cats allow for good teleportation fidelity. A theoretical generalization to the teleportation of two qubits is also discussed.
Quantum superpositions of coherent states are produced both in microwave and optical domains, and are considered realizations of the famous “Schroedinger cat” state. The recent progress shows an increase in the number of components and the number of modes involved. Our work gives a theoretical treatment of multicomponent two-mode Schroedinger cat states. We consider a class of single-mode states, which are superpositions of N coherent states lying on a circle in the phase space. In this class we consider an orthonormal basis created by rotationally-invariant circular states (RICS). A two-mode extension of this basis is created by splitting a single-mode RICS on a balanced beam-splitter. After performing a symmetric (Loewdin) orthogonalization of the sets of coherent states in both modes we obtain the Schmidt decomposition of the two-mode state, and therefore an analytic expression for its entanglement. We show that the states obtained by splitting a RICS are generalizations of Bell states of two qubits to the case of N -level systems encoded into superpositions of coherent states on the circle, and we propose for them the name of generalized quasi-Bell states. We show that an exact probabilistic teleportation of arbitrary superposition of coherent states on the circle is possible with such a state used as shared resource.
Quantum teleportation of one- and two-photon superposition states based on EPR entanglement of continuous-wave two-mode squeezed state is discussed. The fidelities of teleportation are deduced for two different input quantum states. The dependence of the fidelity on the parameters of EPR entanglement and the gain of the classical channels are shown numerically. Comparing with the teleportation of Fock state and coherent state, it is pointed out that for given EPR entanglement and classical gain, the higher the nonclassicality of the input state, the lower the accessible fidelity of teleportation.
In continuous-variable quantum information, non-Gaussian entangled states that are obtained from Gaussian entangled states via photon subtraction are known to contain more entanglement. This makes them better resources for quantum information processing protocols, such as, quantum teleportation. We discuss the teleportation of non-Gaussian, non-classical Schrödinger-cat states of light using two-mode squeezed vacuum light that is made non-Gaussian via subtraction of a photon from each of the two modes. We consider the experimentally realizable cat states produced by subtracting a photon from the single-mode squeezed vacuum state. We discuss two figures of merit for the teleportation process, (a) the fidelity, and (b) the maximum negativity of the Wigner function at the output. We elucidate how the non-Gaussian entangled resource lowers the requirements on the amount of squeezing necessary to achieve any given fidelity of teleportation, or to achieve negative values of the Wigner function at the output.
Quantum teleportation of one- and two-photon superposition states based on EPR entanglement of continuous-wave two-mode squeezed state is discussed. The fidelities of teleportation axe deduced for two different input quantum states. The dependence of the fidelity on the parameters of EPR entanglement and the gain of the classical channels are shown numerically. Comparing with the teleportation of Fock state and coherent state, it is pointed out that for given EPR entanglement and classical gain, the higher the nonclassicality of the input state, the lower the accessible fidelity of teleportation.
We investigate the entanglement swapping of the continuous variable states by taking the pair Schrödinger cat states as the input entangled states, in which the two-mode squeezed vacuum and the pair cat states serve as the quantum channel, respectively. The entanglement of the initial states as well as the final states is analyzed by adopting the logarithmic negativity as the measure of entanglement. The quantum teleportation task by exploiting the swapped states as the quantum channel is also considered, where a coherent state serves as the target state and the average fidelity is examined.