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Quantum Information and Computation

Teleportation via the entangled derivative of coherent state

OthmanAnas

Published Feb 1, 2019• 0 citations
Publisher

Abstract

Recently, David Yevick and I published an article [Othman, A. & Yevick, D. Int J Theor Phys 57, 2293 (2018)] about constructing a superposition of two nearly identical coherent states (near coheren...
DOI
10.5555/3370239.3370241

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Recently, David Yevick and I published an article [Othman, A. \& Yevick, D. Int J Theor Phys {\bf 57}, 2293 (2018)] about constructing a superposition of two nearly identical coherent states (near coherent state). We showed that this state becomes a superposition of a derivative state and a coherent state. Here, we use the definition of the derivative state to create the entangled derivative of coherent state (EDCS). We show that this state can be used to teleport qubits encoded in the near coherent states. The decoherence of EDCS is also studied. In addition, we propose an experimental scheme to produce the EDCS and to perform teleportation.
The concept of a near superposition [Othman A, Yevick D. Int. J. Theor. Phys. 2018; 57:2293–2308] has recently been introduced as the superposition of two semi-identical states and has, in particular, been realized with coherent states. This paper provides a higher-order generalization of this procedure and, in particular, examines the ‘derivative limit’ for which the phases of all the lower-order states are identical and equal to a particular constant. In the derivative limit, the near coherent state superposition is transformed after successive derivative operations into a high-order Derivative Coherent State (DCS). The DCS is accordingly generated by constructing and subsequently displacing a certain stationary seed state formed by superimposing only even or odd Fock states. The mathematical and statistical properties of the DCS display several behaviours and non-classical features that are pronounced for high-order states. These non-classical properties include the Q-Mandel, higher-order antibunching, linear squeezing, and amplitude squared squeezing.
Othman and Yevick [Int. J. Theor. Phys. 57, 2293 (2018)] introduced a new class of states defined as “near” coherent states attached to the simple harmonic oscillator. Such states can be expressed as superposition of a standard coherent state and a derivative state, which are neither completely quantum nor completely classical. Here, we introduce photon-added (-depleted) near coherent states [PA(D)NCS] through “m” times application of creation (annihilation) operators â†(â) to the near coherent state. A general analysis of nonclassical properties of the PA(D)NCS, such as sub-Poissonian statistics and squeezing effect, is given analytically and numerically in the context of the conventional quantum optics. We also derive the Wigner distribution function of the PA(D)NCS over phase space which may bear negative values, which is a good indication of their nonclassical properties. Finally, an experimental procedure for generating the PA(D)NCSs is established.