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Quantum Information and Computation

Teleportation via the entangled derivative of coherent state

Anas Othman

Published Feb 1, 2019• 2 citations
Publisher

Abstract

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.

DOI
10.26421/qic19.1-2-2

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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.
When a superposition $(|\ensuremath{\alpha}〉\ensuremath{-}|\ensuremath{-}\ensuremath{\alpha}〉)$ of two coherent states with opposite phase falls upon a 50-50 beam splitter, the resulting state is entangled. Remarkably, the amount of entanglement is exactly 1 ebit, irrespective of \ensuremath{\alpha}, as was recently discovered by Hirota and Sasaki [LANL e-print quant-ph/0101018]. Here we discuss decoherence properties of such states and give a simple protocol that teleports one qubit encoded in Schr\"odinger cat states.
We propose a scheme to teleport a two-mode entangled coherent state encoded with two-qubit information, which is better than the two schemes recently proposed by Liao and Kuang ( 2007 J. Phys. B: At. Mol. Opt. Phys. 40 1183 ) and by Phien and Nguyen (2008 Phys. Lett. A 372 2825) in that our scheme gives higher value of minimum assured fidelity and minimum average fidelity without using any nonlinear interactions. For involved coherent states | ± α⟩, minimum average fidelity in our case is ⩾0.99 for |α| ⩾ 1.6 (i.e. |α| 2 ⩾ 2.6), while previously proposed schemes referred above report the same for |α| ⩾ 5 (i.e. |α| 2 ⩾ 25). Since it is very challenging to produce superposed coherent states of high coherent amplitude (|α|), our teleportation scheme is at the reach of modern technology.
In the present paper, we will review the methods to produce superposition of entangled coherent state using polarizing beam splitter and Kerr non linearity. These coherent states have many attractive features and can be used in various schemes. Entanglement, refers to the superposition of a multiparticle system and explains a new type of correlations between any two subsystems of the quantum system, which is not existing in the classical physics. The present paper deals with the use of these states in quantum teleportation, entanglement diversion and entanglement swapping schemes. Entanglement diversion and entanglement-swapping refers to a scheme which may entangle those particles which had never interacted before. In the swapping scheme, two pairs of entangled state are taken. One particle from each pair is subjected to a Bell-state-measurement. This would result in projection of the other two outgoing particles in an entangled pair. Quantum Teleportation of two mode and three modes states is also studied with perfect fidelity. Minimum assured fidelity which is defined as the minimum of the fidelity for any unknown quantum information of the states is also discussed. It is also shown how the success rate of teleportation of a superposition of odd and even coherent states can be increased from 50% to almost 100%. The scheme suggested by van Enk and Hirota was modified by Prakash, Chandra, Prakash and Shivani in 2007. We find that an almost teleportation, diversion and swapping is possible by simply separating vacuum state from the even state. The present paper also deals with study of effect of decoherence and noise on these states and the effect of noise on fidelity and minimum assured fidelity. It is also discussed that these schemes can also be applied to the process of entanglement diversion and entanglement swapping.
The possibility of producing entangled superpositions of strong coherent states is discussed. A recent proposal by Howell and Yeazell (2000 Phys. Rev. A 62 012102) of a device that entangles two strong coherent states is modified. It is shown that the modified scheme can generate non-classical states that violate Bell inequality. Moreover, a detailed analysis of the effect of losses and decoherence on the degree of entanglement is accomplished. It reveals the high sensitivity of the device to any disturbances and the fragility of generated states.