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arXiv:quant-ph/0302086 · Physical Review Letters

Entanglement Capabilities in Infinite Dimensions: Multidimensional Entangled Coherent States

S. J. van Enk

Published Jul 3, 2003• 89 citations
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Abstract

An example is given of an interaction that produces an infinite amount of entanglement in an infinitely short time, but only a finite amount in longer times. The interaction arises from a standard Kerr nonlinearity and a 50/50 beam splitter, and the initial state is a coherent state. For certain finite interaction times multidimensional generalizations of entangled coherent states are generated, for which we construct a teleportation protocol. Similarities between probabilistic teleportation and unambiguous state discrimination are pointed out.

DOI
10.1103/physrevlett.91.017902

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An example is given of an interaction that produces an infinite amount of entanglement in an infinitely short time, but only a finite amount in longer times. The interaction arises from a standard Kerr nonlinearity and a 50/50 beam splitter, and the initial state is a coherent state. For certain finite interaction times multidimensional generalizations of entangled coherent states are generated, for which we construct a teleportation protocol. Similarities between probabilistic teleportation and unambiguous state discrimination are pointed out.
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.
The authors of this paper propose an optical scheme for the generation of entangled coherent states which include the multi-mode and high-dimensional entangled coherent states.The scheme is based on the interaction of nonlinear Kerr medium and optical fields.The authors find that muliti-mode and high-dimensional entangled coherent states can be generated through proper selections of the fields′ initial states,the time of the interaction and the generalized bell measurement.The authors also find that the interaction of nonlinear Kerr media can generate entanglement when the states of input modes are prepared in coherent state and superposed Fock states.
We propose a nearly perfect optical scheme for the quantum teleportation of entangled coherent states using optical devices such as nonlinear Kerr media, beam splitters, phase shifters, and photon detectors. Different from those previous schemes, our scheme needs only ``yes'' or `no' measurements of the photon number of the related modes, i.e. nonzero- and zero-photon measurements, while in previous schemes one has to exactly identify the even or odd parity character of the photon numbers detected by detectors.
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.