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Physical Review A

Cluster-type entangled coherent states: Generation and application

Nguyen Ba An, Jaewan Kim

Published Oct 20, 2009• 36 citations
Publisher

Abstract

We consider a type of $(M+N)$-mode entangled coherent states and propose a simple deterministic scheme to generate these states that can fly freely in space. We then exploit such free-flying states to teleport certain kinds of superpositions of multimode coherent states. We also address the issue of manipulating size and type of entangled coherent states by means of linear optics elements only.

DOI
10.1103/physreva.80.042316

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We consider a type of (M+N)(M+N)(M+N)-mode entangled coherent states and propose a simple deterministic scheme to generate these states that can fly freely in space. We then exploit such free-flying states to teleport certain kinds of superpositions of multimode coherent states. We also address the issue of manipulating size and type of entangled coherent states by means of linear optics elements only.
The four Bell-type entangled coherent states, $\ensuremath{\mid}\ensuremath{\alpha}⟩\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha}⟩\ifmmode\pm\else\textpm\fi{}\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha}⟩\ensuremath{\mid}\ensuremath{\alpha}⟩$ and $\ensuremath{\mid}\ensuremath{\alpha}⟩\ensuremath{\mid}\ensuremath{\alpha}⟩\ifmmode\pm\else\textpm\fi{}\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha}⟩\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha}⟩$, can be discriminated with a high probability using only linear optical means, as long as $\ensuremath{\mid}\ensuremath{\alpha}\ensuremath{\mid}$ is not too small. Based on this observation, we propose a simple scheme to almost completely teleport a superposed coherent state. The nonunitary transformation that is required to complete the teleportation can be achieved by embedding the receiver's field state in a larger Hilbert space consisting of the field and a single atom and performing a unitary transformation on this Hilbert space.
Defining a computational basis of pseudo-number states, we interpret a coherent state of large amplitude, |α|⪢d/2π, as a qudit — a d-level quantum system — that is an even (meaning same size of amplitudes) superposition of d pseudo-number basis states. A pair of such coherent-state qudits can be maximally entangled by generalized Controlled-Z operation that is based on cross-Kerr nonlinearity, which can be weak for large d. Hence, a coherent-state optical qudit cluster state can be prepared by repetitive application of the generalized Controlled-Z operation to a set of coherent states. We thus propose an optical qudit teleportation as a simple demonstration of cluster state quantum computation.