Controlled dense coding for continuous variables using three-particle entangled states

Abstract

In the development of theoretical and experimental studies of quantum information, the quantum teleportation that is the disembodied transport of an unknown quantum state from a sender to a remote receiver @1# and the dense coding in which the single bit sent from a sender to a receiver can successfully carry two bits of classical information @2#, have attracted extensive interests. The nonlocal quantum entanglement plays a determinant role in the quantum information processing. Towards possible applications in quantum communication, both theoretical and experimental investigations increasingly focus on quantum states of continuous variables in an infinite-dimensional Hilbert space, since the EinsteinPodolsky-Rosen ~EPR! entangled state can be efficiently generated using squeezed light and beam splitters, for instance, the entangled EPR pairs resulting from two-mode squeezed vacuum state have been successfully employed in demonstrating unconditional quantum teleportation @3#. Later, the schemes realizing highly efficient dense coding for continuous variables are theoretically proposed, in which the two-mode squeezed-state entanglement is utilized to achieve unconditional signal transmission @4–6#. The bright EPR beams have been experimentally produced with a nondegenerate optical parametric amplifier ~NOPA! @7# and the dense coding for continuous variables based on bright EPR beam has been demonstrated initially @8#. Loock and Braunstein have given that the superposition of more than independently squeezed states can yield multipartite entanglement for continuous variables and presented the scheme of quantum teleportation using entangled three-mode state @9#. The fidelity in this scheme depends on the measurement of the third particle. Controlled dense coding for discrete variables was proposed recently using the Greenberger-Horne-Zeilinger state ~GHZ! @10#. Inspired by the similarity and difference between dense coding and quantum teleportation, in this paper we study dense coding using the tripartite entangled state. It is shown that when using the tripartite entangled state, the information transmission capacity of dense coding is controlled by the measurement of the third particle. We introduce a simple, experimentally realizable, controlled dense coding protocol for continuous variables by exploring nondegenerate optical parametric amplifier. Due to adopting the