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Physical Review A

Controlled dense coding using the Greenberger-Horne-Zeilinger state

Jiu-Cang Hao, Chuan‐Feng Li, Guang‐Can Guo

Published Apr 11, 2001• 183 citations
Publisher

Abstract

In this paper we investigate the dense coding with a three-particle entangled state. In this case one party (Alice) can send information to the second party (Bob), whereas the local measurement of the third party (Cliff) serves as quantum erasure. The quantum channel between Alice and Bob is controlled by Cliff via the measurement.
DOI
10.1103/physreva.63.054301

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A controlled quantum dense coding protocol with GHZ-class state is proposed. In this case the sender (Alice) can send information to the receiver (Bob), whereas the supervisor (Cliff) can control the quantum channel between Alice and Bob via his local measurement. The amount of classical information is shown to be controlled by the supervisor through adjustments of the local measurement angles and depend on the coefficients of the original GHZ-class state. We also give two concrete methods for Alice to deal with one of Cliff's measurement result which is more complicated.
A scheme of controlled dense coding was proposed by using non-symmetric quantum channel in3×2×2 dimensional entangled state.The collapse of the state and entanglement between Alice and Bob were controlled by Charlie's local measurement on his particle in two dimension.Then the 3×2 dimensional non-symmetric quantum channel was controlled.It can be seen that the average amount of transmitted information of dense coding was controlled by Charlie's measurement angle.One can find that the average amount of information is more than 2 bits by using maximally entangled state in the non-symmetric quantum channel.Thus,this scheme is high-efficiency.In the case the entanglement is non-maximally,the transmitted information is determined by the measurement angle 6 and the coefficient /3 of the entangled state.
We consider a situation in which two parties, Alice and Bob, share a 3-qubit system coupled in an initial maximally entangled, GHZ state. By manipulating locally two of the qubits, Alice can prepare any one of the eight 3-qubit GHZ states. Thus the sending of Alice's two qubits to Bob, entails 3 bits of classical information which can be recovered by Bob by means of a measurement distinguishing the eight (orthonormal) GHZ states. This contrasts with the 2-qubit case, in which Alice can prepare any of the four Bell states by acting locally only on one of the qubits.
Usually it is assumed that quantum dense coding is due to quantum entanglement between two parties. We show that this phenomenon has its origin in {\em correlations} between two parties rather than simply in entanglement. In order to justify our argument we evaluate a capacity of the noiseless channel for two cases: (1) when Bob performs measurement just on the particle received from Alice and (2) in the case when he utilizes the whole potential of the dense coding, that is, he performs the measurement on the received particle and the particle he had prior to the communication. We also present a simple classical scenario which might serve as a prototype of the dense coding. We generalize our results also for qudits.