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Physical Review A

Dense coding in entangled states

Hyuk‐Jae Lee, Doyeol Ahn, Sung Woo Hwang

Published Aug 5, 2002• 69 citations
Publisher

Abstract

We consider the dense coding of entangled qubits shared between two parties, Alice and Bob. The efficiency of classical information gain through quantum entangled qubits is also considered for the case of pairwise entangled qubits and maximally entangled qubits. We conclude that using the pairwise entangled qubits can be more efficient when two parties communicate whereas using the maximally entangled qubits can be more efficient when the N parties communicate.

DOI
10.1103/physreva.66.024304

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We consider the dense coding of entangled qubits shared between two parties, Alice and Bob. The efficiency of classical information gain through quantum entangled qubits is also considered for the case of pairwise entangled qubits and maximally entangled qubits. We conclude that using the pairwise entangled qubits can be more efficient when two parties communicate whereas using the maximally entangled qubits can be more efficient when the N parties communicate.
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.
Quantum dense coding is considered to be one of the most remarkable demonstrations of the existence of quantum entanglement. In this paper, we analyze the role of correlations (both classical and quantum) in quantum communication protocols. We study how the capacity of a single-qubit quantum channel depends on correlations between Alice and Bob. In particular, we consider a scenario when Alice and Bob share a pair of qubits in a state such that Alice's qubit is in the state described by the density operator $\ensuremath{\varrho}=\frac{1}{2}1+\stackrel{\ensuremath{\rightarrow}}{n}\ensuremath{\cdot}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}.$ 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 correlations that have been established prior to the communication. We present a simple classical scenario which might serve as a prototype of quantum dense coding. We generalize our results also for qudits. In addition, we address some aspects of the issue of security in correlation-assisted communication protocols.
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.