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Physical Review Letters

Quantum Dense Coding with Atomic Qubits

Tobias Schaetz, M. D. Barrett, D. Leibfried, John Chiaverini, J. Britton, Wayne M. Itano, John D. Jost, C. Langer, D. J. Wineland

Published Jul 22, 2004• 132 citations
Publisher

Abstract

We report the implementation of quantum dense coding on individual atomic qubits with the use of two trapped 9Be+ ions. The protocol is implemented with a complete Bell measurement that distinguishes the four operations used to encode two bits of classical information. We measure an average transmission fidelity of 0.85(1) and determine a channel capacity of 1.16(1).

DOI
10.1103/physrevlett.93.040505

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We report the implementation of quantum dense coding on individual atomic qubits with the use of two trapped 9Be+ ions. The protocol is implemented with a complete Bell measurement that distinguishes the four operations used to encode two bits of classical information. We measure an average transmission fidelity of 0.85(1) and determine a channel capacity of 1.16(1).
An experimentally feasible scheme for implementing four-atom quantum dense coding of an atom–cavity system is proposed. The cavity is only virtually excited and no quantum information will be transferred from the atoms to the cavity. Thus the scheme is insensitive to cavity decay and the thermal field. In the scheme, Alice can send faithfully 4 bits of classical information to Bob by sending two qubits. Generalized Bell states can be exactly distinguished by detecting the atomic state, and quantum dense coding can be realized in a simple way.
Ideal dense coding protocols allow one to use prior maximal entanglement to send two bits of classical information by the physical transfer of a single encoded qubit. We investigate the case when the prior entanglement is not maximal and the initial state of the entangled pair of qubits being used for the dense coding is a mixed state. We find upper and lower bounds on the capability to do dense coding in terms of the various measures of entanglement and in terms of the average mutual distinguishability of the signal states.
Quantum communication, as a vital area of quantum information science, aims to leverage quantum phenomena—particularly entanglement—to achieve tasks that are impossible or inefficient in classical systems. It plays a key role in the development of secure communication protocols and advanced information processing. This paper focuses on one such protocol, dense coding, which enables the transmission of two classical bits using only one entangled quantum particle.”We introduce the mathematical and physical foundations of quantum communication, such as the entangled state and Kronecker product. Then we propose the quantum communication protocol, namely dense coding using Bell states. It offer unique advantages that are beyond the classical parts. For this purpose, we in detail analyze the quantum measurements using Pauli gates and identity matrix, as well as the transmission of particle from Alice to Bob. They are necessary steps for dense coding. Then we analyze how Bob finishes the protocol using measurement over two qubits.
Ideal dense coding protocols allow one to use prior maximal entanglement to send two bits of classical information by the physical transfer of a single encoded qubit. We investigate the case when the prior entanglement is not maximal and the initial state of the entangled pair of qubits being used for the dense coding is a mixed state. We find upper and lower bounds on the capability to do dense coding in terms of the various measures of entanglement. Our results can also be reinterpreted as giving bounds on purification procedures in terms of dense coding capacities.
Ideal dense coding protocols allow one to use prior maximal entanglement to send two bits of classical information by the physical transfer of a single encoded qubit. We investigate the case when the prior entanglement is not maximal and the initial state of the entangled pair of qubits being used for the dense coding is a mixed state. We find upper and lower bounds on the capability to do dense coding in terms of the various measures of entanglement. Our results can also be reinterpreted as giving bounds on purification procedures in terms of dense coding capacities.
We consider the fundamental protocol of dense coding of classical information assuming that noise affects both the forward and backward communication lines between Alice and Bob. Assuming that this noise is described by the same quantum channel, we define its dense coding capacity by optimizing over all adaptive strategies that Alice can implement, while Bob encodes the information by means of Pauli operators. Exploiting techniques of channel simulation and protocol stretching, we are able to establish the dense coding capacity of Pauli channels in arbitrary finite dimension, with simple formulas for depolarizing and dephasing qubit channels.