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Journal of Modern Optics

Mixed state dense coding and its relation to entanglement measures

Sougato Bose, Martin Bodo Plenio, Vlatko Vedral

Published Feb 15, 2000• 16 citations
Publisher

Abstract

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.

DOI
10.1080/095003400148213

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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.
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.
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.
According to the theory that quantum entanglement can be used in quantum dense coding and increase the classical information capacity of a quantum channel, we discuss and compare the upper bound of capacity for dense coding in two case of using entangled input states and using product input states though a noiseless channel, when using a pure entanglement resource and get the result,i. e. , the capacity of dense coding using entangled input states is no larger than the capacity for product input states.