Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Influence of noise on the fidelity and the entanglement fidelity of states

L.-M. Duan, Guang‐Can Guo

Published Dec 1, 1997• 24 citations

Abstract

The fidelity and the entanglement fidelity are two important quantities in describing the transmission of quantum information through (possibly noisy) quantum channels. In this paper these two quantities are calculated for different kinds of state which are transmitted in noisy channels. A general equation is obtained for these fidelities. Some examples are given to illustrate the general result and possible applications of these results to quantum cryptography and teleportation via noisy channels are discussed.

DOI: 10.1088/1355-5111/9/6/008

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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Influence of noise on the fidelity and the entanglement fidelity of states

L.-M. Duan, Guang‐Can Guo

Published Dec 1, 1997• 24 citations

Publisher

Abstract

DOI: 10.1088/1355-5111/9/6/008

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1/2,

which is smaller than the best possible value of

2/3

obtained only by the classical communication. On the other hand, if the noisy quantum channel is modeled by a single Lindblad operator, the average fidelity is always greater than

2/3.

{\mathit{E}}^{\mathit{Q}}

. Two interesting quantities can be defined for this process: the entanglement fidelity

{\mathit{F}}_{\mathit{e}}

and the entropy exchange

{\mathit{S}}_{\mathit{e}}

. It turns out that neither of these quantities depends in any way on the system R, but only on the initial state and dynamical evolution of Q.

{\mathit{F}}_{\mathit{e}}

and

{\mathit{S}}_{\mathit{e}}

are related to various other fidelities and entropies and are connected by an inequality reminiscent of the Fano inequality of classical information theory. Some insight can be gained from these techniques into the security of quantum cryptographic protocols and the nature of quantum error-correcting codes. \textcopyright{} 1996 The American Physical Society.

R

and

Q

, after which

Q

is subjected to a dynamical evolution given by the superoperator $\superop^{Q}$. Two interesting quantities can be defined for this process: the entanglement fidelity

F_{e}

and the entropy production

S_{e}

. It turns out that neither of these quantities depends in any way on the system

R

, but only on the initial state and dynamical evolution of

Q

F_{e}

and

S_{e}

are related to various other fidelities and entropies, and are connected by an inequality reminiscent of the Fano inequality of classical information theory. Some insight can be gained from these techniques into the security of quantum cryptographic protocols and the nature of quantum error-correcting codes.