Sending entanglement through noisy quantum channels

TLDR

This paper addresses general questions of quantum information theory arising from the transmission of quantum entanglement through noisy quantum channels. A pure entangled state of systems R and Q is prepared, then Q undergoes evolution via superoperator E^Q, defining entanglement fidelity F_e and entropy exchange S_e for the process. F_e and S_e depend only on Q’s initial state and evolution, are linked by an inequality reminiscent of Fano’s, and provide insight into quantum cryptographic security and error‑correcting codes. © 1996 The American Physical Society.

Abstract

This paper addresses some general questions of quantum information theory arising from the transmission of quantum entanglement through (possibly noisy) quantum channels. A pure entangled state is prepared of a pair of systems R and Q, after which Q is subjected to a dynamical evolution given by the superoperator ${\mathit{E}}^{\mathit{Q}}$. 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.