Eur. Phys. J. D 38, 389-396 (2006)
https://doi.org/10.1140/epjd/e2006-00006-6

Effects of single-qubit quantum noise on entanglement purification

¹ Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, Via Valleggio 11, 22100 Como, Italy
² Istituto Nazionale per la Fisica della Materia, Unità di Como and Istituto Nazionale di Fisica Nucleare, Sezione di Milano, 20133 Milano, Italy
³ Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, 20133 Milano, Italy
⁴ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italy

Corresponding author: ^a giuliano.benenti@uninsubria.it

Received: 19 September 2005
Published online: 10 January 2006

Abstract

We study the stability under quantum noise effects of the quantum privacy amplification protocol for the purification of entanglement in quantum cryptography. We assume that the E91 protocol is used by two communicating parties (Alice and Bob) and that the eavesdropper Eve uses the isotropic Bužek-Hillery quantum copying machine to extract information. Entanglement purification is then operated by Alice and Bob by means of the quantum privacy amplification protocol and we present a systematic numerical study of the impact of all possible single-qubit noise channels on this protocol. We find that both the qualitative behavior of the fidelity of the purified state as a function of the number of purification steps and the maximum level of noise that can be tolerated by the protocol strongly depend on the specific noise channel. These results provide valuable information for experimental implementations of the quantum privacy amplification protocol.