Entanglement Purification

Abstract

In Chap. 7 the theory of quantum error correction was presented. The present chapter describes an alternative method of overcoming decoherence which is particularly useful for quantum state communication. The main idea is to distill from a large set of (pairs of) entangled particles, possibly degraded in entanglement purity by decoherence, a subset of particles with enhanced entanglement purity. Section 8.2 describes the general principles of entanglement purification. Specific examples are local filtering (Sect. 8.3), suitable for increasing the entanglement for pure states, and quantum privacy amplification (Sect. 8.4), designed to increase the security of quantum cryptography over noisy quantum channels. The generalisation of purification to multiparticle entanglement will be addressed in Sect. 8.5. Section 8.6 shows how to create maximally entangled EPR pairs between spatially distant atoms, each of them inside a high-Q optical cavity, by sending photons through a noisy channel, such as a standard optical fibre. As the absorption probability of photons during the transmission grows exponentially with the distance, so will the required number of repetitions for a successful transmission. Section 8.7 presents the quantum repeater method, which reduces the growth of the required number of operations as function of the transmission distance from exponential to polynomial.