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Physical Review A

More efficient entanglement purification

NASSER METWALLY

Published Nov 18, 2002• 23 citations
Publisher

Abstract

An improved version of the so-called Oxford protocol for entanglement purification is described, in which the usual local unitary transformations are only performed when they are really helpful. For some initial states, the modified protocol is equivalent to the original one, but for all other initial states it converges faster, is more efficient, and needs fewer operations.

DOI
10.1103/physreva.66.054302

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An improved version of the so-called Oxford protocol for entanglement purification is described, in which the usual local unitary transformations are only performed when they are really helpful. For some initial states, the modified protocol is equivalent to the original one, but for all other initial states it converges faster, is more efficient, and needs fewer operations.
In order to perform faithfully quantum communication protocols such as quantum teleportation, superdense coding, quantum key distribution, and quantum secret sharing, we need the entanglement purification process to make a maximal entanglement out of many copies of the partially entangled pairs by using local operations and classical communication. In this dissertation,\nwe analyze the efficiency of several entanglement purification protocols for qubit states and qudit states, and present a new efficient entanglement purification protocol. Furthermore, we show that our method can be applied to the existing best protocol\nso as to improve the efficiency.
Purification schemes for multiparticle entangled states cannot be treated as straightforward extensions of those two-particle ones because of the lack of symmetry they possess. We propose purification protocols for a wide range of mixed entangled states of many particles. These are useful for understanding entanglement, and could be of practical significance in multiuser cryptographic schemes or distributed quantum computation and communication. We show that operating locally on multiparticle entangled states directly is more efficient than relying on two-particle purification.
Purification schemes for multiparticle entangled states cannot be treated as straightforward extensions of those two-particle ones because of the lack of symmetry they possess. We propose purification protocols for a wide range of mixed entangled states of many particles. These are useful for understanding entanglement, and could be of practical significance in multiuser cryptographic schemes or distributed quantum computation and communication. We show that operating locally on multiparticle entangled states directly is more efficient than relying on two-particle purification.
Bipartite entanglement purification is the conversion of copies of weakly entangled pairs shared between two separated parties into a smaller number of strongly entangled shared pairs using only local operations and classical communication. Choosing between different entanglement purification protocols generally involves weighing up a trade-off between the ratio of strongly entangled pairs produced to weakly entangled pairs consumed, which we call the rate of the protocol, and the degree of the entanglement of the strongly entangled pairs, typically measured by the fidelity of those pairs to maximally entangled states. By randomly choosing a protocol according to a probability distribution over a list of protocols for each pair we want to produce, we can achieve rates and fidelities not achieved by any of the original protocols. Here, we show how to choose this distribution to maximize the rate at which we produce qubit pairs with a given fidelity to a Bell state or, equivalently, to maximize the fidelity to a Bell state of the qubit pairs produced at a given rate. We investigate both the asymptotic case, where the number of initial pairs goes to infinity, and the finite-size regime, where protocols are restricted to a finite number of weakly entangled pairs.