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Physical Review A

Entanglement purification in cavity QED using local operations

José Luis Romero, Luis Roa, J. C. Retamal, C. Saavedra

Published May 7, 2002• 31 citations
Publisher

Abstract

We study a physical implementation of an entanglement purification protocol using a cavity quantum electrodynamics based proposal, in both the microwave and the optical domain. The protocol consists of local quantum operations of each particle of an entangled system with one auxiliary particle (ancilla). After the above interaction a measurement on ancillas is carried out. In the microwave region the quantum information is stored in field states inside two distant cavities. We also give a procedure for quantifying the degree of entanglement between quantum fields, which allows verifying the efficiency of the purification process. In the optical domain, we study a setup of cold trapped ions inside cavities, where quantum bits are defined by two electronic levels of ions. This latter proposal is extended to create multiparticle entangled states among distant quantum systems. Entanglement is achieved through a set of local measurements on pairs of entangled particles.

DOI
10.1103/physreva.65.052319

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We study a physical implementation of an entanglement purification protocol using a cavity quantum electrodynamics based proposal, in both the microwave and the optical domain. The protocol consists of local quantum operations of each particle of an entangled system with one auxiliary particle (ancilla). After the above interaction a measurement on ancillas is carried out. In the microwave region the quantum information is stored in field states inside two distant cavities. We also give a procedure for quantifying the degree of entanglement between quantum fields, which allows verifying the efficiency of the purification process. In the optical domain, we study a setup of cold trapped ions inside cavities, where quantum bits are defined by two electronic levels of ions. This latter proposal is extended to create multiparticle entangled states among distant quantum systems. Entanglement is achieved through a set of local measurements on pairs of entangled particles.
We propose schemes for entanglement concentration and purification for qubit systems encoded in flying atomic pairs. We use cavity-quantum electrodynamics as an illustrative setting within which our proposals can be implemented. Maximally entangled pure states of qubits can be produced as a result of our protocols. In particular, the concentration protocol yields Bell states with the largest achievable theoretical probability while the purification scheme produces arbitrarily pure Bell states. The requirements for the implementation of these protocols are modest, within the state of the art, and we address all necessary steps in two specific setups based on experimentally mature microwave technology.
We propose an entanglement purification scheme based on material qubits and ancillary coherent multiphoton states. We consider a typical QED scenario where material qubits implemented by two-level atoms fly sequentially through a cavity and interact resonantly with a single mode of the radiation field. We explore the theoretical possibilities of realizing a high-fidelity two-qubit quantum operation necessary for the purification protocol with the help of a postselective balanced homodyne photodetection. We demonstrate that the obtained probabilistic quantum operation can be used as a bilateral operation in the proposed purification scheme. It is shown that the probabilistic nature of this quantum operation is counterbalanced in the last step of the scheme where qubits are not discarded after inadequate qubit measurements. As this protocol requires present-day experimental setups and generates high-fidelity entangled pairs with high repetition rates, it may offer interesting perspectives for applications in quantum information theory.
Summary form only given. Entanglement is one of the most striking features of quantum mechanics and was a source of many debates among the early founders of this theory. More recently, entanglement was considered as one of the key points in the field of quantum information processing. Those potential applications require however the deterministic production of entanglement implying a large number of subsystems. Spontaneous phenomena, generally used to entangle 2 systems, are therefore not easily extendable towards those requirements. Recent works have succeeded in producing entangled state of three or more particles by using spontaneous parametric down-conversion or a unitary operation on a ensemble of trapped ions. We have created an entangled state between two atoms and a mode of the electromagnetic field stored in a cavity. The particles are separated by centimetric distances, which allows for individual addressing. The entangled state is prepared by unitary reversible operations acting on one or two of the particles at the same time. The analysis of the state is performed by detecting correlations between individual observables.
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.