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arXiv:quant-ph/0701220 · Physical Review A

Concentration and purification of entanglement for qubit systems with ancillary cavity fields

C. D. Ogden, Mauro Paternostro, M. S. Kim

Published Apr 23, 2007• 25 citations
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Abstract

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.

DOI
10.1103/physreva.75.042325

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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.
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.
This paper presents an optimal entanglement concentration protocol (ECP) for entangled solid-state systems, using the coherent-state input–output process working in the low-Q cavity quantum electrodynamics regime. The solid-state system can be described as a three-level atom confined in a one-side optical microcavity. Using the ancillary coherent optical pulse to perform the cavity input–output process, different state-dependent phase shifts of the output coherent state can be discriminated by homodyne detection, and a less-entangled atomic pair can be concentrated to maximally entangled state in a certain probability between two remote parties nonlocally. By repeating the concentration process, the remote parties can further obtain a higher success probability. Compared with conventional ECPs, only one pair of less-entangled atoms is needed in the proposed protocol, and the coherent-state input–output process is working in a low-Q cavity in the atom–cavity intermediate coupling region. With feasible technologies, this protocol may be widely used in quantum repeaters and long-distance quantum communication.
We present a physical scheme for entanglement concentration of unknown atomic entangled states via cavity decay.In the scheme,each of the atoms is a three-level system,which has two ground states(｜g〉,｜e〉),and an excited state(｜r〉),the atomic state is used as stationary qubit and photonic state as flying qubit.There are two nonmaximally entangled atom-pairs,one atom of every atom-pairs are capped in two leaked cavity,respectively.In the case of large detuning and the upper level ｜r〉 can be decoupled from the evolution during the interaction,applying classical laser pulses on the capped atoms and by detecting the photons leaked from the cavities,a close maximally entangled state can be obtained from the two pairs of partially atomic entangled states probabilistically.Our scheme is practical and the remote entangled states concentration via high quality fiber will be convenient.
By utilizing Faraday rotation of photons, we present a highly efficient protocol for entanglement concentration of atomic Bell states, which departs from the conventional method of sequential interactions between the auxiliary photon and two optical cavities. Instead, the simultaneous interaction of the auxiliary photon with two atomic cavities is involved in order to significantly reduce the time requirement for achieving atomic Bell state entanglement concentration. By employing iterative applications of the protocol for entanglement concentration, the discarded states can be repeatedly concentrated, efficiently increasing the probability of success. Furthermore, our entanglement concentration protocols (ECPs) operate in low-Q cavities, which are easier to implement in practical applications than high-Q cavities. Finally, it can be generalized to an N -atom GHZ states entanglement concentration protocol.