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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Entanglement swapping with local certification: Application to remote micromechanical resonators

M. Abdi, Stefano Pirandola, P. Tombesi, David Vitali

Published May 1, 2013• 3 citations
Publisher

Abstract

Entanglement swapping allows to entangle two distant systems which never interacted. This paper applies this protocol to an initial tripartite systems of two identical cavity optomechanical systems. Each system is formed by a micro-mechanical resonator playing the role of the remote mode, coupled to two independently driven optical cavity modes with different frequencies, whose output field are sent to Bell and certification modes.

DOI
10.1109/cleoe-iqec.2013.6801729

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Entanglement swapping allows to entangle two distant systems which never interacted. This paper applies this protocol to an initial tripartite systems of two identical cavity optomechanical systems. Each system is formed by a micro-mechanical resonator playing the role of the remote mode, coupled to two independently driven optical cavity modes with different frequencies, whose output field are sent to Bell and certification modes.
We propose a protocol for entanglement swapping which involves tripartite systems. The generation of remote entanglement induced by the Bell measurement can be easily certified by additional local measurements. We illustrate the protocol in the case of continuous variable systems where the certification is effective for an appropriate class of three-mode gaussian states. We then apply the protocol to optomechanical systems, showing how mechanical entanglement between two remote micromechanical resonators can be generated and certified via local optical measurements.
We introduce a modification of the standard entanglement swapping protocol where the generation of entanglement between two distant modes is realized and verified using only local optical measurements. We show, indeed, that a simple condition on the purity of the initial state involving also an ancillary mode is sufficient to guarantee the success of the protocol by local measurements [M. Abdi, S. Pirandola, P. Tombesi, and D. Vitali, Phys. Rev. Lett. 109, 143601 (2012)]. We apply the proposed protocol to a tripartite optomechanical system where the never interacting mechanical modes become entangled and certified using only local optical measurements.
Abstract In this study, we present two protocols for entanglement swapping and quantum teleportation using an optomechanical cavity, wherein the moving mirror behaves as an auxiliary mode. The initial state of the system comprises two distinct entangled state pairs: one between atoms 1 and 2 and the other between cavity fields 3 and 4 (which are prepared in an entangled state of number and coherent states). By interacting the atom 2, field 3 and the auxiliary mode of the moving mirror, initially in the ground state ∣0〉 m , inside the optomechanical cavity, and applying the detection method, a tripartite entangled state is generated via entanglement swapping process. As a result, the initial atom 1–atom 2 and also field 3–field 4 entanglements are converted into the tripartite system, atom 1, field 4, and the auxiliary mode. We then evaluate and analyze the influence of the optomechanical coupling coefficient on the significant quantities in the entanglement swapping model, such as the success probability of the detection process, the fidelity, and the linear entropy (as a measure of entanglement). Finally, we demonstrate that the optomechanical cavity can be employed to teleport a bipartite entangled state with perfect fidelity by utilizing a quantum channel in the form of an unknown tripartite entangled state.
Systems of coupled mechanical resonators are useful for quantum information processing and fundamental tests of physics. Direct coupling is only possible with resonators of very similar frequency, but by using an intermediary optical mode, non-degenerate modes can interact and be independently controlled in a single optical cavity. Here we demonstrate coherent optomechanical state swapping between two spatially and frequency separated resonators with a mass ratio of 4. We find that, by using two laser beams far detuned from an optical cavity resonance, efficient state transfer is possible. Although the demonstration is classical, the same technique can be used to generate entanglement between oscillators in the quantum regime.Coupled mechanical resonators where each mode can be separately controlled are a promising system for quantum information processing. Here, Weaver et al. demonstrate coherent swapping of optomechanical states between two separate resonators.
We propose an experiment to create and verify entanglement between remote mechanical objects by use of an optomechanical interferometer. Two optical cavities, each coupled to a separate mechanical oscillator, are coherently driven such that the oscillators are laser cooled to the quantum regime. The entanglement is induced by optical measurement and comes about by combining the output from the two cavities to erase which-path information. It can be verified through measurements of degrees of second-order coherence of the optical output field. The experiment is feasible in the regime of weak optomechanical coupling. Realistic parameters for the membrane-in-the-middle geometry suggest entangled state lifetimes on the order of milliseconds.
A protocol able to prepare two remote and initially uncorrelated microwave modes in an entangled stationary state, which is certifiable using only local optical homodyne measurements id proposed. The protocol is an extension of continuous variable entanglement swapping, and exploits two hybrid quadripartite opto‐electro‐mechanical systems in which a nanomechanical resonator acts as a quantum interface able to entangle optical and microwave fields. The proposed protocol allows to circumvent the problems associated with the fragility of microwave photons with respect to thermal noise and may represent a fundamental tool for the realization of quantum networks connecting distant solid‐state and superconducting qubits, which are typically manipulated with microwave fields. The certifying measurements on the optical modes guarantee the success of entanglement swapping without the need of performing explicit measurements on the distant microwave fields.