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arXiv:1312.0981 · Physical Review A

Continuous-variable-entanglement swapping and its local certification: Entangling distant mechanical modes

Mehdi Abdi, Stefano Pirandola, Paolo Tombesi, David Vitali

Published Feb 19, 2014• 38 citations
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Abstract

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.

DOI
10.1103/physreva.89.022331

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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.
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We study the detection of continuous-variable entanglement, for which most of the existing methods designed so far require a full specification of the devices, and we present protocols for entanglement detection in a scenario where the measurement devices are completely uncharacterized. We first generalize, to the continuous variable regime, the seminal results by Buscemi [Phys. Rev. Lett. 108, 200401 (2012)PRLTAO0031-900710.1103/PhysRevLett.108.200401] and Branciard et al. [Phys. Rev. Lett. 110, 060405 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.060405], showing that all entangled states can be detected in this scenario. Most importantly, we then describe a practical protocol that allows for the measurement-device-independent certification of entanglement of all two-mode entangled Gaussian states. This protocol is feasible with current technology as it makes use only of standard optical setups such as coherent states and homodyne measurements.
We present a protocol for generating multipartite quantum correlations across a quantum network with a continuous-variable architecture. An arbitrary number of users possess two-mode entangled states, keeping one mode while sending the other to a central relay. Here a suitable multipartite detection is implemented, by multiple homodyne detections at the outputs of the interferometer, to conditionally generate a cluster state on the retained modes. This cluster state can be suitably manipulated by the parties and used for tasks of quantum communication in a fully optical scenario. More interestingly, the protocol can be used to create a purely-mechanical cluster state starting from a supply of optomechanical systems. We show that detecting the optical parts of optomechanical cavities may efficiently swap entanglement into their mechanical modes, creating cluster states up to five modes under suitable cryogenic conditions.