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arXiv:1712.08085 · Physical Review A

Multipartite entanglement swapping and mechanical cluster states

Carlo Ottaviani, Cosmo Lupo, Alessandro Ferraro, Mauro Paternostro, Stefano Pirandola

Published Mar 13, 2019• 14 citations
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Abstract

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.

DOI
10.1103/physreva.99.030301

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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.
Greenberger-Horne-Zeilinger (GHZ) and cluster states are two typical kinds of multipartite entangled states and can respectively be used for realizing quantum networks and one-way computation. We propose a feasible scheme for generating Gaussian GHZ and cluster states of multiple mechanical oscillators by pulsed cavity optomechanics. In our scheme, each optomechanical cavity is driven by a blue-detuned pulse to establish quantum steerable correlations between the cavity output field and the mechanical oscillator, and the cavity outputs are combined at a beam-splitter array with given transmissivity and reflectivity for each beam splitter. We show that by harnessing the light-mechanical steerable correlations, the mechanical GHZ and cluster states can be realized via homodyne detection on the amplitude and phase quadratures of the output fields from the beam-splitter array. These achieved mechanical entangled states can be viewed as the output states of an effective mechanical beam-splitter array with the mechanical inputs prepared in squeezed states with the light-mechanical steering. The effects of detection efficiency and thermal noise on the achieved mechanical states are investigated. The present scheme does not require externally injected squeezing and it can also be applicable to other systems such as light-atomic-ensemble interface, apart from optomechanical systems.
We present a convenient and efficient scheme to generate multipartite continuous-variable entanglement via mechanical oscillator displacement induced by two strong input pump fields in a conventional single-cavity optomechanical system. It is shown that multipartite entanglement among the outputs of the two pump fields and any number of relatively weak probe fields can be realized and optimized when the two pump fields with suitable amplitude ratio and relative initial phase are, respectively, tuned to the red and blue mechanical sidebands of a single-cavity mode and each probe field is red detuned by the mechanical frequency with respect to a different neighboring cavity mode. This method can, in principle, be extended to flexibly and conveniently generate an arbitrary number of nondegenerate bright entangled fields by using only coherent laser fields, and may find promising applications in realistic quantum communication and networks.
Cluster states are multipartite entangled states that are maximally connected and resilient to decoherence, making them valuable resources for quantum information processing. Continuous-variable (CV) cluster states have been extensively investigated for such applications. Here we present a pulsed protocol for generating CV cluster states in a phononic quantum network composed of phonon waveguides, mechanical resonators, and optical cavities. A key feature of this architecture is its modular design, where pairs of mechanical modes serve as building blocks with only local, tunable interactions between mechanical and cavity modes. We characterize the generated cluster states through the average nullifier of the CV modes. Our numerical results show that high-quality CV cluster states can be generated with moderate squeezing parameters, whereas strong squeezing and the resulting large phonon occupations can degrade the cluster states in the presence of finite dissipation. We further show that, under moderate squeezing and dissipation, the average nullifier can decrease with increasing system size NNN, demonstrating the scalability of the proposed scheme. As a direct application, we demonstrate that distant mechanical modes can be entangled through local 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.
Quantum information has reached a stage where real-world applications stimulate an intense research for the implementation of reliable and practical protocols for quantum communication and information processing. The implementation of such protocols, though, requires distributing quantum correlations (entanglement) among a number of degrees of freedom (modes) increasing with the complexity of the task to achieve. In the large-number-of-modes regime, the most promising example is probably one-way quantum computation in which the computation is achieved by applying local measurements to a set of modes initially in a cluster state [1]. However the generation of multipartite entangled states requires experimental configurations whose complexity increases with the number of the modes involved by means of optical devices. In contrast, a practical source should be compact, scalable, and permit to master the quantum properties of the generated states even when the number of modes is very large.