Quantifying entanglement in two-mode Gaussian states

Tserkis, Spyros; Ralph, T. C.

doi:10.1103/physreva.96.062338

Cited by 47 publications

(50 citation statements)

References 32 publications

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“…We see that, as expected, 2ν − serves as a lower bound for the inseparability I. Since this bipartite Gaussian state is approximately symmetric, from 2ν − we can calculate the entanglement of formation, which is accepted as a proper measure of quantum correlations as a resource [14,27,28].…”

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confidence: 72%

Entanglement of propagating optical modes via a mechanical interface

et al. 2020

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Many applications of quantum information processing (QIP) require distribution of quantum states in networks, both within and between distant nodes [1]. Optical quantum states are uniquely suited for this purpose, as they propagate with ultralow attenuation and are resilient to ubiquitous thermal noise. Mechanical systems are then envisioned as versatile interfaces between photons and a variety of solid-state QIP platforms [2, 3]. Here, we demonstrate a key step towards this vision, and generate entanglement between two propagating optical modes, by coupling them to the same, cryogenic mechanical system. The entanglement persists at room temperature, where we verify the inseparability of the bipartite state and fully characterize its logarithmic negativity by homodyne tomography. We detect, without any corrections, correlations corresponding to a logarithmic negativity of E N = 0.35. Combined with quantum interfaces between mechanical systems and solid-state qubit processors already available [4, 5, 6, 7] or under development [8,9], this paves the way for mechanical systems enabling long-distance quantum information networking over optical fiber networks.Entanglement is a crucial resource for QIP [10]. As such, the ability to entangle fields of arbitrary wavelength will be important for linking nodes in heterogeneous QIP networks. Mechanical oscillators are uniquely poised in their ability to create such links, thanks to the frequency-independence of the radiation pressure interaction. The ability to entangle two radiation fields via a common mechanical interaction was outlined 20 years ago [11,12], and the intervening decades have seen the development of optomechanical devices [13] which are robustly quantum mechanical and routinely integrated into hybrid systems.Recently, mechanically-mediated entanglement has been reported between propagating microwave fields [14] as well as two superconducting qubits [15]. In both cases, the entanglement remained confined to the dilution refrigerator in which it was created. Here, we utilize an extremely coherent mechanical platform 1 arXiv:1911.05729v2 [quant-ph]

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confidence: 72%

Entanglement of propagating optical modes via a mechanical interface

et al. 2020

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“…for finite squeezing ζ and loss on one arm of the two-mode squeezed state η [26]. For the case of the error-corrected channel, the covariance matrix of the Gaussian approximated output state was calculated from the first and second moments of the output state (calculations shown in the Appendix) and the GEOF was calculated following Ref.…”

Section: The Error-correction Protocolmentioning

confidence: 99%

Quantum error correction of continuous-variable states with realistic resources

Dias

Ralph

2018

Phys. Rev. A

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Gaussian noise induced by loss on Gaussian states may be corrected by distributing Einstein-Podolsky-Rosen entanglement through the loss channel, purifying the entanglement using a noiseless linear amplifier (NLA), and then using it for continuous-variable teleportation of the input state. Linear optical implementations of the NLA unavoidably introduce small amounts of excess noise and detection, and source efficiency will be limited in current implementations. In this paper, we analyze the error-correction protocol with nonunit efficiency sources and detectors and show the excess noise may be partially compensated by adjusting the classical gain of the teleportation protocol. We present a strong case for the potential of demonstrable error-correction with current technology.

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“…By applying a phase rotation to V bp (ω n ), it can be transformed into the standard form V Bipartite entanglement can be characterized by calculating the entanglement of formation (EOF) [63,64], which quantifies the entanglement of a state in terms of the entropy of entanglement of the least entangled pure state needed to prepare it (under local operations and classical communication). Even though, in general, EOF lacks an analytical expression, for states charactered by a covariance matrix such as V (s) bp (ω n ), the EOF can be written as [65,66] E F ≡ cosh 2 r 0 log 2 (cosh 2 r 0 ) − sinh 2 r 0 log 2 (sinh 2 r 0 ), (27) where, for entangled states, r 0 (characterizing the minimum amount of two-mode squeezing needed to create a state) is given by…”

Section: Switchable Bipartite Entanglementmentioning

confidence: 99%

Switchable bipartite and genuine tripartite entanglement via an optoelectromechanical interface

et al. 2020

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Controllable multipartite entanglement is a crucial element in quantum information processing. Here we present a scheme that generates switchable bipartite and genuine tripartite entanglement between microwave and optical photons via an optoelectromechanical interface, where microwave and optical cavities are coupled to a mechanical mode with controllable coupling constants. We show that by tuning an effective gauge phase between the coupling constants to the "sweet spots", bipartite entanglement can be generated and switched between designated output photons. The bipartite entanglement is robust against the mechanical noise and the signal loss to the mechanical mode when the couplings are chosen to satisfy the impedance matching condition. When the gauge phase is tuned away from the "sweet spots", genuine tripartite entanglement can be generated and verified with homodyne measurement on the quadratures of the output fields. Our result can lead to the implementation of controllable and robust multipartite entanglement in hybrid quantum systems operated in distinctively different frequencies.

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Quantifying entanglement in two-mode Gaussian states

Cited by 47 publications

References 32 publications

Entanglement of propagating optical modes via a mechanical interface

Entanglement of propagating optical modes via a mechanical interface

Quantum error correction of continuous-variable states with realistic resources

Switchable bipartite and genuine tripartite entanglement via an optoelectromechanical interface

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