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Journal of the Optical Society of America B

$O(\sqrt\eta)$ efficiency entanglement distillation with one-time photon subtraction over near-zero transmittance bosonic channel

ShengLi Zhang

Published Dec 12, 2019• 1 citation
Publisher

Abstract

Entanglement distillation is an efficient method to retrieve high-quality entanglement from a large number of noise-damped entanglement states. Many investigations on continuous variable entanglement distillation have focused on low-loss or medium-loss channels. Herein, we primarily study entanglement distillation in extremely lossy (total channel transmittance η ≪ 1 ) or even near-zero transmittance ( η ≈ 0 ) channels. In particular, we analyze the manner in which entanglement and success probability decrease as η → 0 . The performances of conventional biside photon subtraction and one-time photon subtraction on two optical modes separated by L km are investigated. The motivation for our study includes the recent advancements in twin-field quantum key distribution, wherein single-photon detection is sufficient to provide a useful private key. In the same vein, we propose an entanglement distillation scheme with an efficiency of O ( η ) using one-time photon subtraction and weak coherent state injection. Thus, our proposed scheme provides a method for distilling extremely damped entanglement states for continuous variable quantum information processing.

DOI
10.1364/josab.381090

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O(η)O(\sqrt\eta)O(η​) efficiency entanglement distillation with one-time photon subtraction over near-zero transmittance bosonic channel
Entanglement distillation is an efficient method to retrieve high-quality entanglement from a large number of noise-damped entanglement states. Many investigations on continuous variable entanglement distillation have focused on low-loss or medium-loss channels. Herein, we primarily study entanglement distillation in extremely lossy (total channel transmittance η ≪ 1 ) or even near-zero transmittance ( η ≈ 0 ) channels. In particular, we analyze the manner in which entanglement and success probability decrease as η → 0 . The performances of conventional biside photon subtraction and one-time photon subtraction on two optical modes separated by L km are investigated. The motivation for our study includes the recent advancements in twin-field quantum key distribution, wherein single-photon detection is sufficient to provide a useful private key. In the same vein, we propose an entanglement distillation scheme with an efficiency of O ( η ) using one-time photon subtraction and weak coherent state injection. Thus, our proposed scheme provides a method for distilling extremely damped entanglement states for continuous variable quantum information processing.
We present a detailed theoretical analysis for the distillation of one copy of a mixed two-mode continuous-variable entangled state using beam splitters and coherent photon-detection techniques, including conventional on-off detectors and photon-number-resolving detectors. The initial Gaussian mixed-entangled states are generated by transmitting a two-mode squeezed state through a lossy bosonic channel, corresponding to the primary source of errors in current approaches to optical quantum communication. We provide explicit formulas to calculate the entanglement in terms of logarithmic negativity before and after distillation, including losses in the channel and the photon detection, and show that one-copy distillation is still possible even for losses near the typical fiber channel attenuation length. A lower bound for the transmission coefficient of the photon-subtraction beam splitter is derived, representing the minimal value that still allows to enhance the entanglement.
Photon subtraction (PS), due to its feasibility in physical implementation, has been widely utilized in Gaussian entanglement distillation. However, in this paper, we will show that photon addition (PA) can be employed to provide an additional enhancement in both the quality of distilled entanglement and the success probability if the input state is a weak two-mode squeezed vacuum state. Moreover, compared with biside PS, the distillation probability gains a $O(\frac{1}{{\ensuremath{\lambda}}^{2}})$ improvement, which increases rapidly when $\ensuremath{\lambda}\ensuremath{\ll}1$. Our PA-based scheme is obtained first by single-photon injection and later by vacuum state projection. The performance of PA in the presence of both an approximated single photon and amplitude-damping noise has been analyzed. Our result sheds more light on the indispensable non-Gaussian ingredients in Gaussian-state distillation and could be of great use in developing more efficient distillation schemes. Finally, the sensitivity of the PA scheme to inefficient photon detection has also been investigated.
Entanglement distillation is a probabilistic quantum operation which tries to repair entanglement after environment-induced decoherence. All known distillations of continuous variable entanglement always assume that the entanglement is distributed via a standard attenuating channel with fixed photon loss rate, which is fairly idealized without many realistic effects taken into account. Here we investigate the problem of distillation of entanglement transmitted via atmospheric channel, with transmittance being highly probabilistic and unfixed. Two typical distillation schemes, i.e., single-sided photon subtraction and bi-sided photon subtraction, are investigated.
Quantum entanglement distillation is a probabilistic process which protects entanglement from environment-induced decoherence. In this paper, we investigate the distillation of a continuousvariable optic entangled state with noiseless linear amplification (NLA). NLA schemes perform better than the conventional photon-subtraction-based distillation scheme, particularly in distributing entanglement over extremely low efficiency quantum channels. Finally, a comparison between the NLA-based scheme and the local squeezing-enhanced photon subtraction scheme is also investigated.
Recently, the strong single-mode squeezed vacuum state of light with −15-15−15−15 dB of classic noise has been created [Phys. Rev. Lett.117, 110801 (2016)10.1103/PhysRevLett.117.110801]. This is an important resource in continuous variable (CV) quantum communication and fault-tolerant quantum computing. Nevertheless, strong squeezing means a non-negligible population in high-photon-number subspace and may pose a strong challenge to photon-based technology, for example, entanglement distillation. Entanglement distillation is an efficient method for retrieving a higher quality of entanglement from a weakly entangled state. Up till now, almost all the schemes for entanglement distillation are restricted to the low-squeezing regime. The distillation of strong-squeezing induced entanglement is an interesting but open topic in the near future. Here, we take the single-mode squeezed entangled state (SMSE) as an example and show that conventional photon subtraction based distillation fails to generate a higher quality of entanglement with experimentally feasible optical beam splitters. To this point, we show that the superposition of photon annihilation and creation could be an effective method. A practical scheme for implementing such a superposition with on-line squeezing is suggested. Our method is verified numerically by the calculation of a 25 dB SMSE state with an ideal photon detector and for distillation of 20.5 dB SMSE state with practical dichotic on-off detectors. The analysis of the distillation of the strong squeezing effect could be extended straightforwardly to other squeezing-based quantum information processing, such as quantum metrology and quantum illumination.
In this paper, we study entanglement distillation of multipartite continuous-variable Gaussian entangled states. Following Opatrný \emph{et al.}'s photon subtraction (PS) scheme, the probability of successful distillation decreases exponentially with the number of parties NNN. However, here, we shall propose an entanglement distillation scheme whose success probability scales as a constant with NNN. Our protocol employs several local squeezers, but it requires only a single PS operation. Using the logarithmic negativity as a measure of entanglement, we find that both the success probability and the distilled entanglement can be improved at the same time. Moreover, an NNN-mode transfer theorem (transferring states from phase space to Hilbert space) is presented.