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Journal of the Optical Society of America B

Local squeezing-assisted two-copy and single-copy continuous variable entanglement distillation

ShengLi Zhang, Chenhui Jin, Jiansheng Guo, Jianhong Shi, Wan‐Su Bao, Xu‐Bo Zou, Guang‐Can Guo

Published Mar 13, 2014• 0 citations
Publisher

Abstract

Entanglement distillation is a physically feasible operation which helps to partially or completely eliminate noise-induced decoherence in the distribution of entangled states. In this paper, we investigate the two-copy and single-copy distillation of an amplitude-damped continuous variable two-mode squeezed vacuum state. We consider local squeezing as one of the important tools [Phys. Rev. A84, 062309 (2011)] to enhance distillation. Our result is twofold. First, we show that local squeezing is useful to improve the distillation of two-copy interference-based distillation. Second, we show single-copy photon subtraction-based distillation is more efficient in providing more entangled outputs. However, such an advantage would diminish and two-copy distillation could succeed with much higher probability of success for a fixed amount of distilled entanglement.

DOI
10.1364/josab.31.000810

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Entanglement distillation is a physically feasible operation which helps to partially or completely eliminate noise-induced decoherence in the distribution of entangled states. In this paper, we investigate the two-copy and single-copy distillation of an amplitude-damped continuous variable two-mode squeezed vacuum state. We consider local squeezing as one of the important tools [Phys. Rev. A84, 062309 (2011)] to enhance distillation. Our result is twofold. First, we show that local squeezing is useful to improve the distillation of two-copy interference-based distillation. Second, we show single-copy photon subtraction-based distillation is more efficient in providing more entangled outputs. However, such an advantage would diminish and two-copy distillation could succeed with much higher probability of success for a fixed amount of distilled 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.
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.
We study entanglement concentration of continuous-variable Gaussian states by local photon subtractions enhanced by coherent displacements. Instead of the previously considered symmetric two-mode squeezed vacuum states, we investigate the protocol for input states in the form of split single-mode squeezed vacuum (i.e., states obtained by mixing a single-mode squeezed vacuum with a vacuum state on a beam splitter), which is an experimentally highly relevant configuration. We analyze two scenarios in which the displacement-enhanced photon subtraction is performed either only on one or on both of the modes and show that local displacements can lead to improved performance of the concentration protocol.
We propose a theoretical scheme for entanglement distillation of the two-mode squeezed vacuum state (TMSVS) by nondeterministic optical nonlinear amplification based on the work of Anisimov et al. [Phys. Rev. Lett.104, 103602 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.103602]. By applying the quantum-scissors operations to both modes of the TMSVS, only the twin vacuum and the twin one-photon components can survive in the resulting state. We show that both entanglement and squeezing can be enhanced in the high-transmissivity and low-squeezing region. In addition, a comparison with symmetrical single-photon subtraction and quantum catalysis shows that the proposed states can achieve a better entanglement enhancement than the photon subtraction in a high-transmissivity region, and a similar property is shared by the catalyzed states in low-transmissivity regions.
Entangled photons are ideally suited to the transmission of photonic quantum information. Mitigating the effects of decoherence is fundamental to distributing photonic entanglement across large distances. One such proposal is entanglement distillation, in which operations on a large ensemble of weakly entangled states generate a smaller ensemble of more strongly entangled states. In this thesis, we experimentally and theoretically analyse various tools required for demonstrating continuous-variable (CV) entanglement distillation, following the proposal by Browne et al., [Phys. Rev. A 67, 062320 (2003)]. Specifically, we propose figures of merit to account for the practical limitations of non-deterministic non-Gaussian operations, and analyse the experimental parameters necessary to optimise them. We develop a source of pulsed two-mode squeezed states, which are the initial states of our entanglement distillation protocol. We use weak-field homodyne detection as a phase-dependent photon counting detector, and demonstrate its utility in conditional state generation. Using these states, we demonstrate sub-binomial light as a tool for benchmarking quantum states. Finally, we applied two-mode weak-field homodyne detection to two entangled states and demonstrate correlations in the photon counting statistics which depend on a joint phase from two independent local oscillators. This setup is sufficient to apply an entanglement witness developed by Puentes et al. [New J. Phys. 12, 033042 (2010)]. Despite encouraging simulations, we do not witness entanglement with this scheme, which we attribute to a noise source unaccounted for in the simulations. Although we do not demonstrate entanglement distillation outright, the tools we develop to do so represent a general, hybrid approach to CV quantum optics. Developing tools such as phase-resolved projective measurement on two-mode states allows us to probe both the wave and particle nature of entangled light at the single-photon level. Using and expanding these techniques to probe larger quantum systems may prove useful in studies of fundamental physics and quantum enhanced technologies.