Maximal entanglement distillation with single-photon subtraction

Entanglement is an indispensable quantum resource for quantum information technology. In continuous-variable quantum optics, photon subtraction can increase the entanglement between Gaussian states of light, but for mixed states the extent of this entanglement increase is poorly understood. In this work, we use an entanglement measure based the Rényi-2 entropy to prove that single-photon subtraction increases bipartite entanglement by no more than log 2. This value coincides with the maximal amount of bipartite entanglement that can be achieved with one photon. The upper bound is valid for all Gaussian input states, regardless of the number of modes and the purity.Entanglement is an indispensable quantum resource for quantum information technology. In continuous-variable quantum optics, photon subtraction can increase the entanglement between Gaussian states of light, but for mixed states the extent of this entanglement increase is poorly understood. In this work, we use an entanglement measure based the Rényi-2 entropy to prove that single-photon subtraction increases bipartite entanglement by no more than log 2. This value coincides with the maximal amount of bipartite entanglement that can be achieved with one photon. The upper bound is valid for all Gaussian input states, regardless of the number of modes and the purity.

arXiv:2103.09197QuantumMay 2, 20227 citations

Purification of Gaussian States by Photon Subtraction

Kun Zhang, Hui‐jun Li, Jietai Jing +2 more

Photon subtraction can enhance entanglement, which for pure states induces a decrease in the purity of reduced states. In contrast, by analyzing the purities of Gaussian states before and after subtracting a single photon, we prove that the purity of a Gaussian state can also be increased by less than 20%. On the one hand, it reveals that photon subtraction can reduce entanglement, and on the other hand, it reveals that it can achieve a limited amount of Gaussian state purification. Through the analysis of some examples, we demonstrate the inherent mechanism and applicable scope of photon-subtraction-based purification. In a multimode system, we find that photon subtraction can increase entanglement and purify some of the reduced states simultaneously. We thus present purification through the suppression of Gaussian noise as a new application for photon subtraction in continuous-variable quantum information processing.Photon subtraction can enhance entanglement, which for pure states induces a decrease in the purity of reduced states. In contrast, by analyzing the purities of Gaussian states before and after subtracting a single photon, we prove that the purity of a Gaussian state can also be increased by less than 20%. On the one hand, it reveals that photon subtraction can reduce entanglement, and on the other hand, it reveals that it can achieve a limited amount of Gaussian state purification. Through the analysis of some examples, we demonstrate the inherent mechanism and applicable scope of photon-subtraction-based purification. In a multimode system, we find that photon subtraction can increase entanglement and purify some of the reduced states simultaneously. We thus present purification through the suppression of Gaussian noise as a new application for photon subtraction in continuous-variable quantum information processing.

arXiv:2409.03473Sep 5, 20240 citations

Continuous-variable-entanglement distillation with photon addition

ShengLi Zhang, YuLi Dong, Xu‐Bo Zou +2 more

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.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.

Physical Review ASep 27, 201338 citations

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

ShengLi Zhang

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.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.

Journal of the Optical Society of America BDec 12, 20191 citation

Multipartite continuous-variable entanglement distillation using local squeezing and only one photon-subtraction operation

Yang, Song, Xu‐Bo Zou, ShengLi Zhang +3 more

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 $N$ . However, here, we shall propose an entanglement distillation scheme whose success probability scales as a constant with $N$ . 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 $N$ -mode transfer theorem (transferring states from phase space to Hilbert space) is presented.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 $N$. However, here, we shall propose an entanglement distillation scheme whose success probability scales as a constant with $N$. 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 $N$-mode transfer theorem (transferring states from phase space to Hilbert space) is presented.

arXiv:1106.1536Jun 8, 20112 citations

Entanglement enhancement in multimode integrated circuits

Zacharie M. Léger, Aharon Brodutch, Amr Saher Helmy

The faithful distribution of entanglement in continuous-variable systems is essential to many quantum information protocols. As such, entanglement distillation and enhancement schemes are a cornerstone of many applications. The photon subtraction scheme offers enhancement with a relatively simple setup and has been studied in various scenarios. Motivated by recent advances in integrated optics, particularly the ability to build stable multimode interferometers with squeezed input states, a multimodal extension to the enhancement via photon subtraction protocol is studied. States generated with multiple squeezed input states, rather than a single input source, are shown to be more sensitive to the enhancement protocol, leading to increased entanglement at the output. Numerical results show the gain in entanglement is not monotonic with the number of modes or the degree of squeezing in the additional modes. Consequently, the advantage due to having multiple squeezed input states can be maximized when the number of modes is still relatively small (e.g., four). The requirement for additional squeezing is within the current realm of implementation, making this scheme achievable with present technologies.The faithful distribution of entanglement in continuous-variable systems is essential to many quantum information protocols. As such, entanglement distillation and enhancement schemes are a cornerstone of many applications. The photon subtraction scheme offers enhancement with a relatively simple setup and has been studied in various scenarios. Motivated by recent advances in integrated optics, particularly the ability to build stable multimode interferometers with squeezed input states, a multimodal extension to the enhancement via photon subtraction protocol is studied. States generated with multiple squeezed input states, rather than a single input source, are shown to be more sensitive to the enhancement protocol, leading to increased entanglement at the output. Numerical results show the gain in entanglement is not monotonic with the number of modes or the degree of squeezing in the additional modes. Consequently, the advantage due to having multiple squeezed input states can be maximized when the number of modes is still relatively small (e.g., four). The requirement for additional squeezing is within the current realm of implementation, making this scheme achievable with present technologies.

arXiv:1803.05981Physical Review AJun 4, 20183 citations

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efficiency entanglement distillation with one-time photon subtraction over near-zero transmittance bosonic channel

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. However, here, we shall propose an entanglement distillation scheme whose success probability scales as a constant with

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. 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

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