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arXiv:2509.15065 · Quantum Science and Technology

Simplified scheme for continuous-variable entanglement distillation: multicopy distillation of Gaussian entanglement without heralding Gaussian measurements

Jaromı́r Fiurášek

Published Jan 12, 2026• 0 citations
arXivHTMLPDF

Abstract

Abstract Entanglement of continuous-variable Gaussian states can be distilled by combination of de-Gaussifying operation such as single-photon subtraction and iterative heralded Gaussification. Here we present and analyze a simplified equivalent version of such entanglement distillation protocol, where the Gaussian measurements utilized in heralded Gaussification are eliminated and are absorbed into the preparation of suitable input Gaussian states of the simplified protocol. The simplified scheme contains less detectors and its overall success probability increases in comparison with the original scheme, while producing completely equivalent outputs. Our simplification of the entanglement distillation protocol closely parallels the recently proposed simplification of a scheme for breeding optical single-mode Gottesman–Kitaev–Preskill states (Aghaee Rad et al 2025 Nature 638 912 ). We investigate operation of the simplified entanglement distillation scheme for both pure and mixed input states and clarify how multicopy distillation of Gaussian entanglement emerges in a setup without any heralding Gaussian measurements.

DOI
10.1088/2058-9565/ae36cd

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Abstract Entanglement of continuous-variable Gaussian states can be distilled by combination of de-Gaussifying operation such as single-photon subtraction and iterative heralded Gaussification. Here we present and analyze a simplified equivalent version of such entanglement distillation protocol, where the Gaussian measurements utilized in heralded Gaussification are eliminated and are absorbed into the preparation of suitable input Gaussian states of the simplified protocol. The simplified scheme contains less detectors and its overall success probability increases in comparison with the original scheme, while producing completely equivalent outputs. Our simplification of the entanglement distillation protocol closely parallels the recently proposed simplification of a scheme for breeding optical single-mode Gottesman–Kitaev–Preskill states (Aghaee Rad et al 2025 Nature 638 912 ). We investigate operation of the simplified entanglement distillation scheme for both pure and mixed input states and clarify how multicopy distillation of Gaussian entanglement emerges in a setup without any heralding Gaussian measurements.
We study the entanglement distillation in continuous-variable systems when a photon replacement protocol is employed. A cascaded protocol is studied and we find that the resultant entanglement increases by increasing the number of repetitions. Interestingly, the entanglement enhancement is not sensitive to the asymmetry of the protocol and gives the same result for any arrangement in the absence of loss. The non-Gaussianity of the outcome state is also studied and it is found that the non-Gaussianity of the state dramatically depends on the experimental arrangements. We also consider the case of imperfect detectors and show that the main results are valid provided high-efficiency detectors are employed. By providing practical information on photon replacement operation, this work is one step towards the realization of universal quantum computation; in particular, in setups where de-Gaussifying protocols are only applicable to one of the parties.
Entanglement distribution between distant parties is an essential component to most quantum communication protocols. Unfortunately, decoherence effects such as phase noise in optical fibres are known to demolish entanglement. Iterative (multistep) entanglement distillation protocols have long been proposed to overcome decoherence, but their probabilistic nature makes them inefficient since the success probability decays exponentially with the number of steps. Quantum memories have been contemplated to make entanglement distillation practical, but suitable quantum memories are not realised to date. Here, we present the theory for an efficient iterative entanglement distillation protocol without quantum memories and provide a proof-of-principle experimental demonstration. The scheme is applied to phase-diffused two-mode-squeezed states and proven to distil entanglement for up to three iteration steps. The data are indistinguishable from those that an efficient scheme using quantum memories would produce. Since our protocol includes the final measurement it is particularly promising for enhancing continuous-variable quantum key distribution.
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.
Entanglement distillation is a key primitive for distributing high-quality entanglement between remote locations. Probabilistic noiseless linear amplification based on the quantum scissors is a candidate for entanglement distillation from noisy continuous-variable (CV) entangled states. Being a non-Gaussian operation, the quantum scissors is challenging to analyze. We present a derivation of the non-Gaussian state heralded by multiple quantum scissors in a pure loss channel with two-mode squeezed vacuum input. We choose the reverse coherent information (RCI), a proven lower bound on the distillable entanglement of a quantum state under one-way local operations and classical communication (LOCC), as our figure of merit. We evaluate a Gaussian lower bound on the RCI of the heralded state. We show that it can exceed the unlimited two-way LOCC-assisted direct transmission entanglement distillation capacity of the pure loss channel. The optimal heralded Gaussian RCI with two quantum scissors is found to be significantly more than that with a single quantum scissors, albeit at the cost of decreased success probability. Our results fortify the possibility of a quantum repeater scheme for CV quantum states using the quantum scissors.
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 R\'enyi-2 entropy to prove that single-photon subtraction increases bipartite entanglement by no more than log2. This value coincides with the maximal amount of bipartite entanglement that can be achieved with one photon.
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.