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arXiv:1812.00355 · Physical Review A

Continuous-variable entanglement distillation over a pure loss channel with multiple quantum scissors

Kaushik Parasuram Seshadreesan, Hari Krovi, Saikat Guha

Published Aug 13, 2019• 35 citations
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Abstract

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.

DOI
10.1103/physreva.100.022315

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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.
In this work we focus on evaluating the effectiveness of two non-Gaussian operations, photon subtraction (PS) and quantum scissors (QS) in terms of Continuous Variable (CV)-Quantum Key Distribution (QKD) over lossy channels. Each operation is analysed in two scenarios, one with the operation applied transmitter-side to a Two- Mode Squeezed Vacuum (TMSV) state and a second with the operation applied to the TMSV state receiver-side. We numerically evaluate the entanglement and calculate the QKD key rates produced in all four possible scenarios. Our results show that for a fixed value of initial squeezing in the TMSV state, the states produced by the non-Gaussian operations are more robust to loss, being capable of generating higher key rates for a given loss. More specifically, we find that for values of initial TMSV squeezing below 1.5dB the highest key rates are obtained by means of transmitter-QS. On the other hand, for squeezing above 1.5dB we find that receiver-PS produces higher key rates. Our results will be important for future CV-QKD implementations over free-space channels, such as the Earth-satellite channel.
Quantum repeaters have been proposed as a way of extending the reach of quantum communication. First-generation approaches use entanglement swapping to connect entangled links along a long-distance channel. Recently, there have been proposals for first-generation quantum repeaters for continuous variables. In this paper, we present an improved continuous-variable (CV) repeater scheme using optimal Gaussian entanglement swapping. Our scheme uses the noiseless linear amplifier for entanglement distillation. We show that with the simplest configuration of the noiseless linear amplifier and under the assumption of good quantum memories and perfect sources and detectors, our scheme beats the direct transmission upper limit for shorter distances and can offer advantages over previous CV repeater schemes.
The entanglement structure between different frequency components within broadband quantum light pulses, forged at entanglement creation, represents a promising route to the practical delivery of many multipartite quantum information applications. However, the scalability of such applications is largely limited by the entanglement decoherence caused by photon loss. One promising method to combat such losses is noiseless linear amplification. However, while there have been various procedures that implement noiseless linear amplification on single-mode states, no realization has thus far been proposed for noiseless linear amplification on quantum states carrying a multimode structure. In this work we close this gap, proposing a noiseless linear amplifier (NLA) with photon catalysis (PC), namely, the PC-NLA. Constructing a multimode version of an existing NLA that uses quantum scissors (QS), the QS-NLA, we then show how the PC-NLA is compatible with the QS-NLA, even though the former uses half the physical resources of the latter. We then apply our multimode NLA frameworks to the problem of continuous-variable (CV) entanglement distillation, determining how the multimode structure of the entanglement impacts the performance of the NLAs. Different from single-mode NLA analyses, we find that a multimode NLA is only effective as a CV entanglement distillation strategy when the channel loss is beyond some threshold---a threshold largely dependent on the multimode structure. The results provided here will be valuable for real-world implementations of multipartite quantum information applications that utilize complex entanglement structure within broadband light pulses.