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arXiv:2111.00948 · Optics Express

Cross talk compensation in multimode continuous-variable entanglement distribution

Olena Kovalenko, Vladyslav C. Usenko, Radim Filip

Published Jun 20, 2021• 6 citations
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Abstract

Two-mode squeezed states are scalable and robust entanglement resources for continuous-variable and hybrid quantum information protocols that are realized at a distance. We consider the effect of a linear cross talk in the multimode distribution of two-mode squeezed states propagating through parallel similar channels. First, to reduce degradation of the distributed Gaussian entanglement, we show that the initial two-mode squeezing entering the channel should be optimized already in the presence of a small cross talk. Second, we suggest simultaneous optimization of relative phase between the modes and their linear coupling on a receiver side prior to the use of entanglement, which can fully compensate the cross talk once the channel transmittance is the same for all the modes. For the realistic channels with similar transmittance values for either of the modes, the cross talk can be still largely compensated. This method relying on the mode interference overcomes an alternative method of entanglement localization in one pair of modes using measurement on another pair and feed-forward control. Our theoretical results pave the way to more efficient use of multimode continuous-variable photonic entanglement in scalable quantum networks with cross talk.

DOI
10.1364/oe.428628

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Two-mode squeezed states are scalable and robust entanglement resources for continuous-variable and hybrid quantum information protocols that are realized at a distance. We consider the effect of a linear cross talk in the multimode distribution of two-mode squeezed states propagating through parallel similar channels. First, to reduce degradation of the distributed Gaussian entanglement, we show that the initial two-mode squeezing entering the channel should be optimized already in the presence of a small cross talk. Second, we suggest simultaneous optimization of relative phase between the modes and their linear coupling on a receiver side prior to the use of entanglement, which can fully compensate the cross talk once the channel transmittance is the same for all the modes. For the realistic channels with similar transmittance values for either of the modes, the cross talk can be still largely compensated. This method relying on the mode interference overcomes an alternative method of entanglement localization in one pair of modes using measurement on another pair and feed-forward control. Our theoretical results pave the way to more efficient use of multimode continuous-variable photonic entanglement in scalable quantum networks with cross talk.
We address the role of linear inter-mode cross talk in continuous-variable quantum key distribution in the most typical prepare-and-measure scenario. Considering coherent and well as squeezed signal states and either homodyne or heterodyne detection in the receiver station, we show how the cross talk deteriorates the secret key rate and robustness of the protocols to the channel noise. We show how optimization of the signal modulation can improve the performance of the protocols in the presence of cross talk and point out possibilities for further cross talk compensation.
Preserving entanglement during the teleportation of multipartite quantum states is a central challenge in continuous-variable quantum communication, particularly when experimentally feasible finite-dimensional entangled resources are employed. In this work, we investigate whether the entanglement of a two-mode continuous-variable state can be preserved when only one of its modes is teleported through a multimode interferometry-based protocol using a three-dimensional discrete entangled channel. Two representative entangled states, namely the two-mode squeezed vacuum and discrete-modulation states, are considered under both ideal conditions and four standard quantum noise channels: bit-flip, phase-flip, depolarizing, and amplitude-damping. The protocol is evaluated in terms of teleportation fidelity, success probability, logarithmic negativity, Wigner-function evolution, and state purity to provide a comprehensive assessment of both teleportation quality and entanglement preservation. The results show that, in the absence of noise, the protocol preserves most of the initial entanglement while maintaining high teleportation fidelity. Under noisy conditions, the residual entanglement remains remarkably robust against amplitude-damping and phase-flip noise, whereas bit-flip noise causes the most pronounced degradation. The phase-space structure and purity of the teleported states are likewise largely retained over a broad range of noise strengths. These findings demonstrate that multimode interferometry with finite-dimensional entangled channels provides an effective and noise-resilient approach for preserving continuous-variable entanglement during quantum teleportation, offering a practical route toward realistic quantum communication networks.
Preserving entanglement during the teleportation of multipartite quantum states is a central challenge in continuous-variable quantum communication, particularly when experimentally feasible finite-dimensional entangled resources are employed. In this work, we investigate whether the entanglement of a two-mode continuous-variable state can be preserved when only one of its modes is teleported through a multimode interferometry-based protocol using a three-dimensional discrete entangled channel. Two representative entangled states, namely the two-mode squeezed vacuum and discrete-modulation states, are considered under both ideal conditions and four standard quantum noise channels: bit-flip, phase-flip, depolarizing, and amplitude-damping. The protocol is evaluated in terms of teleportation fidelity, success probability, logarithmic negativity, Wigner-function evolution, and state purity to provide a comprehensive assessment of both teleportation quality and entanglement preservation. The results show that, in the absence of noise, the protocol preserves most of the initial entanglement while maintaining high teleportation fidelity. Under noisy conditions, the residual entanglement remains remarkably robust against amplitude-damping and phase-flip noise, whereas bit-flip noise causes the most pronounced degradation. The phase-space structure and purity of the teleported states are likewise largely retained over a broad range of noise strengths. These findings demonstrate that multimode interferometry with finite-dimensional entangled channels provides an effective and noise-resilient approach for preserving continuous-variable entanglement during quantum teleportation, offering a practical route toward realistic quantum communication networks.
The structural aspects of tripartite entanglement in three-mode Gaussian states of continuous variable systems have been studied in [Adesso G, Serafini A and Illuminati F 2006 Phys. Rev. A {\\bf 73} 032345]. Here we focus our attention on the usefulness of such states in the context of realistic processing of continuous-variable quantum information. We introduce and discuss in detail several examples of pure and mixed three-mode states that stand out for their informational and/or entanglement properties. We then describe practical schemes to engineer such states with linear optics. In particular, we introduce a simple procedure -- based on passive optical elements -- to produce pure three-mode Gaussian states with {\\em arbitrary} entanglement structure (upon availability of an initial single-mode squeezed state). We analyze in detail the properties of distributed entanglement, showing that the promiscuity of entanglement sharing is a feature peculiar to symmetric Gaussian states that survives even in the presence of significant degrees of mixedness and decoherence. Next, we discuss the suitability of the considered tripartite entangled states to the implementation of quantum information and communication protocols with continuous variables. This will lead to a feasible experimental proposal to test the promiscuous sharing of continuous-variable entanglement, in terms of the optimal fidelity of teleportation networks with Gaussian resources. As a byproduct, optimal resource states for various communication protocols (among which asymmetric telecloning) will be exactly determined.