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Computer Optics

Numerical approach to compound quantum repeater scheme with coherent states

Irina Vorontsova, R. Goncharov, D. V. Tupyakov, Fedor Dmitrievich Kiselev, V.I. Egorov

Published Feb 1, 2024• 0 citations
Publisher

Abstract

A numerical model of a quantum repeater operating with Schrödinger cat states is constructed. The model describes the performance of such a system in the presence of decoherence effects, namely, noise in the quantum channel and the efficiency of the photon-number-resolving detector. In the framework of the numerical model, a theoretical analysis of the system functioning is carried out for the elementary link by calculating its performance characteristics. Namely, we calculate photodetector click probabilities and fidelity for various sets of decoherence parameters. These estimates are necessary in the context of further experimental research at the junction with other branches of quantum communications, so that to use the entanglement distribution when it comes to operating quantum teleportation and quantum key distribution protocols based on entanglement. The model will be developed further as a versatile drag-and-drop software simulating the full-fledged entanglement swapping protocol operation.

DOI
10.18287/2412-6179-co-1322

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A numerical model of a quantum repeater operating with Schrödinger cat states is constructed. The model describes the performance of such a system in the presence of decoherence effects, namely, noise in the quantum channel and the efficiency of the photon-number-resolving detector. In the framework of the numerical model, a theoretical analysis of the system functioning is carried out for the elementary link by calculating its performance characteristics. Namely, we calculate photodetector click probabilities and fidelity for various sets of decoherence parameters. These estimates are necessary in the context of further experimental research at the junction with other branches of quantum communications, so that to use the entanglement distribution when it comes to operating quantum teleportation and quantum key distribution protocols based on entanglement. The model will be developed further as a versatile drag-and-drop software simulating the full-fledged entanglement swapping protocol operation.
We analyze how the performance of a quantum-repeater network depends on the protocol employed to distribute entanglement, and we find that the choice of repeater-to-repeater link protocol has a profound impact on entanglement-distribution rate as a function of hardware parameters. We develop numerical simulations of quantum networks using different protocols, where the repeater hardware is modeled in terms of key performance parameters, such as photon generation rate and collection efficiency. These parameters are motivated by recent experimental demonstrations in quantum dots, trapped ions, and nitrogen-vacancy centers in diamond. We find that a quantum-dot repeater with the newest protocol ('MidpointSource') delivers the highest entanglement-distribution rate for typical cases where there is low probability of establishing entanglement per transmission, and in some cases the rate is orders of magnitude higher than other schemes. Our simulation tools can be used to evaluate communication protocols as part of designing a large-scale quantum network.
Entangled coherent states can be prepared remotely by subtracting nonlocally a single photon from two quantum superpositions of coherent states, the so-called “Schrödinger’s cat” state. Such entanglement can further be distributed over longer distances by successive entanglement swapping operations using linear optics and photon-number resolving detectors. The aim of this paper is to evaluate the performance of this approach to quantum repeaters for long-distance quantum communications. Despite many attractive features at first sight, we show that, when using state-of-the-art photon counters and quantum memories, they do not achieve higher entanglement generation rates than repeaters based on single-photon entanglement. We discuss potential developments, which may take better advantage of the richness of entanglement based on continuous variables, including in particular efficient parity measurements.
Abstract We analyze the performance of quantum repeaters where the protocols of entanglement generation and swapping are based on multimode optical Schrödinger cat states produced using electro-optic modulation of single-mode optical cats. We employ both the mean-only approximation and exact results to calculate the distance dependencies of the mean waiting time and the repeater rate depending on the number of elementary links. The results are compared with the rates of quantum repeater schemes based on photon pairs generated via spontaneous parametric down-conversion.
This thesis is an exploration of quantum repeaters from a practical point of view. Quantum repeaters are devices which help improve the quantum communication capacity of a lossy bosonic channel (which include photonic channels such as optical fiber) beyond what is possible using a purely lossy channel. The analyses in this thesis involve modeling the experimental imperfections inherent in the various devices which comprise a quantum repeater, then combining these models to calculate various quantities of interest. \n \nTwo systems are analyzed in this thesis. One is a simple quantum repeater, while the other is a potential building block for more complex quantum repeaters. \n \nThe simple quantum repeater scheme can be implemented with currently available technology. In it, two parties perform quantum key distribution (QKD) by exchanging photons with two quantum memories placed between them. Its secret key rate ideally scales as the square root of the transmittivity of the optical channel, which is superior to QKD schemes based on direct transmission because key rates for the latter scale at best linearly with transmittivity. Taking into account imperfections in the setup, such as detector efficiency and dark counts, we present parameter regimes in which our protocol outperforms protocols based on direct transmission. We find that implementing our scheme with trapped ions is a promising way to reach the necessary parameter regimes, and that the regimes are easier to reach if the optical channels are very lossy. \n \nThe creation of entanglement between two quantum memories is an important building block in some quantum repeater schemes. We consider a specific quantum memory consisting of an atom trapped in a cavity. The system allows a CNOT operation to be performed between an atom and a photon. We study three methods for taking advantage of this to entangle two atoms: (1) interacting a coherent pulse with each atom, then performing an entangling measurement on the pulses; (2) interacting a single coherent pulse with each atom sequentially; (3) emitting an entangled photon from one atom and interacting it with the other atom. The success probability of each method is compared, as well as the quality of the entangled states produced by each one, taking into account imperfections which appear in a specific experimental implementation of such memories. We find that there is a tradeoff between success probability and entangled state quality when coherent states are used, and that method 3 provides higher-quality entangled states than is possible with the other two methods.
Quantum entanglement-based networks enjoy extreme security due to quantum mechanics, but must distribute entanglement over communications channels that will introduce quantum decoherence processes. Quantum teleportation serves the fundamental mechanism in quantum entanglement networks, but involves two quantum channels going through different decoherence processes. This situation suggests imbalanced phase distortions due to different quantum decoherence processes in two channels, and consequently disrupt the normal operation of quantum teleportation and further entanglement swapping protocols. By modeling quantum decoherence in a quantum channel in terms of a unitary phase rotation, we analyze both quantum entanglement-based networking protocols that utilize Bell states and derive closed-form expressions for teleportation fidelity and the success probability of quantum swapping, a vital mechanism that facilitates quantum repeaters in quantum communication networks. We discover a simple, yet paramount result: operation performance depends on the mismatch between the two quantum channels by a pair of Bell-state particles, rather than the absolute phase distortions of each channel, which suggests the desirable factor of entanglement distribution in a quantum communication network and distributed quantum computing.
Quantum repeaters are essential for scalable long-distance quantum networking. As quantum information processing moves toward fault-tolerant and error-corrected operations, it becomes increasingly important to study quantum repeaters that also move beyond raw physical entanglement and towards logical entanglement. In this paper, we implement and simulate the quantum repeater with encoding and classical error correction (QRE-CEC) protocol in SeQUeNCe, a discrete-event simulator of quantum networks. The protocol distributes logical Bell pairs, performs encoded entanglement swapping, and uses classical error correction for the decoding of entanglement swapping measurement outcomes to determine Pauli-frame corrections. For this study, we extend SeQUeNCe with a stabilizer-based backend, add support for CSS code-based encoded operations, and integrate gate, measurement, idle decoherence, and state-initialization noise models. Our simulation results show that QRE-CEC suppresses all modeled errors to the second order. Also, QRE-CEC can distribute logical Bell pairs with 0.91 fidelity over a distance of 2000 km under the parameter regimes we study. Beyond protocol-level performance evaluation, our implementation exposes practical simulator and control-plane challenges that are typically abstracted away in theoretical studies.