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arXiv:2408.00141 · Advanced Quantum Technologies

Quantum Repeater Protocol for Deterministic Distribution of Macroscopic Entanglement

Alexey N. Pyrkov, I. D. Lazarev, Tim Byrnes

Published Feb 6, 2025• 3 citations
arXivHTMLPDF

Abstract

Abstract Distributing long‐distance entanglement is a fundamental goal that is necessary for a variety of tasks such as quantum communication, distributed quantum computing, and quantum metrology. Currently quantum repeater schemes typically aim to distribute one ebit at a time, the equivalent of one Bell pair's worth of entanglement. Here, a scheme is presented to distribute a macroscopic amount of entanglement across long‐distances using a number of operations that scales only linearly with the chain length in the ideal case (without decoherence). The scheme involves ensembles of qubits and entangling them with an interaction, which can be realized using atomic gas ensembles coupled by a shared optical mode. Using only local measurements on the intermediate ensembles, this leaves the ensembles at the ends of the chain entangled. It is showed that there are particular “magic” interaction times that allow for distribution of entanglement with perfect fidelity, with no degradation with chain length. The scheme is deterministic, such that with suitable local conditional unitary corrections, the same entangled state can always be prepared with good approximation.

DOI
10.1002/qute.202400524

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Abstract Distributing long‐distance entanglement is a fundamental goal that is necessary for a variety of tasks such as quantum communication, distributed quantum computing, and quantum metrology. Currently quantum repeater schemes typically aim to distribute one ebit at a time, the equivalent of one Bell pair's worth of entanglement. Here, a scheme is presented to distribute a macroscopic amount of entanglement across long‐distances using a number of operations that scales only linearly with the chain length in the ideal case (without decoherence). The scheme involves ensembles of qubits and entangling them with an interaction, which can be realized using atomic gas ensembles coupled by a shared optical mode. Using only local measurements on the intermediate ensembles, this leaves the ensembles at the ends of the chain entangled. It is showed that there are particular “magic” interaction times that allow for distribution of entanglement with perfect fidelity, with no degradation with chain length. The scheme is deterministic, such that with suitable local conditional unitary corrections, the same entangled state can always be prepared with good approximation.
Abstract High-fidelity entanglement distribution is a crucial objective for various applications in quantum technologies, including quantum communication, distributed quantum computing, and quantum metrology. Current methods for that, mainly centered around quantum repeaters, focus on distributing only microscopic amounts of entanglement at a time. In this paper, we discuss a novel approach that was proposed for efficient distributing a macroscopic amount of entanglement across a chain of macroscopic Bose–Einstein condensates (BECs) or cold atomic ensembles. The framework employs BECs at each node, which are connected via a shared optical mode and enables the high-fidelity long-distance distribution of macroscopic entanglement while requiring only local measurements on the intermediate ensembles, the ensembles at the ends of the chain remain entangled, under ideal conditions without decoherence. We discuss that at specific “magic” interaction times the macroscopic entanglement can be distributed with perfect fidelity, regardless of the chain length. It paves a way for development of quantum repeaters for macroscopic entanglement distribution.
The distribution of entanglement is a crucial task for quantum communication towards realizing a globe-spanning quantum internet. Recently a protocol for deterministic long-distance distribution of macroscopic entanglement over a network of ensembles of qubits was introduced [Adv. Quantum Technol. 2025, 8, 2400524]. It was shown that this protocol allows for the propagation of macroscopic amounts of entanglement with a protocol complexity that is independent on the ensemble size. However, questions remained on whether the scheme is viable, particularly for a large particle number, which is the case for realistic atomic ensembles. Here we develop improved numerical techniques that allow calculation of realistic ensemble sizes up to 10^6 with a negligible loss of accuracy. We find that moderate dephasing leaves the entanglement largely intact at the magic times, whereas stronger noise monotonically suppresses the entanglement. Our results demonstrate that the protocol retains its functionality towards the macroscopic regime and provides quantitative benchmarks for its robustness under a realistic level of decoherence.
Quantum repeater is one of the important building blocks for long distance quantum communication network. The previous quantum repeaters based on atomic ensembles and linear optical elements can only be performed with a maximal success probability of 1/2 during the entanglement creation and entanglement swapping procedures. Meanwhile, the polarization noise during the entanglement distribution process is harmful to the entangled channel created. Here we introduce a general interface between a polarized photon and an atomic ensemble trapped in a single-sided optical cavity, and with which we propose a high-efficiency quantum repeater protocol in which the robust entanglement distribution is accomplished by the stable spatial-temporal entanglement and it can in principle create the deterministic entanglement between neighboring atomic ensembles in a heralded way as a result of cavity quantum electrodynamics. Meanwhile, the simplified parity-check gate makes the entanglement swapping be completed with unity efficiency, other than 1/2 with linear optics. We detail the performance of our protocol with current experimental parameters and show its robustness to the imperfections, i.e., detuning and coupling variation, involved in the reflection process. These good features make it a useful building block in long distance quantum communication.
We describe a practical quantum repeater protocol for long-distance quantum communication. In this scheme, entanglement is created between the intermediate nodes of the quantum channel by using a weak dispersive light-matter interaction and distributing the outgoing intense coherent light pulses among the nodes. Noisy entangled pairs of electronic spin are then prepared with high success probability via homodyne detection including postselection. The local gates for entanglement purification and swapping are deterministic and measurement-free, based upon the same coherent-light resources and weak interactions as for the initial entanglement distribution. Finally, the entanglement is stored in a nuclear-spin-based quantum memory. Simulations of the system show qubit-communication rates approaching 100 Hz and fidelities above 99 % for reasonable local gate errors.
Quantum communication deals with absolutely secure transfer of classical messages by means of quantum cryptography or faithful transfer of unknown quantum states by means of quantum teleportation between distant sites. The essential element for quantum communication is to create remote entangled pairs of high fidelity. The main difficulty to create such a distant entangled pair is that both photon loss and decoherence grow exponentially with distance. However, with the help of quantum repeater, it is demonstrated that both the entanglement sources and the time needed to create a single distant entangled pair of high fidelity could scale polynomially with the communication length. Here we propose a robust quantum repeater by extending the original Duan-Lukin-Cirac-Zoller (DLCZ) scheme based on atomic ensembles and linear optics. Our protocol entails the advantage of two photon interference, which is more robust than single photon interference used in the DLCZ scheme. In comparison with our previous proposal, the entangled memory qubits are manipulated across long distance, and local entanglement pairs are avoided. Our proposal provides an exciting possibility for realistic long distance quantum communication.
We present a hybrid quantum repeater protocol for the long-distance distribution of atomic entangled states beyond qubits. In our scheme, imperfect noisy entangled pairs of two qudits, i.e., two discrete-variable ddd-level systems, each of, in principle, arbitrary dimension ddd, are initially shared between the intermediate stations of the channel. This is achieved via local, sufficiently strong light-matter interactions, involving optical coherent states and their transmission after these interactions, and optical measurements on the transmitted field modes, especially efficient continuous-variable homodyne detections (``hybrid'' here refers to the simultaneous exploitation of discrete- and continuous-variable degrees of freedom for the local processing and storage of entangled states as well as their nonlocal distribution, respectively) and unambiguous state discrimination. For qutrits we quantify the light-matter entanglement that can be effectively shared through an elementary lossy channel, and for a repeater spacing of up to 10 km we show that the realistic (lossy) qutrit entanglement is even larger than any ideal (loss-free) qubit entanglement. After including qudit entanglement purification and swapping procedures, we calculate the long-distance entangled-pair distribution rates and the final entangled-state fidelities for total communication distances of up to 1280 km. For example, employing unambiguous state discrimination, with three rounds of purification, entangled qudit pairs of near-unit fidelity can be distributed over 1280 km at an ideal maximal rate (assuming perfect gate operations) on the order of 100 Hz.