PRX QUANTUM 1, 020317 (2020) Teleportation Systems Toward a Quantum Internet Raju Valivarthi ,1,2 Samantha I. Davis,1,2 Cristián Peña,1,2,3 Si Xie ,1,2 Nikolai Lauk,1,2 Lautaro Narváez ,1,2 Jason P. Allmaras ,4 Andrew D. Beyer,4 Yewon Gim,2,5 Meraj Hussein,2 George Iskander ,1 Hyunseong Linus Kim ,1,2 Boris Korzh ,4 Andrew Mueller,1 Mandy Rominsky,3 Matthew Shaw,4 Dawn Tang ,1,2 Emma E. Wollman,4 Christoph Simon,6 Panagiotis Spentzouris,3 Daniel Oblak,6 Neil Sinclair,1,2,7 and Maria Spiropulu1,2,* 1 Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, California 91125, USA 2 Alliance for Quantum Technologies (AQT), California Institute of Technology, Pasadena, California 91125, USA 3 Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA 4 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA 5 AT&T Foundry, Palo Alto, California 94301, USA 6 Institute for Quantum Science and Technology, and Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada 7 John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA (Received 28 July 2020; accepted 16 October 2020; published 4 December 2020; corrected 22 July 2021) Quantum teleportation is essential for many quantum information technologies, including long-distance quantum networks. Using fiber-coupled devices, including state-of-the-art low-noise superconducting nanowire single-photon detectors and off-the-shelf optics, we achieve conditional quantum teleportation of time-bin qubits at the telecommunication wavelength of 1536.5 nm. We measure teleportation fidelities of ≥ 90% that are consistent with an analytical model of our system, which includes realistic imperfec- tions. To demonstrate the compatibility of our setup with deployed quantum networks, we teleport qubits over 22 km of single-mode fiber while transmitting qubits over an additional 22 km of fiber. Our sys- tems, which are compatible with emerging solid-state quantum devices, provide a realistic foundation for a high-fidelity quantum Internet with practical devices. DOI: 10.1103/PRXQuantum.1.020317 I. INTRODUCTION set of quantum processors, sensors, or users thereof that are mutually connected over a network capable of allocat- Quantum teleportation [1], one of the most captivating ing quantum resources (e.g., qubits and entangled states) predictions of quantum theory, has been widely investi- between locations. Many architectures for quantum net- gated since its seminal demonstrations over 20 years ago works require quantum teleportation, such as star-type net- [2–4]. This is due to its connections to fundamental physics works that distribute entanglement from a central location [5–14] and its central role in the realization of quantum or quantum repeaters that overcome the rate-loss trade-off information technology such as quantum computers and of direct transmission of qubits [19,23–26]. networks [15–19]. The goal of a quantum network is to Quantum teleportation of a qubit can be achieved by distribute qubits between different locations, a key task for performing a Bell-state measurement (BSM) between the quantum cryptography, distributed quantum computing, qubit and another that forms one member of an entan- and sensing. A quantum network is expected to form part gled Bell state [1,18,27]. The quality of the teleportation of a future quantum Internet [20–22]: a globally distributed is often characterized by the fidelity F =ψ| ρ |ψ of the teleported state ρ with respect to the state |ψ accom- *[email protected] plished by ideal generation and teleportation [15]. This metric is becoming increasingly important as quantum net- Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Fur- works move beyond specific applications, such as quantum ther distribution of this work must maintain attribution to the key distribution, and toward the quantum Internet. author(s) and the published article’s title, journal citation, and Polarization qubits have been preferred for demonstra- DOI. tions of quantum teleportation over free-space channels 2691-3399/20/1(2)/020317(16) 020317-1 Published by the American Physical Society RAJU VALIVARTHI et al. PRX QUANTUM 1, 020317 (2020) [28–30], including the recent ground-to-satellite quantum used for improvements of the entanglement quality and teleportation [31], because of their ease of preparation and distribution, with emphasis on implementation of proto- measurement, as well as the lack of polarization rotation cols with complex entangled states toward advanced and in free space. Qubits encoded by the time of arrival of complex quantum communications channels. These will individual photons, i.e., time-bin qubits [32], are useful assist in studies of systems that implement new teleporta- for fiber networks due to their simplicity of generation, tion protocols the gravitational duals of which correspond interfacing with quantum devices, as well as the inde- to wormholes [47], error-correlation properties of worm- pendence of dynamic polarization transformations of real- hole teleportation, and on-chip codes as well as possible world fibers. Individual telecom-band photons (around implementation of protocols on quantum optics commu- 1.5 μm wavelength) are ideal carriers of qubits in networks nication platforms. Hence the systems serve both funda- due to their ability to rapidly travel over long distances in mental quantum information science as well as quantum deployed optical fibers [17,33–35] or atmospheric chan- technologies. nels [36], among other properties. Moreover, the improve- Here, we perform quantum teleportation of time-bin ment and growing availability of sources and detec- qubits, conditioned on a successful BSM, at a wavelength tors of individual telecom-band photons has accelerated of 1536.5 nm with an average F ≥ 90%. This is accom- progress toward workable quantum networks and associ- plished using a compact setup of fiber-coupled devices, ated technologies, such as quantum memories [37], trans- including low-dark-count single-photon detectors and off- ducers [38,39], or quantum nondestructive measurement the-shelf optics, allowing straightforward reproduction for devices [40]. multinode networks. To illustrate network compatibility, Teleportation of telecom-band photonic time-bin qubits teleportation is performed with up to 44 km of single- has been performed inside and outside the laboratory, mode fiber between the qubit generation and the mea- with impressive results [33–35,41–46]. Despite this, there surement of the teleported qubit, and is facilitated using has been little work to increase F beyond approximately semiautonomous control, monitoring, and synchronization 90% for these qubits, in particular using practical devices systems, with results collected using scalable acquisition that allow straightforward replication and deployment of hardware. Our system, which operates at a clock rate of 90 quantum networks (e.g., using fiber-coupled and com- MHz, can be run remotely for several days without inter- mercially available devices). Moreover, it is desirable to ruption and can yield teleportation rates of a few Hertz develop teleportation systems that are forward compat- using the full length of fiber. Our qubits are also compatible ible with emerging quantum devices for the quantum with erbium-doped crystals, e.g., Er : Y2SiO5, which are Internet. used to develop quantum network devices such as mem- In the context of the California Institute of Technology ories and transducers [48–50]. The 1536.5-nm operating (Caltech) multidisciplinary multi-institutional collabora- wavelength is within the low-loss (C-band) telecommuni- tive public-private research program on Intelligent Quan- cation window for long-haul communication and where a tum Networks and Technologies (IN-Q-NET) founded in variety of off-the-shelf equipment is available. Finally, we 2017 with AT&T as well as the Fermi National Accelera- develop an analytical model of our system, which includes tor Laboratory and the Jet Propulsion Laboratory, we have experimental imperfections, predicting that the fidelity designed, built, commissioned, and deployed two quantum can be improved further toward unity by well-understood teleportation systems: one at Fermilab, the Fermilab Quan- methods (such as improvement in photon indistinguisha- tum Network (FQNET), and one at Caltech’s Lauritsen bility). Our demonstrations provide a step toward a work- Laboratory for High Energy Physics, the Caltech Quan- able quantum network with practical and replicable nodes, tum Network (CQNET). The CQNET system serves as a such as the ambitious U.S. Department of Energy quan- research and development (R&D), prototyping, and com- tum research network envisioned to link the U.S. National missioning system, while FQNET serves as an expandable Laboratories. system, for scaling up to long distances, and is used in In the following, we describe the components of multiple projects funded currently by the United States our systems as well as characterization measurements (U.S.) Department of Energy’s Office of High Energy that support our teleportation results, including the Physics (HEP) and Advanced Scientific Research Comput- fidelity of our entangled Bell state and the Hong-Ou- ing (ASCR). The material- and devices-level R&D of both Mandel (HOM) interference [51] that underpins the suc- systems is facilitated