**On high fidelity quantum teleportation for practical quantum networks**

*Figure 1. Instruments of high-fidelity quantum teleportation. Fiber optics cables connect off-the-shelf devices (shown above), as well as those of state-of-the-art R&D (e.g SNSPD’s not shown above) that perform the experiment.*

**Quantum teleportation** is a “disembodied” transfer of quantum states from one location to another. It is one of the most intriguing, and consequently one of the most popularized, predictions of quantum physics. Since its first demonstrations over 20 years ago (see https://doi.org/10.1038/37539 and 10.1126/science.282.5389.706), it has been realized and studied in various physical systems and under diverse conditions. Beyond fundamental physics interest, it plays a central role in actualizing quantum information technology, including quantum computers and quantum networks. In this context, quantum teleportation of quantum bits (qubits), the basic unit of quantum information, is essential.

For quantum networks, quantum teleportation and entanglement swapping are used to distribute quantum information between distant locations. This process allows the realization of quantum cryptographic schemes or distributed quantum tasks, such as sensing or computing. Importantly, quantum teleportation is vital in order to extend the distance of quantum networks using quantum memories and quantum repeaters. This development will form part of a global quantum network: a so-called Quantum Internet.

In particular, the quality of teleportation, referred to as the fidelity, characterizing the proximity of the teleported qubit to the original, has become increasingly crucial as quantum technology matures. This high fidelity is important especially in the case of quantum networks designed to connect advanced quantum devices, including quantum sensors.

**Teleportation and systems towards a Quantum Internet**

In the paper “Teleportation systems towards a Quantum Internet”, a joint team of researchers from Caltech, Fermilab, NASA JPL, Calgary, Harvard, and AT&T demonstrate quantum teleportation of qubits of photons (quanta of light) with a fidelity greater than 90%, using state-of-the-art single photon detectors and off-the-shelf equipment. A detailed analytical model, including experimental imperfections, supports the results and indicates that a workable and high-fidelity quantum network using practical devices can be built. The U.S. Department of Energy envisioned such an ambitious quantum network to link the Office of Science National Laboratories.

The team performed quantum teleportation of time-bin (or time-of-arrival of) qubits of light at the telecommunication wavelength of 1.5 microns. This approach is well-suited for photons that travel over low-loss fiber optics cables– the same used by the telecommunication industry today. Time-bin qubits are compatible with several quantum devices, such as detectors, solid-state quantum memories, or transducers that store qubits. The team built two testbeds using fiber-coupled, commercially available equipment, one at Caltech (CQNET) and one at Fermilab (FQNET), allowing straightforward replication and deployment of quantum networks.

To demonstrate the deployability, teleportation is performed with up to 44 km of fiber optics cable between the qubit generation and the teleported qubit’s measurement. It is facilitated using semi-autonomous control, monitoring, and synchronization systems. Data is collected using scalable data acquisition hardware and software, and results are derived near-real time. The networks run remotely for long periods, up to a week at a time, without human intervention.

Quantum teleportation of a qubit is achieved using quantum entanglement. Entangled states are formed of at least two qubits, each of which cannot be described faithfully separately. Teleportation is commonly depicted as a user scenario or protocol where Alice has a qubit that she wants to teleport to Bob. Bob generates an entangled two-qubit state, keeps one for himself, and sends the other to Alice, who performs a joint measurement on this qubit and her own. The measurement outcome, which is classical and reveals nothing about any of the qubits, is sent to Bob by legacy means, e.g., a phone call. Bob recovers Alice’s qubit by rotating it according to this result, or conversely, orienting his measurement apparatus when he wants to use the qubit for a task.

**Experimental Setup**

Figure 2 illustrates the experimental setup of the teleportation testbeds built, where an additional user, Charlie, performs the joint measurement for Alice, a common scenario in quantum network systems in order to achieve longer distance teleportation. Alice, indicated by the box on the left, prepares the time-bin qubit and sends it to Charlie through fiber wound in a spool. Bob prepares time-bin entangled qubits (box on the right), sending one qubit to Charlie (middle) using a second fiber spool. Charlie performs the joint measurement, while Bob verifies the teleportation by measuring the remaining qubit. The data acquisition (DAQ) system collects all measurement outcomes for analysis.

*Figure 2. Schematic diagram of quantum teleportation. See text for details. Instruments used for the experiment are indicated in the legend.*

**Results**

The measured teleportation fidelities are shown in Figure 3. Researchers teleported the so-called “early” and “late” qubits, photons generated earlier or later than the other, and quantum superposition states of early and late. These qubits are specifically chosen and are used as the basis of more complex qubits. Two different methods extract fidelity. The first uses “quantum state tomography”. Bob performed several measurements of the teleported qubit over different runs of the experiment to reconstruct and compare it to that accomplished through ideal generation and teleportation. The second method is based upon the technique of “decoy states”, an approach known from quantum cryptography. Since the qubits generated by Alice are not based on single photons, instead obtained from very weak laser pulses that contain potentially many photons, this method allows estimating the teleportation fidelity of the experiment as if Alice uses single photons. This step is crucial for evaluating the teleportation fidelity since the most commonly used method assumes qubits encoded into single quantum systems, in this case, photons.

*Figure 3. Measured teleportation fidelities for different time-bin qubits. The qubit |e> (|l>) refers to qubits prepared early (late) while |+> refers to the quantum superposition state of early and late. The average teleportation fidelity considering all states is shown on the far right. The grey and blue bars represent fidelities calculated by quantum state tomography and decoy states, respectively, see the main text.*

**Outlook**

The analytical model and detailed measurements of the teleportation fidelity and rates presented in this work suggest that straightforward improvements in the design specifications of the devices and equipment used can bring orders-of-magnitude improvements in rates, and achieve near-unity fidelity. The team is working on the systems upgrades and integration of additional quantum devices at the edges and in the quantum interconnects.

Source:* INQNET. INQNET, On high fidelity quantum teleportation for practical quantum networks… *

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