Non-Gaussian continuous-variable quantum states represent a pivotal resource in many quantum information protocols. Production of such states can occur through photonic subtraction processes either at the transmitter side prior to sending a state through the channel, or at the receiver side on receipt of a state that has traversed the channel. In the context of quantum protocols implemented over communication channels to and from Low-Earth-Orbit (LEO) satellites it is unclear what photonic subtraction set-up will provide for the best performance. In this work we show that for a popular version of continuousvariable Quantum Key Distribution (QKD) between terrestrial stations and LEO satellites, photon subtraction at the transmitter side is the preferred set-up. Such a result is opposite to that found for fiber-based implementations. Our results have implications for all future space-based missions that seek to take advantage of the opportunities offered by non-Gaussian quantum states.

Quantum Key Distribution (QKD) via satellite offers up the possibility of unconditionally secure communications on a global scale. Increasing the secret key rate in such systems, via photonic engineering at the source, is a topic of much ongoing research. In this work we investigate the use of photon-added states and photon-subtracted states, derived from two mode squeezed vacuum states, as examples of such photonic engineering. Specifically, we determine which engineered-photonic state provides for better QKD performance when implemented over channels connecting terrestrial receivers with Low-Earth-Orbit satellites. We quantify the impact the number of photons that are added or subtracted has, and highlight the role played by the adopted model for atmospheric turbulence and loss on the predicted key rates. Our results are presented in terms of the complexity of deployment used, with the simplest deployments ignoring any estimate of the channel, and the more sophisticated deployments involving a feedback loop that is used to optimize the key rate for each channel estimation. The optimal quantum state is identified for each deployment scenario investigated.

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Summary Non‐Gaussian operations have been studied intensively in recent years due to their ability to increase the secret key rate for certain CV‐QKD protocols. However, most previous studies on such protocols are carried out in a single‐mode setting, even though in reality any quantum state contains multimode components in frequency space. In this work, we investigate the use of non‐Gaussian operations in a multimode CV‐QKD system. Our main finding is that, contrary to single‐mode CV‐QKD systems, in generic multimode CV‐QKD systems, it is possible to use non‐Gaussian operations to increase the optimized secret key rate. More specifically, we find that at losses of order 30dB, which represents a distance of order 160km and the effective maximum distance for CV‐QKD, the key rate for multimode non‐Gaussian operations can be orders of magnitude higher than single‐mode operations. Our results are important for real‐world CV‐QKD systems, especially those dependent on quantum error correction—a process that requires non‐Gaussian effects.

In developing the global Quantum Internet, quantum communication with low-Earth-orbit satellites will play a pivotal role. Such communication will need to be two way: effective not only in the satellite-to-ground (downlink) channel but also in the ground-to-satellite channel (uplink). Given that losses on this latter channel are significantly larger relative to the former, techniques that can exploit the superior downlink to enhance quantum communication in the uplink should be explored. In this work we do just that -explore how continuous variable entanglement in the form of two-mode squeezed vacuum (TMSV) states can be used to significantly enhance the fidelity of ground-to-satellite quantum-state transfer relative to direct uplink-transfer. More specifically, through detailed phase-screen simulations of beam evolution through turbulent atmospheres in both the downlink and uplink channels, we demonstrate how a TMSV teleportation channel, created by the satellite, can be used to dramatically improve the fidelity of uplink coherent-state transfer relative to direct transfer. We then show how this, in turn, leads to the uplink-transmission of a higher alphabet of coherent states. Additionally, we show how non-Gaussian operations, acting on the received component of the TMSV state at the ground station, can lead to even further enhancement. Since TMSV states can readily be produced in situ on a satellite platform and form a reliable teleportation channel for most quantum states, our work suggests that future satellites forming part of the emerging Quantum Internet should be designed with uplink-communication via TMSV teleportation in mind.

Non-Gaussian operations have been studied intensively in recent years due to their ability to enhance the entanglement of quantum states. However, most previous studies on such operations are carried out in a single-mode setting, even though in reality any quantum state contains multi-mode components in frequency space. Whilst there have been general frameworks developed for multi-mode photon subtraction (PS) and photon addition (PA), an important gap exists in that no framework has thus far been developed for multi-mode photon catalysis (PC). In this work we close that gap. We then apply our newly developed PC framework to the problem of continuous variable (CV) entanglement distribution via quantumenabled satellites. Due to the high pulse rate envisioned for such systems, multi-mode effects will be to the fore in space-based CV deployments. After determining the entanglement distribution possible via multi-mode PC, we then compare our results with the entanglement distribution possible using multi-mode PS and PA. Our results show that multi-mode PC carried out at the transmitter is the superior non-Gaussian operation when the initial squeezing is below some threshold. When carried out at the receiver, multi-mode PC is found to be the superior non-Gaussian operation when the mean channel attenuation is above some threshold. Our new results should prove valuable for nextgeneration deployments of CV quantum-enabled satellites.

Hybrid entanglement between discrete-variable (DV) and continuous-variable (CV) quantum systems is an essential resource for heterogeneous quantum networks. Our previous work showed that in lossy channels the teleportation of DV qubits, via CV-entangled states, can be significantly improved by a new protocol defined by a modified Bell state measurement at the sender. This work explores whether a new, similarly modified, CV-based teleportation protocol can lead to improvement in the transfer of hybrid entangled states. To set the scene, we first determine the performance of such a modified protocol in teleporting CV-only qubits, showing that significant improvement over traditional CV-based teleportation is obtained. We then explore similar modifications in the teleportation of a specific hybrid entangled state showing that significant improvement over traditional CV-based teleportation is again found. For a given channel loss, we find teleporting the DV qubit of the hybrid entangled state can always achieve higher fidelity than teleporting the CV qubit. We then explore the use of various non-Gaussian operations in our modified teleportation protocol, finding that, at a cost of lower success probability, quantum scissors provides the most improvement in the loss tolerance. Our new results emphasize that in lossy conditions, the quantum measurements undertaken at the sender can have a surprising and dramatic impact on CV-based teleportation.

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