Heterogeneous quantum networks consisting of mixed-technologies - Continuous Variable (CV) and Discrete Variable (DV) - will become ubiquitous as global quantum communication matures. Hybrid quantum-entanglement between CV and DV modes will be a critical resource in such networks. A leading candidate for such hybrid quantum entanglement is that between Schrödinger-cat states and photon-number states. In this work, we explore the use of Two-Mode Squeezed Vacuum (TMSV) states, distributed from satellites, as a teleportation resource for the re-distribution of our candidate hybrid entanglement pre-stored within terrestrial quantum networks. We determine the loss conditions under which teleportation via the TMSV resource outperforms direct-satellite distribution of the hybrid entanglement, in addition to quantifying the advantage of teleporting the DV mode relative to the CV mode. Our detailed calculations show that under the loss conditions anticipated from Low-Earth-Orbit, DV teleportation via the TMSV resource will always provide for significantly improved outcomes, relative to other means for distributing hybrid entanglement within heterogeneous quantum networks.
Heterogeneous quantum networks consisting of mixed-technologies - Continuous Variable (CV) and Discrete Variable (DV) - will become ubiquitous as global quantum communication matures. Hybrid quantum-entanglement between CV and DV modes will be a critical resource in such networks. A leading candidate for such hybrid quantum entanglement is that between Schrödinger-cat states and photon-number states. In this work, we explore the use of Two-Mode Squeezed Vacuum (TMSV) states, distributed from satellites, as a teleportation resource for the re-distribution of our candidate hybrid entanglement pre-stored within terrestrial quantum networks. We determine the loss conditions under which teleportation via the TMSV resource outperforms direct-satellite distribution of the hybrid entanglement, in addition to quantifying the advantage of teleporting the DV mode relative to the CV mode. Our detailed calculations show that under the loss conditions anticipated from Low-Earth-Orbit, DV teleportation via the TMSV resource will always provide for significantly improved outcomes, relative to other means for distributing hybrid entanglement within heterogeneous quantum networks.
Hybrid entanglement swapping supports the teleportation of any arbitrary states, regardless of whether the quantum information in the state is encoded in Discrete Variables (DV) or Continuous Variables (CV). In this work, we study the CV teleportation channel created between two ground receivers via direct lossy-distribution from a low-Earth-orbit (LEO) satellite. Such a flexible teleportation protocol has the potential to interconnect a global array of quantum-enabled devices regardless of the different intrinsic technology upon which the devices are built. However, past studies of hybrid entanglement swapping have not accounted for channel transmission loss. Here we derive the general framework for teleporting an arbitrary input mode over a lossy CV teleportation channel. We investigate the specific case where the input modes are part of DV states entangled in the photon number basis, then identify the optimal teleportation strategy. Our results show that, relative to DV photon-number entanglement sourced directly from the satellite, there are circumstances where our teleported DV states retain higher entanglement quality. We discuss the implications of our new results in the context of generating a global network of ultra-secure communications between different quantum-enabled devices which possess line-of-sight connections to LEO satellites. Specifically, we illustrate the impact the teleportation process has on the key rates from a Quantum Key Distribution protocol.
The wave-particle duality of light has led to two different encodings of optical quantum information. One approach, referred to as the discrete-variable (DV) one, relies on finite dimensional quantum systems, while the other one, referred to as the continuous-variable (CV) one, is based on wave-like states belonging to an infinite dimensional Hilbert space. These two encodings have historically been separated, but recently, new hybrid protocols which aim at combining the advantages of the two encodings have emerged [1] . In that prospect our recent demonstration of the measurement-induced generation of hybrid entanglement between discrete- and continuous-variable quantum states [2] , [3] , located at distant places and connected by a lossy channel, has opened the way to the implementation of hybrid protocols and heterogeneous quantum networks. Following the first protocols based on this resource, such as the remote preparation of continuous-variable qubits [4] , or a violation of an Einstein-Podolsky-Rosen steering inequality [5] , we will here report our latest experimental results on entanglement swapping and quantum teleportation protocols using hybrid entangled states based on different encodings [6] .
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.
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 article, we do just that—exploring 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 further enhancement of the fidelity. Since TMSV states can readily be producedin situon 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 quantum teleportation in mind.
A key technical requirement of any future quantum network is the ability to distribute quantum-entangled resources between two spatially separated points at a high rate and high fidelity. Entanglement distribution protocols based on satellite platforms, which transmit and receive quantum resources directly via free-space optical propagation, are therefore excellent candidates for quantum networking, since the geometry and loss characteristics of satellite networks feasibly allow for up to continental-scale (∼103 km) over-the-horizon communication without the infrastructure, cost, or losses associated with equivalent fibre-optic networks. In this work, we explore two network topologies commonly associated with quantum networks - entanglement distribution between two satellites in low-Earth orbit mediated by a third satellite and entanglement distribution between two ground stations mediated by a satellite in low-Earth orbit, and two entanglement distribution schemes - one where the central satellite is used as a relay, and the other where the central satellite is used to generate and distribute the entangled resource directly. We compute a bound on the rate of distribution of distillable entanglement achieved by each protocol in each network topology as a function of the network channels for both single-rail discrete- (DV) and continuous-variable (CV) resources and use or non-use of probabilistic noiseless linear quantum amplification (NLA). In the case of atmospheric channels we take into account the turbulent and optical properties of the free-space propagation. We determine that for the triple-satellite network configuration, the optimal strategy is to perform a distributed NLA scheme in either CV or DV, and for the ground-satellite-ground network the optimal strategy is to distribute a DV resource via the central satellite.
The Schrödinger's-cat state is created from the macroscopic superposition of coherent states and is well-known to be a useful resource for quantum information processing protocols. In order to extend such protocols to a global scale, we study the continuous variable (CV) teleportation of the cat state via a satellite in low-Earth-orbit. Past studies have shown that the quantum character of the cat state can be preserved after CV teleportation, even when taking into account the detector efficiency. However, the channel transmission loss has not been taken into consideration. Traditionally, optical fibers with fixed attenuation are used as teleportation channels. Our results show that in such a setup, the quantum character of the cat state is lost after 5dB of channel loss. We then investigate the free-space channel between the Earth and a satellite, where the loss is caused by atmospheric turbulence. For a down-link channel of less than 500km and 30dB of loss, we find that the teleported state preserves higher fidelity relative to a fixed attenuation channel. The results in this work will be important for deployments over Earth-Satellite channels of protocols dependent on cat-state qubits.