Satellite-Relayed Global Quantum Communication without Quantum Memory

Photon loss is the fundamental issue toward the development of quantum networks. To circumvent loss quantum repeaters were proposed, which need high-performance quantum memories. We present an alternative proposal to mitigate photon loss even at large distances and hence to create a global-scale quantum communication architecture without quantum repeaters. In this proposal, photons are sent directly through space, using a chain of co-moving low-earth orbit satellites. This satellite chain would bend the photons to move along the Earth’s curvature and control photon loss due to diffraction by effectively behaving like a set of lenses on an optical table. Numerical modeling of photon propagation through these “satellite lenses” shows that diffraction loss in entanglement distribution can be almost eliminated even at global distances of 20 000 km while considering beam truncation at each satellite and the effect of different errors (e.g., “satellite lens” focal-length fluctuation). In the absence of diffraction loss, the effect of other losses (especially reflection loss) becomes relevant and they are investigated in detail. The total loss is estimated to be less than 30 dB at 20 000 km if other losses are constrained to 2% at each satellite, with 120-km satellite separation and 60-cm diameter satellite telescopes eliminating diffraction loss. Such a low-loss satellite-based optical-relay protocol would enable robust, multimode global quantum communication and would not require either quantum memories or repeater protocol. The protocol can also be the least lossy in almost all distance ranges available (200–20 000 km). Recent advances in space technologies may soon enable an affordable launch facility for such a satellite-relay network. We further introduce the “qubit transmission” protocol, which has a plethora of advantages with both the photon source and the detector remaining on the ground. A specific lens setup was designed for the “qubit transmission” protocol, which performed well in simulation that included atmospheric turbulence in the satellite uplink.

Figure 1

Different quantum communication schemes using a chain of reflector satellites, i.e., using an all-satellite quantum network (ASQN). (a) Qubit transmission—photons transmitted from the source in one ground station is reflected through space by a chain of reflector satellites to another ground station while beam diffraction is controlled by focusing. The three dots imply many satellites in between (not shown here). (b) Entanglement distribution—two options each for source and collection are shown. Two alternatives are shown for placing an entanglement source, one on satellite (S1) and one on ground (S2). Photon transmission and control of beam diffraction is similar as in (a). Transmitted entangled photons can be collected in ground stations in a detector (C1), e.g., to perform QKD or Bell inequality violation test, or they can be collected (C2) for further analysis (e.g., building a quantum internet, as shown in Fig. 9 in Sec. 7).

Figure 2

Schematic diagrams explaining how a particular lens setup can completely contain beam divergence due to diffraction indefinitely. This is achieved with a uniform lens separation as large as the Rayleigh range ($z_R=\pi w_0^2/\lambda$).

Figure 3

Diffraction loss in entanglement distribution. (a) Schematic diagram showing the entangled pair source containing “satellite lens” in the middle and the ground links at both the ends. The effective “satellite lenses” contain diffraction by controlling beam divergence. (b) Numerical simulation of diffraction loss showing entanglement distribution probability at 20 000 km for different telescope diameters ($d$) and satellite separations ($L_0$), without considering ground link. (b),(c) Essentially the same graphs with different scales (regular and logarithmic) showing, respectively, low (b) and high (c) loss regions clearly. (d),(e) Diffraction is simulated with ground links included. In (d) using $(f_{N-1},f_N)=(L_0/2,L_0/2)$ results in poor performance for small $L_0$ values. However, on optimizing $(f_{N-1},f_N)$ a plot closer to the original one (b) is found in (e).

Figure 4

Diffraction loss in qubit transmission. (a) Schematics of qubit transmission protocol has been shown with lenses (gray colored) and apertures (brown colored), which are basically lenses with infinite focal length. The protocol here starts from the uplink receiving telescope and the ground link in the downlink is shown in the right. See the text for details. (b) Diffraction loss for qubit transmission at 20 000 km for different telescope radius ($d$) and satellite separation values ($L_0$) are shown. Ground links are not considered (neither the initial uplink nor the eventual downlink) while 800-nm light is used. (c) Photon transmission probabilities are shown with distance with $d=60\mathrm{cm}$ and $L_0=120\mathrm{km}$ for both qubit transmission and entanglement distribution. Both down links are considered for entanglement distribution while only the eventual downlink is considered for qubit transmission. Uplink loss in tens of dB is too large to see any comparison. Hence, uplink loss is included only in Figs. 5 and 5. Initially probability falls quickly for qubit transmission due to some beam truncation and diffraction at the apertures, although this produces less than 2-dB additional loss.

Figure 5

Total loss in photon propagation. (a),(b) Total loss for entanglement distribution with 2% absorption loss for each satellite. The same graph is shown in (a) and (b) with (b) showing loss in the decibel scale. Only points with loss up to 45 dB are shown in (b) to clearly show the loss values for smaller $L_0$ values. In both graphs there exist a minimum loss (at an optimum $L_0$) for each $d$ value, either occurring inside the plotted region or outside. (c) The same plot as (b) with 5% satellite loss and showing points up to 100-dB loss. (d) Entangled distribution loss is shown with distance for different ($d$, $L_0$) values and diffraction loss values (satellite loss 2% of 5%) for a total propagation of 20 000 km. (e) Qubit transmission protocol total loss values (including both uplink and downlink loss, satellite loss of 2%, and other losses) are shown for different ($d$, $L_0$) values. (f) Qubit transmission loss is shown with distance for $d=60\mathrm{cm}$, $L_0=120\mathrm{km}$ and 2% satellite loss.

Figure 6

Effect of uplink turbulence in the qubit-transmission proposal is numerically simulated. (a) Atmospheric turbulence, modeled using successive phase screens, completely fragments the initial Gaussian beam by the time it reaches the satellite. (b)–(d) The receiving telescope in the satellite accepts only a small part of the large fragmented beam (b), which is focused at a later satellite (c). This focused beam (c) is then transmitted through successive satellites (or “satellite lenses”) to as far as 20 000 km and the final beam (d) emerges largely unaffected from this long propagation due to effective confinement by the lenses. The light beam suffers only a small loss, much smaller compared to the initial turbulence-induced loss. (e) This is evident when average light propagation loss is plotted with propagation distance, over 300 iterations (with $d=60\mathrm{cm}$, $L_0=80\mathrm{km}$ and for two cases of satellite chain elevation—200 and 500 km).

Figure 7

Simulation of light propagation in ASQN for 500-km satellite elevation. (a) Light transmission probability at 20,000 km in entanglement distribution protocol for different satellite telescope diameters ($d$) and satellite separations ($L_0$) are shown for a ground telescope diameter of 1.2 m. (b),(c) Total loss for entanglement distribution with 2% satellite loss showing an extra loss of only 3 dB compared to 200-km orbit. (d) The total loss for qubit transmission with 2% satellite loss increases a bit more (around 10 dB) due to the effect of uplink turbulence.

Figure 8

(a)–(d) The different possible telescope setups suitable for a chain of satellite reflectors are depicted, showing beam focusing and bending. Off-axis telescope setups are shown in (a),(b) while (c) shows an on-axis setup. The on-axis setup (without the folding mirrors) can be modeled by the screen-lens-screen system shown in (d). Diffraction loss through such an on-axis system can be contained by using vortex beams. (e) A simulation of entangled photon-pair propagation through 20 000 km in vortex beam profile through the on-axis system shows nearly identical initial and final beams (after 10 000-km propagation by each photon). (f) Entangled pair transmission probability is plotted with distance (ground link or other losses not included).

Figure 9

Quantum internet protocol using ASQN. (a) Quantum internet by entanglement distribution with entangled source on satellite (S1) and on ground station (S2). Transmitted entangled photons can be collected in ground stations to establish entanglement deterministically for use in quantum internet schemes. This requires quantum memories (QMs), quantum nondemolition (QND) measurements, and classical communication (CC). See text for details. (b) Quantum internet using a repeater scheme—the quantum internet can be established by doing a Bell-state measurement using ground-based detectors in the middle without needing QND detectors. However, the entanglement generation rate can be increased multifold by using the optional QND detector and quantum memory in the middle. (c) Multiple teleportations without using quantum memories. Using low-loss entanglement distribution protocol asymmetrically (with unequal arms), a qubit can be teleported to one place and teleported back (or sent to another place), with the help of redundancy.

Figure 10

The effect of “satellite lens” focal length ($f$) and position ($z$ or $xy$) error on beam propagation, (i.e., on diffraction loss) is shown. (a) Occurrence of the error processes are shown schematically. (b)–(e) The effect of $f$ error (b), $z$ error (c) or $xy$ error (d) are shown each for two different amounts of error. In each case, transmission probability through 10 000 km is calculated over 300 repetitions using a uniform error distribution from where mean and standard deviation (std) is derived. The error values taken are 5% and 10% of $f$ for $f$ error, 5% and 20% of $L_0$ for $z$ error and 1% and 10% of $r$ ($d/2$) for $xy$ error. Combined effect of all these errors is shown in (e) for two different sets of parameter values. $f$, $z$, and $xy$ error values of (2.5%, 5% and 1%) results in transmission probability of 78% at 10 000 km while large errors of (5%, 10%, and 2%) results in 48% transmission. For all plots, $d=60\mathrm{cm}$, $L_0=120\mathrm{km}$ and $\lambda =800\mathrm{nm}$.