Composable security for continuous variable quantum key distribution: Trust levels and practical key rates in wired and wireless networks

Continuous variable (CV) quantum key distribution (QKD) provides a powerful setting for secure quantum communications, thanks to the use of room-temperature off-the-shelf optical devices and the potential to reach much higher rates than the standard discrete-variable counterpart. In this paper, we provide a general framework for studying the composable finite-size security of CV-QKD with Gaussian-modulated coherent-state protocols under various levels of trust for the loss and noise experienced by the parties. Our paper considers both wired (i.e., fiber-based) and wireless (i.e., free-space) quantum communications. In the latter case, we show that high key rates are achievable for short-range optical wireless (LiFi) in secure quantum networks with both fixed and mobile devices. Finally, we extend our investigation to microwave wireless (WiFi) discussing security and feasibility of CV-QKD for very short-range applications.

Figure 1

Quantum communication scenario between transmitter (Alice) and receiver (Bob) separated by a quantum channel with transmissivity ${\eta }_{\text{ch}}$ and thermal number ${\overline{n}}_e={\overline{n}}_B/(1-{\eta }_{\text{ch}})$. Bob's setup has quantum efficiency ${\eta }_{\text{eff}}$ and extra thermal photons ${\overline{n}}_{\text{ex}}$. The mean number of photons at the input (${\overline{n}}_T$) and output (${\overline{n}}_R$) follow Eq. (2), while the input classical variable ($x$) and the output one ($y$) follow Eq. (4). We also describe the various trust levels for the receiver. In the scenario “Eve (1)”, the eavesdropper is assumed to attack the external channel only. In the scenario “Eve (2)”, there is also a passive side-channel attack where the eavesdropper collects leakage from the receiver's setup. Finally, in the scenario “Eve (3)”, we assume that the eavesdropper is also able to perform an active side-channel attack, so that the noise internal to the setup has to be considered untrusted.

Figure 2

Setup noise as a function of the total transmissivity $\tau$ expressed in decibels. (a) We plot the equivalent number of thermal photons ${\overline{n}}_{\text{ex}}$ associated with the setup noise, for the TLO (black lines) and the LLO (blue lines), considering the homodyne protocol (solid lines) and the heterodyne protocol (dashed lines). (b) As in (a) but we plot the setup excess noise ${\xi }_{\text{ex}}$. Parameters are chosen as in the text. See Eq. (17).

Figure 3

Eve's collective attack under the assumption of trusted noise in the receiver's setup, i.e., Eve (2) in Fig. 1.

Figure 4

Composable secret key rate (bits/use) versus total loss (decibels) for the heterodyne protocol with LLO. We plot the rates against collective attacks assuming a trusted-loss and trusted-noise receiver (black dotted), a trusted-noise receiver (black dashed), and an untrusted receiver (solid black). We also show the performance achievable with the untrusted receiver in the presence of general attacks (red). The gray line is the total excess noise ${\xi }_{\text{tot}}$ in shot noise units. Finally, the blue lines refer to line-of-sight security (discussed in Sec. 3a) for trusted-loss and trusted-noise receiver (blue dotted), and trusted-noise receiver (blue dashed). Physical and protocol parameters are chosen as in Tables 1 and 2.

Figure 5

Optical-wireless QKD with fixed devices. We plot the composable secret key rate (bits/use) versus free-space distance (meters) for the heterodyne protocol with LLO. In particular, we show the rates against collective attacks assuming a trusted-loss-and-noise receiver (black dotted), a trusted-noise receiver (black dashed), and an untrusted receiver (solid black). We also show the performance achievable with the untrusted receiver versus general attacks (red). The blue lines refer to line-of-sight security (discussed in Sec. 3a) for trusted-loss-and-noise receiver (blue dotted), and trusted-noise receiver (blue dashed). Physical parameters are chosen as in Table 4, while protocol parameters are in Table 2.

Figure 6

Optical-wireless QKD with mobile devices. We plot the composable secret key rate (bits/use) versus the maximum free-space distance $z_{max}$ of the receiver-device from the transmitter (meters). This is for a pilot-guided post-selected heterodyne protocol with an LLO. We show the rates against collective attacks assuming a trusted-loss-and-noise receiver (black dotted), a trusted-noise receiver (black dashed), and an untrusted receiver (solid black). The blue lines refer to line-of-sight security for trusted-loss-and-noise receiver (blue dotted), and trusted-noise receiver (blue dashed). Physical parameters are chosen as discussed in the main text.

Figure 7

Microwave wireless QKD (at 1 GHz) using the heterodyne protocol under LoS security. We plot the composable secret key rate (bits/use) versus free-space distance $z$ between transmitter and receiver (centimeters). Parameters are chosen as discussed in the main text.