Self-Referenced Continuous-Variable Quantum Key Distribution Protocol

We introduce a new continuous-variable quantum key distribution (CV-QKD) protocol, self-referenced CV-QKD, that eliminates the need for transmission of a high-power local oscillator between the communicating parties. In this protocol, each signal pulse is accompanied by a reference pulse (or a pair of twin reference pulses), used to align Alice’s and Bob’s measurement bases. The method of phase estimation and compensation based on the reference pulse measurement can be viewed as a quantum analog of intradyne detection used in classical coherent communication, which extracts the phase information from the modulated signal. We present a proof-of-principle, fiber-based experimental demonstration of the protocol and quantify the expected secret key rates by expressing them in terms of experimental parameters. Our analysis of the secret key rate fully takes into account the inherent uncertainty associated with the quantum nature of the reference pulse(s) and quantifies the limit at which the theoretical key rate approaches that of the respective conventional protocol that requires local oscillator transmission. The self-referenced protocol greatly simplifies the hardware required for CV-QKD, especially for potential integrated photonics implementations of transmitters and receivers, with minimum sacrifice of performance. As such, it provides a pathway towards scalable integrated CV-QKD transceivers, a vital step towards large-scale QKD networks.

Popular Summary

Quantum key distribution (QKD), which enables the generation of secure shared randomness between two distant parties, is the most advanced quantum technology to date. Continuous-variable QKD is a particular type of QKD that has less stringent demands on hardware for optical transmission and detection than other variants of QKD. Here, we remove one of the remaining hardware complexities of continuous-variable QKD by constructing a protocol that eliminates the need to co-transmit a local oscillator reference between the two communicating parties. The critical step in formulating the new protocol is recognizing the role that the local oscillator plays in establishing a shared reference frame and accomplishing this task using a more nuanced technique. We perform a detailed theoretical analysis of the expected key rates achievable with this new protocol, and we report a proof-of-principle demonstration of our protocol.

Transmitting a high-power local oscillator—desirable for high-fidelity measurements at the receiver’s end—requires dedicated, complex hardware to separate the local oscillator from the signal pulse to avoid contamination of the weak signal pulse. We focus on simplifying the hardware involved in continuous-variable QKD by using reference pulses and postprocessing of data instead of a local oscillator. By removing the need to communicate a local oscillator, our new protocol (“self-referenced continuous-variable QKD”) can perform continuous-variable QKD using hardware that is very similar to conventional coherent communication hardware.

As a result of hardware simplifications, we anticipate that reliable integrated photonics implementations of continuous-variable QKD transmitters and receivers can be realized with existing technologies. Such integrated and miniaturized hardware realizations are critical for the next phase of QKD development, which will be focused on practicality and widespread utilization.

Figure 1

Hardware schematic for the SR-CV-QKD protocol. In contrast to conventional CV-QKD implementations (e.g., Ref. [10]), the hardware requirements are dramatically simplified due to elimination of LO transmission.

Figure 2

The phase-space representation of Alice’s and Bob’s misaligned reference frames. The reference pulse is assumed to be on the $Q_A$ axis for Alice in this example, and the signal pulse is randomly placed.

Figure 3

Expected minimum key rates for the SR-CV-QKD protocol, secure against (a) individual attacks and (b) collective attacks, as functions of the effective transmittance $T_{\mathrm{eff}}=T\eta$. The parameter values used are $V_A=40$, $ϵ=0.01$, $V_{\mathrm{el}}=0.01$ (all in shot-noise units), $\beta =0.95$, ${\delta }_R=1$. As shown in the legend, different curves correspond to different values of the reference-pulse amplitude $V_R^{1/2}$ (specifically, $V_R/V_A=\{10,20,50,100,200,500\}$), along with the curve for $\xi =0$, in which case the key rate is the same as that for the respective conventional CV-QKD protocol with LO transmission. The curves terminate on the left at values of $T_{\mathrm{eff}}$ below which the expected secret key rate is zero.

Figure 4

Schematic of experimental setup for a proof-of-principle demonstration of SR-CV-QKD. The only difference between this schematic and Fig. 1 is the use of a shared laser source between Alice and Bob for experimental convenience.

Figure 5

Phase-drift estimation and compensation for constant signal pulses. Bob’s measured voltages proportional to mean values of $Q$ quadrature (blue dots) and $P$ quadrature (red dots) for (a) reference pulses and (b) signal pulses. (c) Estimated values $\widehat{\theta }$ of the phase difference between Alice’s and Bob’s frames. Each data point is calculated as in Eq. (4) using mean quadrature values $q_{B_R}$ and $p_{B_R}$ obtained from sequential homodyne measurements on a pair of twin reference pulses. (d) Mean values of $Q$ quadrature (blue dots) and $P$ quadrature (red dots) for signal pulses, after a rotation by the angle $-\widehat{\theta }$ to compensate for the phase drift.

Figure 6

The phase-space representation of reconstructed signal pulses after phase-drift compensation.

Figure 7

The phase-space representation of signal pulses reconstructed using quadrature measurements on reference pulses and phase difference estimation.

Figure 8

The variance of the reconstructed signal data as a function of the phase-space location.

Figure 9

Expected key rates as a function of transmission distance for the current experimental setup and a range of postprocessing efficiency values ($\beta$). The parameters used are $V_A=34$, $V_R=900$, ${\delta }_R=0$, $\epsilon =0.01$, $V_{\mathrm{el}}=0.01$, and pulse rate of 250 kHz. The homodyne efficiency was taken to be the average value (this quantity fluctuates in our setup—see main text) of $\eta =0.719$. The transmission loss was taken to be $0.2\mathrm{dB}/\mathrm{km}$.

Figure 10

In situ calibration of a phase EOM using reference pulses and phase-drift compensation. (a) Raw data collected while the modulation voltage is swept from $-3.5\mathrm{V}$ to 3.5 V within the time window (5–58 ms). Red line: In-phase value of the reference pulse. Magenta line: Quadrature value of the reference pulse. Blue line: In-phase value of the phase-modulated pulse. Cyan line: Quadrature value of the phase-modulated pulse. (b) The calibration curve between the applied voltage and the induced phase after phase-drift compensation. Blue dots: Calibration data. Red line: Polynomial fit.