Achieving Ultimate Noise Tolerance in Quantum Communication

At the fundamental level, quantum communication is ultimately limited by noise. For instance, quantum signals cannot be amplified without the introduction of noise in the amplified states. Furthermore, photon loss reduces the signal-to-noise ratio, accentuating the effect of noise. Thus, most of the efforts in quantum communications have been directed towards overcoming noise to achieve longer communication distances, larger secret key rates, or to operate in noisier environmental conditions. Here, we propose and experimentally demonstrate a platform for quantum communication based on ultrafast optical techniques. In particular, our scheme enables the experimental realization of high rates and quantum signal filtering approaching a single spectrotemporal mode, resulting in a dramatic reduction in channel noise. By experimentally realizing a 1-ps optically induced temporal gate, we show that ultrafast time filtering can result in an improvement in noise tolerance by a factor of up to 1200 compared to a 2-ns electronic filter, enabling daytime quantum key distribution or quantum communication in bright fibers.

Figure 1

Conceptual scheme of ultrafast temporal filtering. Quantum signals prepared in a single spectrotemporal mode are found in the presence of spectral and temporal noise. As a first step, an ultrafast temporal filter matching the duration of the signal pulse is applied. By doing so, the noise is largely reduced and the quantum signal left untouched. The beam is then sent through a spectral filter that is matched to the bandwidth of the quantum signal, further increasing the signal-to-noise ratio.

Figure 2

Experimental setup. (a) Experimental setup demonstrating the use of the ultrafast temporal filter in a quantum-communication demonstration. $\mathrm{Ti}$:Sa, titanium sapphire laser; $\lambda /2$, half-wave plate; $\lambda /4$, quarter-wave plate; PBS, polarizing beam splitter; OPO, optical parametric oscillator; ND, neutral density filter; BS, beam splitter; DM, dichroic mirror; SF, spectral filters; VD, variable delay; SMF, single-mode fiber; PD, photodiode; GL, Glan-laser polarizer; APD, avalanche photodiode detectors. (b) Switching efficiency as a function of the pump delay demonstrating the temporal profile of the UTF. (c) Spectrum of signal photons after spectral filtering at the receiver’s stage.

Figure 3

Secret key rates. (a) Secret key rates as a function of noise counts are reported for different channel loss values, $5,10,15,20\mathrm{dB}$. (b) The noise threshold, which is defined as the largest amount of noise for which the mean secret key rate is larger than zero by at least one standard deviation, is shown for different values of channel loss. (c) The noise improvement factor corresponding to the ratio of the noise threshold for the case of UTF over ETF is shown for different values of channel loss. The secret rates as a function of channel loss are reported for (d) ETF and for (e) UTF for different channel noise values, $N$. (f) The loss threshold, which is defined as the largest amount of loss for which the mean secret key rate is larger than zero by at least one standard deviation, is shown for different values of noise counts. (g) The distance improvement factor corresponding to the ratio of the loss threshold for the case of UTF over ETF is shown for different values of noise counts. The shaded areas correspond to channel conditions where an improvement of UTF over ETF is observed.

Figure 4

Efficiency and noise characteristics of the ultrafast temporal filter. Switching efficiency (blue dashed curve) and noise counts due to the pump pulse (red solid curve) as a function of the pump pulse energy measured at the output of the SMF. The switching efficiency follows a quadratic sinusoidal relation and the noise curve follows a quadratic relation. The quadratic scaling is typical of third-order nonlinear processes at the origin of the noise counts from the pump.

Figure 5

Gain. Gain for (a) signal pulses $\mu$ and (b) decoy pulses $\nu$ as a function of noise counts are reported for different channel loss values, $t=5,10,15,20$ dB, respectively, blue circles, orange squares, green triangles, and red diamond, for the case of UTF (solid curves and empty markers) and ETF (dashed curves and full markers), respectively, on the right and the left. Noise counts correspond to counts detected at the APD within the time window of $\mathrm{\Delta }{t}_{\mathrm{coinc}}=1$ ns.

Figure 6

Error rate. Error rate for (a) signal pulses $\mu$ and (b) decoy pulses $\nu$ as a function of noise counts are reported for different channel loss values, $t=5,10,15,20$ dB, respectively, blue circles, orange squares, green triangles, and red diamond, for the case of UTF (solid curves and empty markers) and ETF (dashed curves and full markers), respectively, on the right and the left. Noise counts correspond to counts detected at the APD within the time window of $\mathrm{\Delta }{t}_{\mathrm{coinc}}=1$ ns.

Figure 7

Background rate. Background rate per pulse, $Y_0$, as a function of noise counts that are introduced in the quantum channel by the cw beam. In the case of the UTF, the background rate $Y_0$ is lower bounded by the pump noise counts, i.e., $2.8\times {10}^{-6}$, coming from parasitic nonlinear processes in the SMF.

Figure 8

Numerical simulation of the ultrafast switch. (a) Simulated switching response for the following input experimental parameters: pump pulse energy (2.47 nJ), center wavelength (${\lambda }_{\mathrm{pump}}=800$ nm), spectral bandwidth ($\mathrm{\Delta }{\lambda }_{\mathrm{pump}}=2.1$ nm), signal wavelength (${\lambda }_{\mathrm{signal}}=720.8$ nm), and length of the SMF (10 cm). The switching time given by the FWHM of the switching response is given by 1.02 ps. (b) The switching trace is calculated by calculating the switching efficiency of a signal pulse with a spectral bandwidth of $\mathrm{\Delta }{\lambda }_{\mathrm{signal}}=1.7$ nm as a function of the delay between the pump and signal pulse. The FWHM of the switching trace is given by 0.92 ps. Numerical evaluation of the transmission of various Hermite-Gauss modes of mode order ranging from 0 to 10 for combined temporal and spectral filter (c) and for only spectral filtering (d).

Figure 9

Numerical simulation of the ultrafast switch in the presence of temporal fluctuations.