Experimental measurement-device-independent quantum random-number generation

The randomness from a quantum random-number generator (QRNG) relies on the accurate characterization of its devices. However, device imperfections and inaccurate characterizations can result in wrong entropy estimation and bias in practice, which highly affects the genuine randomness generation and may even induce the disappearance of quantum randomness in an extreme case. Here we experimentally demonstrate a measurement-device-independent (MDI) QRNG based on time-bin encoding to achieve certified quantum randomness even when the measurement devices are uncharacterized and untrusted. The MDI-QRNG is randomly switched between the regular randomness generation mode and a test mode, in which four quantum states are randomly prepared to perform measurement tomography in real time. With a clock rate of 25 MHz, the MDI-QRNG generates a final random bit rate of 5.7 kbps. Such implementation with an all-fiber setup provides an approach to construct a fully integrated MDI-QRNG with trusted but error-prone devices in practice.

Figure 1

Measurement-device-independent QRNG scheme.

Figure 2

Experimental setup of MDI-QRNG including the trusted source (a) and the $Z$ basis measurement part (b). During the verification process of prepared quantum states, the measurement part is reconfigured when $X$ and $Y$ basis measurements are performed (c). LD: laser diode; FPGA: field-programmable gate array; BS: beam splitter; PC: polarization controller; PBS: polarizing beam splitter; AM: amplitude modulator; PM: phase modulator; ATT: attenuator; SPAD: single-photon avalanche diode; TDC: time-to-digital converter.

Figure 3

Intensity traces of four prepared states of $\left|0\right.〉, \left|1\right.〉, \left|+\right.〉$, and $\left|+i\right.〉$ observed in an oscilloscope (a). The measurement part is configured as Fig. 2, while the attenuator is set as the minimal value and a high-speed photodetector is used instead of the SPAD. Early and late time-bin pulses at $T0$ and $T1$ correspond to the states of $\left|1\right.〉$ and $\left|0\right.〉$, respectively. When both the early and late pulses are attenuated by half and the phase of the early pulse is set as 0 ($\frac{\pi }{2}$) by PM1, the state of $\left|+\right.〉$ ($\left|+i\right.〉$) is prepared. However, the intensity traces in two cases are exactly the same. To further distinguish the two states, the measurement part is configured as Fig. 2. When the phase of PM2 is set as 0, $\left|+\right.〉$ and $\left|+i\right.〉$ produce constructive and intermediate interferences, respectively (b).

Figure 4

The measured error rates of four prepared quantum states in the three orthogonal basis.

Figure 5

The NIST test results of the final random data with a size of 390 Mbits. Given an item, when the $p$ value (column) and the proportion (dot) are more than 0.01 and 0.98, respectively, it means that the random data pass the item.