Quantum Coherence Witness with Untrusted Measurement Devices

Coherence is a fundamental resource in quantum information processing, which can be certified by a coherence witness. Due to the imperfection of measurement devices, a conventional coherence witness may lead to fallacious results. We show that the conventional witness could mistake an incoherent state as a state with coherence due to the inaccurate settings of measurement bases. In order to make the witness result reliable, we propose a measurement-device-independent coherence witness scheme without any assumptions on the measurement settings. We introduce the decoy-state method to significantly increase the capability of recognizing states with coherence. Furthermore, we experimentally demonstrate the scheme in a time-bin encoding optical system.

Figure 1

MDICW scheme.

Figure 2

Experimental setup for the MDICW scheme including the source part (a), the measurement part (b), and the phase stabilization part (c). LD: laser diode, FPGA: field-programmable gate array, SYNC: synchronized signal, BS: beam splitter, ATT: attenuator, FRM: Faraday rotator mirror, PS: phase shifter, VDL: variable delay line, HVM: high-voltage module, PID: proportional-integral-derivative algorithm, PC: polarization controller, PBS: polarizing beam splitter, AM: amplitude modulator, PM: phase modulator, SPAD: single-photon avalanche diode, TDC: time-to-digital converter.

Figure 3

Simulation comparison of coherence witness with (solid line) and without (dashed line) decoy state method as a function of channel loss. The simulation parameters include $p_d={10}^{-6}$, $N=3.2\times {10}^6$, ${\eta }_1={\eta }_2={\eta }_3={\eta }_4=1/8$, ${\eta }_5=1/2$, $p_s=0.5$, $n_{\sigma }=3.89$, and zero error rate. The circle point represents the experimental result with decoy state method under the condition of high channel loss of 13.13 dB and nonzero error rate.