Experimental demonstration of kilometer-range quantum digital signatures

We present an experimental realization of a quantum digital signature protocol which, together with a standard quantum key distribution link, increases transmission distance to kilometer ranges, three orders of magnitude larger than in previous realizations. The bit rate is also significantly increased compared with previous quantum signature demonstrations. This work illustrates that quantum digital signatures can be realized with optical components similar to those used for quantum key distribution and could be implemented in existing quantum optical fiber networks.

Figure 1

Experimental setup for kilometer-range quantum digital signatures. Alice uses a pulsed 850-nm-wavelength vertical cavity surface-emitting laser (VCSEL) diode to generate coherent states which are phase encoded using a lithium niobate $\left({\text{LiNbO}}_3\right)$ phase modulator. Alice sends the coherent states through standard telecommunications optical fiber to the receivers, who then perform a phase measurement. Sender and receivers are constructed from polarization-maintaining optical fiber to improve the interferometric visibility. Polarization routing of modulated signal and unmodulated reference was carried out using polarization-dependent beam splitters (PBS) while static polarization controllers (SPCs) corrected for polarization shift induced in the telecommunications fiber.

Figure 2

Experimental results and calculated parameters. In our experiment, measurement statistics for Bob and Charlie were similar. (a) Conditional probabilities for unambiguous state elimination by Bob, with ${\left|\alpha \right|}^2=0.5$. These probabilities are used to calculate the gap $g$ and the required signature length per half-bit. (b) Time required for Alice to send a half-bit to Bob. (c) The gap achieved in the experiments is a calculated from both receivers' cost matrices. (d) The length $L$ required to prevent forging and repudiation, per half-bit of message, for a security level of 0.01%. For all subfigures at 500 m, mean photon number points of 0.1, 0.9, and 1 have been removed. Here, the combination of count rate and the dead time of the detector led to nonlinearity in the detection.

Figure 3

Unambiguous state elimination (USE) success rate at different transmission distances for Bob. Results for Bob and Charlie are again very similar so only results for Bob are shown. The failure rate of USE is on average only 1.7% of the pulse-repetition frequency and is not plotted. For transmission distance 500 m, points for mean photon number 0.1, 0.9, and 1 have been removed, since here the combination of count rate and the dead time of the detector led to nonlinearity in the detection of events.