Sub-shot-noise-limited fiber-optic quantum receiver

We experimentally demonstrate a quantum receiver based on the Kennedy scheme for discrimination between two phase-modulated weak coherent states. The receiver is assembled entirely from standard fiber-optic elements and operates at a conventional telecom wavelength of 1.55 $\mu \text{m}$. The local oscillator and the signal are transmitted through different optical fibers, and the displaced signal is measured with a high-efficiency superconducting nanowire single-photon detector. We show the discrimination error rate is two times below that of a shot-noise-limited receiver with the same system detection efficiency.

Figure 1

Schematics of a displacement-based Kennedy receiver. A mode-matched signal and local oscillator are combined on a 99:1 beam splitter such that after the beam splitter one of the possible states (e.g., $|-\alpha \rangle$) vanishes out due to destructive interference with the local oscillator (LO). The result of interference between the signal and LO is registered by a single-photon detector.

Figure 2

Probability distribution of photocounts for logical “0” (green histogram), and logical “1” (blue histogram). Discrimination errors $e_{10}$ and $e_{01}$ correspond to the first component of the blue histogram (zero number of photocounts) and all-but-first components of the green histogram (nonzero number of photons), respectively. The inset shows the error diagram.

Figure 3

Schematics of the experimental setup. The source of light (LS) is attenuated via a variable attenuator (ATT) and then split into two unequal parts on a polarization beam splitter (PBS). The splitting ratio is controlled by a fiber polarization controller (FPC No. 1). The two parts have the same polarization since one of the fibers is physically rotated by ${90}^{\circ }$. The weaker part is binary phase modulated on an electro-optical modulator (EOM) driven by a radio-frequency generator (RFG). The stronger part serves as a local oscillator that interferes with the signal on a beam splitter (BS). The result of interference is measured by a superconducting nanowire single-photon detector (SNSPD), preceded by a fiber polarization controller (FPC No. 2) to match the highest quantum efficiency of the detector. Time-correlated single-photon counting electronics (TCSPC) is used to synchronize the detector with the modulator.

Figure 4

Schematics of data processing. (a) Initial binary data are encoded into the binary phase-shifted coherent signal. (b) After optical displacement, the binary phase-shift signal is transformed into the binary amplitude-modulated signal with the amplitude modulation extinction around 30 dB. (c) Finally, an amplitude-modulated signal is registered by a single-photon detector. Photocounts (shown by the solid line) are decoded into logical data and matched with the original data (shown by the dashed line). After a comparison of encoded and decoded data, the discrimination errors are calculated.

Figure 5

Discrimination error rate as a function of mean photon number in a signal time bin. The error rate is normalized to the standard quantum limit (SQL), shown by the blue dashed line. Red dots show the experimental error rate of our receiver, including the statistical deviations indicated by black bars. The red dashed-dotted line shows a theoretical fit for the measured error rate. For comparison, we also show the theoretical values for the ideal Kennedy receiver (green solid line) and the Helstrom bound (magenta dotted line).