Photon number resolution enables quantum receiver for realistic coherent optical communications

Journal name:
Nature Photonics
Year published:
Published online


Quantum-enhanced measurements can provide information about the properties of a physical system with sensitivities beyond what is fundamentally possible with conventional technologies. However, this advantage can be achieved only if quantum measurement technologies are robust against losses and real-world imperfections, and can operate in regimes compatible with existing systems. Here, we demonstrate a quantum receiver for coherent communication, the performance of which not only surpasses the standard quantum limit, but does so for input powers extending to high mean photon numbers. This receiver uses adaptive measurements and photon number resolution to achieve high sensitivity and robustness against imperfections, and ultimately shows the greatest advantage over the standard quantum limit ever achieved by any quantum receiver at power levels compatible with state-of-the-art optical communication systems. Our demonstration shows that quantum measurements can provide real and practical advantages over conventional technologies for optical communications.

At a glance


  1. Robust receiver with photon number resolution.
    Figure 1: Robust receiver with photon number resolution.

    a, Schematic of receiver. The quantum receiver implements N adaptive measurements based on displacement operations and PNR detection to discriminate an input coherent state with error probabilities below the SQL. b, Probability of error for the discrimination of four non-orthogonal states in the QPSK format as a function of the mean photon number for receivers implementing N = 4 adaptive measurements with detection efficiency η = 1 and different PNR powers (from PNR(1) to PNR(6)) in the presence of noise and imperfections resulting in a visibility of  = 99%. The case of noiseless PNR(1) with  = 100%, the SQL and the Helstrom bound are also shown for reference. c, Maximum mean photon number that can be reached with error probabilities below the SQL for quantum receivers with η = 1 and N = 4 and with different PNR powers for several levels of noise and imperfections resulting in different . The one red point shows the improvement achieved for a receiver with PNR(6) by increasing the adaptive measurements from N = 4 to N = 5 with  = 98.5%, as indicated by the dashed arrow.

  2. Experimental implementation of a receiver.
    Figure 2: Experimental implementation of a receiver.

    The receiver discriminates among four possible QPSK states, prepared by phase modulator PM1, by performing seven adaptive measurements based on optical displacement of the input state in a 99:1 beamsplitter (BS) (combiner) with the local oscillator field LO(βi) and PNR detection with PNR(3). During each adaptive measurement period i, the single-photon avalanche diode (SPAD) detects di photons and the field-programmable gate array (FPGA) uses the total number of detected photons to optimize subsequent adaptive measurements implemented by controlling the phase of the LO using PM2 based on the strategy with a maximum photon number resolution of 3, PNR(3). That is, while in each period i the SPAD can detect many photons, in our implementation any detection di ≥ 3 is counted as three photon detections. The implementation of higher PNR powers is not limited by our SPAD (because its deadtime and recovery times are 8 × 10−3 times smaller than the period duration), but only by the memory of the FPGA, for real-time data processing. Using an FPGA with larger memory and bandwidth for real-time data processing and feedback would allow the implementation of receivers with higher PNR powers. An acousto-optic modulator (AOM) is used to prepare flat-top light pulses of 37 µs from a HeNe laser source.

  3. Experimental results.
    Figure 3: Experimental results.

    Error probability (blue symbols) for the discrimination of four non-orthogonal states in the QPSK format by receivers with no PNR power, PNR(1) and with a PNR power of 3, PNR(3). The receiver with PNR(3) can discriminate QPSK states below the SQL for a range that extends to high power levels. It discriminates with much lower errors than its counterpart without PNR capabilities, and reaches error rates 14.5 dB below the ideal, perfect 100% efficiency SQL (red line) and 27 dB below the SQL under the same experimental conditions of detection efficiency (green line). The Helstrom bound is shown for comparison. This receiver reaches error probabilities of 10−6 for and the data point towards even lower error probabilities at higher . Error bars represent one statistical standard deviation from four runs of 1 × 106 independent experiments for PNR(1), five runs of 1 × 106 for from 1 to 9, five runs of 4 × 106 for from 10 to 14 and 10 runs of 4 × 106 for from 15 to 20 for PNR(3). The theoretical predictions (crosses) are based on Monte Carlo simulations, with the experimentally determined detection efficiency and visibility for PNR(1) and PNR(3) showing good agreement with the experimental observations.

  4. Minimum codeword length nmin.
    Figure 4: Minimum codeword length nmin.

    a,b, Minimum codeword length nmin to achieve an RS coded error probability of for two sets of input power levels for QPSK (a) and 16QAM (b). The expected performance of the PNR(3) receiver (green dashed lines) is compared with a PNR(1) (red dashed lines) and a conventional SQL-limited receiver (solid blue lines). For completeness, the SQL-limited receiver is also shown scaled to 72% detection efficiency.


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Author information


  1. Center for Quantum Information and Control, MSC07-4220, University of New Mexico, Albuquerque, New Mexico 87131-0001, USA

    • F. E. Becerra
  2. Joint Quantum Institute, University of Maryland, and National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, USA

    • J. Fan &
    • A. Migdall


F.E.B. analysed the theoretical measurement strategy, designed the experimental implementation of the receiver, performed the measurements and analysed the experimental results. J.F. realized the analysis for coded communications. J.F. and A.M. provided assistance and discussions. All authors contributed to writing the manuscript.

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