Time-Resolving Quantum Measurement Enables Energy-Efficient, Large-Alphabet Communication

Information exchange requires a measurement of physical states. Because quantum measurements enable accuracy beyond the classical shot-noise limit, they are successfully used to develop measurement tools and applications. In particular, quantum-measurement-enhanced strategies are used for the discrimination of nonorthogonal coherent states. The efficient discrimination of these states is crucial for optical communication networks, that are now approaching the classical limits of the underlying physical systems. However, quantum-enhanced discrimination strategies demonstrated to date are based on legacy communication protocols designed for classical measurements and thus provide only a limited advantage. In our work, we use photon detection times readily available in quantum measurement, but not accessible by classical means. We measure and use these times to maximize our knowledge about faint nonorthogonal coherent states. We employ communication strategies designed to benefit most from this knowledge. This holistic approach in our experiment has resulted in the record low error rates in discrimination of multiple faint nonorthogonal coherent states carrying energy corresponding to just one photon per bit of transmitted information. We demonstrate successful discrimination of large alphabets of optical states ($4\le M\le 16$) beyond the ideal classical shot-noise limit, showing the scalability of quantum-measurement-enabled communication. This experimental work explores unforeseen advantages of quantum measurement on one hand, and may help address the capacity crunch in modern optical networks caused by the exponential growth of data exchange on the other.

Popular Summary

The connection between information and physics is now well-established. To communicate, one must measure and distinguish different states of a physical system used to store and/or transmit information. Exabytes of information are sent through the Internet monthly, and the demand grows exponentially. The need for energy-efficient communication is universally recognized, driving research efforts for more efficient networks. However, networks are reaching their limits caused by inherent limitations of classical measurements, and only incremental progress is currently possible. Quantum measurements offer many advantages over classical measurements and could help alleviate these limitations. Particularly, quantum measurement-enabled receivers allow energy efficiency beyond the classical limits. Until now, quantum receivers used communication schemes that were originally developed for classical measurement methods.

In our work, we identified information readily available in quantum measurement, but not accessible by classical means. We found a way to harness this additional information about quantum states. The result is the first experimental demonstration of a holistic quantum-enabled communications scheme with record energy efficiency. We report the lowest error rates in discrimination of multiple optical states carrying energy corresponding to just one photon per bit of transmitted information. We demonstrate discrimination of a large number of optical states beyond ideal classical limits, showing the scalability of quantum measurement-enabled communication for the first time. Our holistic approach may be of interest to a wide range of research that employs quantum measurement: from communications and astronomy to biophotonics and microscopy.

Figure 1

Time-resolving quantum receiver. The signal pulse $|{\psi }_s⟩$ is displaced at a 99:1 beam splitter (BS) with the adaptive local oscillator $|{\beta }_h⟩$, whose parameters depend on the hypothesized most probable input state $h$ and followed with a single-photon detector (SPD). Colors represent frequency detunings. The displaced signal for the correct hypothesis nulls the output, whereas an incorrect hypothesis results in a temporal fringe with the probability density of a photon detection varying in time, uniquely for each pair of $|{\psi }_s⟩$ and $|{\beta }_h⟩$. Each detection time $t_k$, $k\in \mathrm{1..}f$, is used to find the posterior hypothesis $h_k$. Inset: an $M=8$ CFSK alphabet schematically depicted in a complex phase diagram starting at the beginning of a symbol pulse. In the rotating frame of the first state, other states revolve around the origin at different rates, represented by the length of arrows.

Figure 2

The a posteriori Bayesian probabilities ${\zeta }_{t_1}(m)$ that the signal is in the state $m$ conditioned on the first photon detection at $t_1$ when the initial hypothesis is set to $h_0=1$. The $M=4$ CFSK modulation is optimized for maximum energy sensitivity of the receiver. $\mathrm{\Delta }\theta =1.96$, $\mathrm{\Delta }\omega T=\pi$, $n_0=2$, assuming ideal displacement and detector.

Figure 3

The Bayesian likelihood $\mathrm{\aleph }(t_k,t_{k-1},|h_{k-1}-m|)$ that the input state is $|{\psi }_m⟩$, $m\in \mathrm{1..}M$ as a function of the current photon detection time $t_k$, previous photon detection time $t_{k-1}<t_k$, and the current state of the LO $h_{k-1}$, for an $M=8$ CFSK protocol. A photon detection at time $t_k$ leads to an update of posterior probabilities ${\zeta }_{t_k}(m)$ that the input state is $m$. To aid real-time calculations, we renormalize likelihood functions such that $max\left[\mathrm{\aleph }(t_k,t_{k-1},|h_{k-1}-m|)\right]=1$.

Figure 4

Experimental implementation of an $M$-ary CFSK receiver. The light from a 633-nm laser is split 99:1 on an FBS and sent to the signal and LO preparation stages. We prepare CFSK and LO states by simultaneous frequency and phase modulation implemented with a double-pass AOM. The displacement is performed by interfering the input state with the LO on another 99:1 FBS. The displaced signal is sent to an SPD. The FPGA registers the times of photon detections, runs the discrimination algorithm and generates rf pulses to control the AOMs. The setup is interferometrically stabilized using a counter-propagating laser at 795 nm, analog photodiode (PD), a piezo mirror, and a stand-alone lock (PID). PBS, polarization beam splitter; $\lambda /2$ and $\lambda /4$, half- and quarter-wave plates. The input of the quantum receiver is connected to the output of the signal fiber with a fiber mating sleeve.

Figure 5

(a) Measured performance (green points) below the SNL of the optimal classical receiver (solid red line) is unconditionally nonclassical. This is seen for a range of approximately $0.5$ to approximately $2.5$ photons/bit. For comparison, we also include the SNL adjusted to the same system efficiency as our receiver (dashed red line). Also shown is the HB and the HB of an 8-PSK protocol and the SNL for 8-PSK as indicated. (b) Measured sensitivity is plotted as a ratio to the SNL (red horizontal line). Error bars correspond to one standard deviation.

Figure 6

The time-resolved receiver’s scalability with $M$. The experimentally measured symbol error rate of the CFSK quantum receiver with the input of 1 photon/bit for protocols optimized for maximal energy sensitivity vs the alphabet length (green filled circles). Labeled are the ideal SNL, the SNL for a receiver with 74.5% system efficiency, and the HB, along with the SNL and HB of the PSK protocol. The best experimental sensitivity for the $M=4$ PSK protocol reported to date [15]—blue star. Same for PPM [17]—purple star. Error bars correspond to one standard deviation. All connecting lines are guides for an eye.

Figure 7

Experimentally measured sensitivity of $M=4,6,12,16$ CFSK quantum receivers. The SNL is shown with a solid red line, the same classical limit adjusted to the experimental system efficiency of our receiver is shown with a dashed red line. The HB is shown with a solid black line. For further comparison, SNLs and HBs of corresponding $M$-ary PSK protocols are shown with solid and dashed blue lines, respectively. Insets: ratios of measured sensitivities to the SNL. Error bars correspond to one standard deviation statistical uncertainties.