Statistical Benchmarking of Scalable Photonic Quantum Systems

Targeting at the realization of scalable photonic quantum technologies, the generation of many photons, their propagation in large optical networks, and a subsequent detection and analysis of sophisticated quantum correlations are essential for the understanding of macroscopic quantum systems. In this experimental contribution, we explore the joint operation of all mentioned ingredients. We benchmark our time-multiplexing framework that includes a high-performance source of multiphoton states and a large multiplexing network, together with unique detectors with high photon-number resolution, readily available for distributing quantum light and measuring complex quantum correlations. Using an adaptive approach that employs flexible time bins, rather than static ones, we successfully verify high-order nonclassical correlations of many photons distributed over many modes. By exploiting the symmetry of our system and using powerful analysis tools, we can analyze correlations that would be inaccessible by classical means otherwise. In particular, we produce on the order of ten photons and distribute them over 64 modes. Nonclassicality is verified with correlation functions up to the 128th order and statistical significances of up to 20 standard deviations.

Figure 1

(a) Benchmark protocol in its spatial representation. Probing the future readiness of our system consists of three steps: the heralded generation of high-photon-number ($N$) states via a high-performance parametric down-conversion (PDC) source, the propagation of many photons in optical networks with many modes ($M$), and the photon-number-resolved detection to determine high-order correlations within and between the modes. (b) Efficient implementation as a time-bin multiplexing setup. Instead of spatial modes, we employ time bins that are separated by using “$+n\tau$” fiber-loop delay lines. Two on-off detectors, which are superconducting nanowire single-photon detectors in our case, record incident photons. At different levels, the multiplexing network can be separated (vertical line) to achieve a certain number of network modes $M$ and a desired photon-number resolution via multiplexing of $D$ single-photon counters [76, 77, 78]. (c) Assigned time bins. With this separation approach, each time bin can be assigned to a network mode, and the number $D$ of possible joint clicks per mode identifies the order of correlation functions that are thereby accessible. Note that, in our experiment, the number of network and detection modes for the signal is much larger, $MD=128$, than in the depicted case, where $MD=16$.

Figure 2

Benchmark of $K$-mode nonclassicality via negative minimal eigenvalue of the matrix of moments ${\mathrm{\Gamma }}_K$ for $N\in \{1,\dots ,10\}$ photons distributed over $M=64$ modes. The classical-quantum boundary, zero, is shown as a gray horizontal line. The pump power for the PDC process is $500\mu \mathrm{W}$, and the adaptive time-bin width is twice the width of the Gaussian pulse width (i.e., $2\sigma$) after propagation through fibers. One standard-deviation error margin is shown as shaded area and includes random and systematic uncertainties. Mean values and random errors are obtained from raw coincidence counts, without any correcting postprocessing for imperfections. For most of the 640 analyzed cases shown here, nonclassicality is verified and increases with the number of photons $N$ and modes $K$ between which correlations are probed.

Figure 3

Significance of verified nonclassicality of heralded $N$-photon states for a pump power of $150\mu \mathrm{W}$. An adaptive binning with $1\sigma$ pulse width is compared to static time bins with 100 and 1000 ps. A 5 standard-deviation significance threshold is shown as horizontal line for reference. For this source characterization, we have 128 detection bins, allowing us to determine single-mode (i.e., $M=1$) nonclassicality with moments up to the 128th order.