Deep learning-based variational autoencoder for classification of quantum and classical states of light

TL;DR

The paper tackles robust, rapid classification of non-classical states of light (SPACS, SPATS, and mixtures) from photon-statistics under low-count measurements and detector losses. It introduces a semi-supervised variational autoencoder (VAE) that learns a shared latent representation for reconstruction and classification, trained on diversified datasets with varying mean photon numbers. The approach demonstrates latent-space separation between SPACS and SPATS, resilience to losses, and strong transfer learning capabilities across different bin sizes and data quality, enabling reliable performance with limited data. This method has practical implications for quantum communication, sensing, and computing by enabling efficient state discrimination even with imperfect detectors.

Abstract

Advancements in optical quantum technologies have been enabled by the generation, manipulation, and characterization of light, with identification based on its photon statistics. However, characterizing light and its sources through single photon measurements often requires efficient detectors and longer measurement times to obtain high-quality photon statistics. Here we introduce a deep learning-based variational autoencoder (VAE) method for classifying single photon added coherent state (SPACS), single photon added thermal state (SPACS), mixed states between coherent/SPACS and thermal/SPATS of light. Our semisupervised learning-based VAE efficiently maps the photon statistics features of light to a lower dimension, enabling quasi-instantaneous classification with low average photon counts. The proposed VAE method is robust and maintains classification accuracy in the presence of losses inherent in an experiment, such as finite collection efficiency, non-unity quantum efficiency, finite number of detectors, etc. Additionally, leveraging the transfer learning capabilities of VAE enables successful classification of data of any quality using a single trained model. We envision that such a deep learning methodology will enable better classification of quantum light and light sources even in the presence of poor detection quality.

Figures (7)

• Figure 1: Experimental setup illustrating the division of a single incoming light beam into four equal paths using three beamsplitters. Each path directs light toward a dedicated click detector, registering the number of photons detected for a single instance. This process is repeated for n trials, where n represents the bin size, yielding a dataset of click counts. Analysis of this data produces a probability distribution showcasing the likelihood of detecting a specific number of photons across all n samples.
• Figure 2: Distinct representation of quantum states of light in low-dimensional embedding space. The low-dimensional embedding spaces for photon statistics data, showcase distinct representations of for SPATS $\&$ SPACS across multiple average photon numbers. (a) The t-SNE model's 3-component representation illustrates a dense overlapping of data points clusters. (b) The 3D-latent space of the VAE model reveals two distinct data clusters with good separation.
• Figure 3: Architecture and accuracy of introduced VAE. (a) Schematic representation of the VAE combined with a classifier network. The VAE consists of three main components: an encoder, a decoder, and a classifier. The encoder takes the input data, denoted as $X$ which comprises probabilities $P_n$ of having $n$ photons in observation. Here, $X$ is defined as $[P_0, P_1, P_2, \ldots, P_n]$, where $n$ represents the number of sensors, and generates a latent representation. The decoder takes this latent representation as input and reconstructs the original data, resulting in $\hat{X}$. The classifier utilizes the latent representation $Z$ obtained from the bottleneck layer and predicts the class label for SPATS $\&$ SPACS. (b) Investigation of the impact of bin size on the classification accuracy of the classifier in the VAE model. The classification accuracy is assessed for varying numbers of binsizes, considering a simulated dataset with an average photon number ($\bar{n}$) = 1.3, without any loss effects.
• Figure 4: Quantum loss and dead time effects on classification accuracy. (a) Illustrates the relationship between the observed average photon number ($\bar{n}_{obs}$) and the theoretical average photon number ($\bar{n}_{the}$) for a fixed quantum efficiency of four sensors. In the simulations, an incoming beam was split into two equal beams using a beam splitter, each having an equal probability of containing a photon. Subsequently, another layer of beam splitters divided these two beams into four beams, each with an equal probability of containing a photon. (b) Depicts the accuracy of the classifier in the VAE model as a function of quantum efficiency for a ${\bar{n}_{obs}}$ = 1.9. As the observed average photon number increases with higher quantum efficiency, the classifier achieves improved accuracy.
• Figure 5: Generalization of VAE performance across bin sizes and average observed photon number. The plot shows the relationship between the accuracy of the classifier in the VAE model and the number of binsizes in the simulated experiment. The curves depict the performance at an average theoretical photon number ($\bar{n}_{the}$) of 1.9, where different quantum efficiencies yield varying observed average photon numbers ($\bar{n}_{obs}$). Each curve's color represents the accuracy for different combinations of quantum efficiency and $\bar{n}_{obs}$.