Deep learning of quantum entanglement from incomplete measurements

The quantification of the entanglement present in a physical system is of paramount importance for fundamental research and many cutting-edge applications. Currently, achieving this goal requires either a priori knowledge on the system or very demanding experimental procedures such as full state tomography or collective measurements. Here, we demonstrate that by employing neural networks we can quantify the degree of entanglement without needing to know the full description of the quantum state. Our method allows for direct quantification of the quantum correlations using an incomplete set of local measurements. Despite using undersampled measurements, we achieve an estimation error of up to an order of magnitude lower than the state-of-the-art quantum tomography. Furthermore, we achieve this result employing networks trained using exclusively simulated data. Finally, we derive a method based on a convolutional network input that can accept data from various measurement scenarios and perform, to some extent, independently of the measurement device.Comment: 10 pages, 5 figures, 1 tabl

Quantum process tomography of a high-dimensional quantum communication channel

The characterization of quantum processes, e.g. communication channels, is an essential ingredient for establishing quantum information systems. For quantum key distribution protocols, the amount of overall noise in the channel determines the rate at which secret bits are distributed between authorized partners. In particular, tomographic protocols allow for the full reconstruction, and thus characterization, of the channel. Here, we perform quantum process tomography of high-dimensional quantum communication channels with dimensions ranging from 2 to 5. We can thus explicitly demonstrate the effect of an eavesdropper performing an optimal cloning attack or an intercept-resend attack during a quantum cryptographic protocol. Moreover, our study shows that quantum process tomography enables a more detailed understanding of the channel conditions compared to a coarse-grained measure, such as quantum bit error rates. This full characterization technique allows us to optimize the performance of quantum key distribution under asymmetric experimental conditions, which is particularly useful when considering high-dimensional encoding schemes.Comment: 13 pages, 6 figure

Compressed sensing of twisted photons

The ability to completely characterize the state of a system is an essential element for the emerging quantum technologies. Here, we present a compressed-sensing-inspired method to ascertain any rank-deficient qudit state, which we experimentally encode in photonic orbital angular momentum. We efficiently reconstruct these qudit states from a few scans with an intensified CCD camera. Since it only requires a small number of intensity measurements, our technique provides an easy and accurate way to identify quantum sources, channels, and systems. (C) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Neural-network quantum state tomography

We revisit the application of neural networks to quantum state tomography. We confirm that the positivity constraint can be successfully implemented with trained networks that convert outputs from standard feedforward neural networks to valid descriptions of quantum states. Any standard neural-network architecture can be adapted with our method. Our results open possibilities to use state-of-the-art deep-learning methods for quantum state reconstruction under various types of noise