Quantum self-testing is a device-independent way to certify quantum states and measurements using only the input-output statistics, with minimal assumptions about the quantum devices. Due to the high demand on tolerable noise, however, experimental s
elf-testing was limited to two-photon systems. Here, we demonstrate the first robust self-testing for multi-particle quantum entanglement. We prepare two examples of four-photon graph states, the Greenberger-Horne-Zeilinger (GHZ) states with a fidelity of 0.957(2) and the linear cluster states with a fidelity of 0.945(2). Based on the observed input-output statistics, we certify the genuine four-photon entanglement and further estimate their qualities with respect to realistic noise in a device-independent manner.
Efficient sampling of complex high-dimensional probability densities is a central task in computational science. Machine Learning techniques based on autoregressive neural networks have been recently shown to provide good approximations of probabilit
y distributions of interest in physics. In this work, we propose a systematic way to remove the intrinsic bias associated with these variational approximations, combining it with Markov-chain Monte Carlo in an automatic scheme to efficiently generate cluster updates, which is particularly useful for models for which no efficient cluster update scheme is known. Our approach is based on symmetry-enforced cluster updates building on the neural-network representation of conditional probabilities. We demonstrate that such finite-cluster updates are crucial to circumvent ergodicity problems associated with global neural updates. We test our method for first- and second-order phase transitions in classical spin systems, proving in particular its viability for critical systems, or in the presence of metastable states.
Quantum no-cloning, the impossibility of perfectly cloning an arbitrary unknown quantum state, is one of the most fundamental limitations due to the laws of quantum mechanics, which underpin the physical security of quantum key distribution. Quantum
physics does allow, however, approximate cloning with either imperfect state fidelity and/or probabilistic success. Whereas approximate quantum cloning of single-particle states has been tested previously, experimental cloning of quantum entanglement -- a highly non-classical correlation -- remained unexplored. Based on a multiphoton linear optics platform, we demonstrate quantum cloning of two photon entangled states for the first time. Remarkably our results show that one maximally entangled photon pair can be broadcast into two entangled pairs, both with state fidelities above 50%. Our results are a key step towards cloning of complex quantum systems, and are likely to provide new insights into quantum entanglement.
Flow-based generative models have become an important class of unsupervised learning approaches. In this work, we incorporate the key idea of renormalization group (RG) and sparse prior distribution to design a hierarchical flow-based generative mode
l, called RG-Flow, which can separate information at different scales of images with disentangled representations at each scale. We demonstrate our method mainly on the CelebA dataset and show that the disentangled representations at different scales enable semantic manipulation and style mixing of the images. To visualize the latent representations, we introduce receptive fields for flow-based models and find that the receptive fields learned by RG-Flow are similar to those in convolutional neural networks. In addition, we replace the widely adopted Gaussian prior distribution by a sparse prior distribution to further enhance the disentanglement of representations. From a theoretical perspective, the proposed method has $O(log L)$ complexity for image inpainting compared to previous generative models with $O(L^2)$ complexity.
Bells theorem shows a profound contradiction between local realism and quantum mechanics on the level of statistical predictions. It does not involve directly Einstein-Podolsky-Rosen (EPR) correlations. The paradox of Greenberger-Horne-Zeilinger (GHZ
) disproves directly the concept of EPR elements of reality, based on the EPR correlations, in an all-versus-nothing way. A three-qubit experimental demonstration of the GHZ paradox was achieved nearly twenty years ago, and followed by demonstrations for more qubits. Still, the GHZ contradictions underlying the tests can be reduced to three-qubit one. We show an irreducible four-qubit GHZ paradox, and report its experimental demonstration. The reducibility loophole is closed. The bound of a three-setting per party Bell-GHZ inequality is violated by $7sigma$. The fidelity of the GHZ state was around $81%$, and an entanglement witness reveals a violation of the separability threshold by $19sigma$.
