Geometry of quantum correlations in space-time

The traditional formalism of non-relativistic quantum theory allows the state of a quantum system to extend across space, but only restricts it to a single instant in time, leading to distinction between theoretical treatments of spatial and temporal quantum correlations. Here we unify the geometrical description of two-point quantum correlations in space-time. Our study presents the geometry of correlations between two sequential Pauli measurements on a single qubit undergoing an arbitrary quantum channel evolution together with two-qubit spatial correlations under a common framework. We establish a symmetric structure between quantum correlations in space and time. This symmetry is broken in the presence of non-unital channels, which further reveals a set of temporal correlations that are indistinguishable from correlations found in bipartite entangled states.Comment: 5 pages, 3 figure

Causal limit on quantum communication

The capacity of a channel is known to be equivalent to the highest rate at which it can generate entanglement. Analogous to entanglement, the notion of a causality measure characterises the temporal aspect of quantum correlations. Despite holding an equally fundamental role in physics, temporal quantum correlations have yet to find their operational significance in quantum communication. Here we uncover a connection between quantum causality and channel capacity. We show the amount of temporal correlations between two ends of the noisy quantum channel, as quantified by a causality measure, implies a general upper bound on its channel capacity. The expression of this new bound is simpler to evaluate than most previously known bounds. We demonstrate the utility of this bound by applying it to a class of shifted depolarizing channels, which results in improvement over previously calculated bounds for this class of channels.Comment: 9 pages, 3 figure

Certifying Out-of-Domain Generalization for Blackbox Functions

Certifying the robustness of model performance under bounded data distribution drifts has recently attracted intensive interest under the umbrella of distributional robustness. However, existing techniques either make strong assumptions on the model class and loss functions that can be certified, such as smoothness expressed via Lipschitz continuity of gradients, or require to solve complex optimization problems. As a result, the wider application of these techniques is currently limited by its scalability and flexibility -- these techniques often do not scale to large-scale datasets with modern deep neural networks or cannot handle loss functions which may be non-smooth such as the 0-1 loss. In this paper, we focus on the problem of certifying distributional robustness for blackbox models and bounded loss functions, and propose a novel certification framework based on the Hellinger distance. Our certification technique scales to ImageNet-scale datasets, complex models, and a diverse set of loss functions. We then focus on one specific application enabled by such scalability and flexibility, i.e., certifying out-of-domain generalization for large neural networks and loss functions such as accuracy and AUC. We experimentally validate our certification method on a number of datasets, ranging from ImageNet, where we provide the first non-vacuous certified out-of-domain generalization, to smaller classification tasks where we are able to compare with the state-of-the-art and show that our method performs considerably better.Comment: 39th International Conference on Machine Learning (ICML) 202