Information theory provides a framework for answering fundamental questions about the optimal performance of many important quantum communication and computational tasks. In many cases, the optimal rates of these tasks can be expressed in terms of regularized formulas that consist of linear combinations of von Neumann entropies optimized over state extensions. However, evaluation of regularized formulas is often intractable, since it involves computing a formula’s value in the limit of infinitely many copies of a state. To find optimized linear entropic functions of quantum states whose regularized versions are tractable to compute, we search for examples which are additive. We use the method of cross2017uniform, which considers bipartite formulas, to identify convex polyhedral cones of tripartite correlation measures which satisfy a stronger a form of additivity called uniform additivity. We rely only on strong subadditivity of the von Neumann entropy and use these cones to prove that three previously established tripartite optimized correlation measures are additive.

Warehouse robotic systems equipped with vacuum grippers must reliably grasp a diverse range of objects from densely packed shelves. However, these environments present significant challenges, including occlusions, diverse object orientations, stacked and obstructed items, and surfaces that are difficult to suction. We introduce TetraGrip, a novel vacuum-based grasping strategy featuring four suction cups mounted on linear actuators. Each actuator is equipped with an optical time-of-flight (ToF) proximity sensor, enabling reactive grasping.We evaluate TetraGrip in a warehouse-style setting, demonstrating its ability to manipulate objects in stacked and obstructed configurations. Our results show that our RL-based policy improves picking success in stacked-object scenarios by 22.9% compared to a single-suction gripper. Additionally, we demonstrate that TetraGrip can successfully grasp objects in scenarios where a single-suction gripper fails due to physical limitations, specifically in two cases: (1) picking an object occluded by another object and (2) retrieving an object in a complex scenario. These findings highlight the advantages of multi-actuated, suction-based grasping in unstructured warehouse environments. The project website is available at: https://tetragrip.github.io/.

How can we characterize different types of correlation between quantum systems? Since correlations cannot be generated locally, we take any real function of a multipartite state which cannot increase under local operations to measure a correlation. Correlation measures that can be expressed as an optimization of a linear combination of entropies are particularly useful, since they can often be interpreted operationally. We systematically study such optimized linear entropic functions, and by enforcing monotonicity under local processing we identify four cones of correlation measures for bipartite quantum states. This yields two new optimized measures of bipartite quantum correlation that are particularly simple, which have the additional property of being additive.