Gentle measurements of quantum states do not entirely collapse the initial state. Instead, they provide a post-measurement state at a prescribed trace distance $α$ from the initial state together with a random variable used for quantum learning of the initial state. We introduce here the class of $α-$locally-gentle measurements ($α-$LGM) on a finite dimensional quantum system which are product measurements on product states and prove a strong quantum Data-Processing Inequality (qDPI) on this class using an improved relation between gentleness and quantum differential privacy. We further show a gentle quantum Neyman-Pearson lemma which implies that our qDPI is asymptotically optimal (for small $α$). This inequality is employed to show that the necessary number of quantum states for prescribed accuracy $ε$ is of order $1/(ε^2 α^2)$ for both quantum tomography and quantum state certification. Finally, we propose an $α-$LGM called quantum Label Switch that attains these bounds. It is a general implementable method to turn any two-outcome measurement into an $α-$LGM.

Learning Gentle Grasping Using Vision, Sound, and T ouch Ken Nakahara 1 and Roberto Calandra 1, 2 Abstract -- In our daily life, we often encounter objects that are fragile and can be damaged by excessive grasping force, such as fruits. For these objects, it is paramount to grasp gently - not using the maximum amount of force possible, but rather the minimum amount of force necessary. This paper proposes using visual, tactile, and auditory signals to learn to grasp and regrasp objects stably and gently. Specifically, we use audio signals as an indicator of gentleness during the grasping, and then train end-to-end an action-conditional model from raw visuo-tactile inputs that predicts both the stability and the gentleness of future grasping candidates, thus allowing the selection and execution of the most promising action. Experimental results on a multi-fingered hand over 1,500 grasping trials demonstrated that our model is useful for gentle grasping by validating the predictive performance (3.27% higher accuracy than the vision-only variant) and providing interpretations of their behavior . Finally, real-world experiments confirmed that the grasping performance with the trained multi-modal model outperformed other baselines (17% higher rate for stable and gentle grasps than vision-only). Our approach requires neither tactile sensor calibration nor analytical force modeling, drastically reducing the engineering effort to grasp fragile objects. I. INTRODUCTION Grasping has been developed in modern robotics, but grasping fragile objects, such as fruits, with an appropriate amount of force remains challenging--a task we refer to as "gentle grasping." Excessive grasping force can damage them, while insufficient force causes slippage or drop. When such delicate robotic grasping is required, it is essential to consider the dynamic interaction with a target object.