Quantum noise constitutes a fundamental obstacle to realizing practical quantum technologies. To address the pivotal challenge of identifying quantum systems least affected by noise, we introduce the purest quantum state identification, which can be used to improve the accuracy of quantum computation and communication. We formulate a rigorous paradigm for identifying the purest quantum state among $K$ unknown $n$-qubit quantum states using total $N$ quantum state copies. For incoherent strategies, we derive the first adaptive algorithm achieving error probability $\exp\left(- \Omega\left(\frac{N H_1}{\log(K) 2^n }\right) \right)$, fundamentally improving quantum property learning through measurement optimization. By developing a coherent measurement protocol with error bound $\exp\left(- \Omega\left(\frac{N H_2}{\log(K) }\right) \right)$, we demonstrate a significant separation from incoherent strategies, formally quantifying the power of quantum memory and coherent measurement. Furthermore, we establish a lower bound by demonstrating that all strategies with fixed two-outcome incoherent POVM must suffer error probability exceeding $ \exp\left( - O\left(\frac{NH_1}{2^n}\right)\right)$. This research advances the characterization of quantum noise through efficient learning frameworks. Our results establish theoretical foundations for noise-adaptive quantum property learning while delivering practical protocols for enhancing the reliability of quantum hardware.

In response to the escalating prevalence of inference attacks on network traffic, traffic shaping emerges as a highly effective strategy to curb the leakage of user privacy information. Although many traffic shaping mechanisms have been proposed, their privacy-preserving performance has mostly been evaluated empirically or by focusing solely on inter-event traffic shaping methods, thereby neglecting intra-event information. In this work, we develop a general framework considering intra-event characteristics for quantifying privacy leakage. The proposed evaluation framework provides quantitative assessments of privacy risks and can guide the design and improvement of traffic-shaping mechanisms. Our theoretical results identify the limitation of existing approaches, namely, the absence of a flexible trade-off between privacy-preserving effectiveness and cost. This trade-off is critical for IoT applications, as devices are highly heterogeneous in terms of resources (i.e., bandwidth) and need to meet service-level objectives (e.g., latency). To achieve this design goal, we model the trade-off problem as multi-armed bandits and propose an online traffic-shaping algorithm named DPShaping. DPShaping has a proven privacy-preserving guarantee and supports flexible trade-offs between effectiveness and communication cost. We compare our approach with three representative algorithms. Experimental results show that compared with state-of-the-art schemes, DPShaping achieves lower attack accuracy (only 16.8%) and reduces bandwidth and delay.

Best Arm Identification (BAI) is a general online pure exploration framework to identify optimal decisions among candidates via sequential interactions. We pioneer the Optimal Arms identification with Knapsacks (OAK) problem, which extends the BAI setting to model the resource consumption. We present a novel OAK algorithm and prove the upper bound of our algorithm by exploring the relationship between selecting optimal actions and the structure of the feasible region. Our analysis introduces a new complexity measure, which builds a bridge between the OAK setting and bandits with knapsacks problem. We establish the instance-dependent lower bound for the OAK problem based on the new complexity measure. Our results show that the proposed algorithm achieves a near-optimal probability bound for the OAK problem. In addition, we demonstrate that our algorithm recovers or improves the state-of-the-art upper bounds for several special cases, including the simple OAK setting and some classical pure exploration problems.