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Theoretical Limits of Language Model Alignment $f$-Divergence Regularized RLHF: Two Tales of Sampling and Unified Analyses A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models When Can Voting Help, Hurt, or Change Course? Exact Structure of Binary Test-Time Aggregation When Semantic Communication Meets Queueing: Cross-Layer Latency and Task Fidelity Optimization Convexity in Disguise: A Theoretical Framework for Nonconvex Low-Rank Matrix Estimation Conditional Diffusion Under Linear Constraints: Langevin Mixing and Information-Theoretic Guarantees Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Expert Routing for Communication-Efficient MoE via Finite Expert Banks Contextual Memory-Enhanced Source Coding for Low-SNR Communications Realizable Bayes-Consistency for General Metric Losses Leveraging Code Automorphisms for Improved Syndrome-Based Neural Decoding A Hierarchical Sampling Framework for bounding the Generalization Error of Federated Learning Dueling DDQN-Based Adaptive Multi-Objective Handover Optimization for LEO Satellite Networks The Causal Description Gap: Information-Theoretic Separations Across Pearl's Hierarchy Optimization of CV-QKD Under Practical Constraints Benchmarking Wireless Representations: High-Dimensional vs. Compressed Embeddings for Efficiency and Robustness Real-Time Text Transmission via LLM-Based Entropy Coding over Fixed-Rate Channels SwiftChannel: Algorithm-Hardware Co-Design for Deep Learning-Based 5G Channel Estimation Evolving Token Communication with Parametric Memory Network Remote Action Generation: Remote Control with Minimal Communication The (Marginal) Value of a Search Ad: An Online Causal Framework for Repeated Second-price Auctions Stabilizing Private LASSO under Heterogeneous Covariates via Anisotropic Objective Perturbation Linear-Readout Floors and Threshold Recovery in Computation in Superposition Soft Graph Diffusion Transformer for MIMO Detection Hierarchical Federated Learning for Networked AI: From Communication Saving to Architecture-Aware Design Exponential families from a single KL identity MIFair: A Mutual-Information Framework for Intersectionality and Multiclass Fairness Diffusion-OAMP for Joint Image Compression and Wireless Transmission Decoupled Descent: Exact Test Error Tracking Via Approximate Message Passing
Quantum Channel Certification with Incoherent Strategies
Omar Fawzi, Nicolas Flammarion, Aurélien Garivier, Aadil Oufkir · 2023-03-02 · via cs.IT updates on arXiv.org

In the problem of quantum channel certification, we have black box access to a quantum process and would like to decide if this process matches some predefined specification or is $\varepsilon$-far from this specification. The objective is to achieve this task while minimizing the number of times the black box is used. Here, we focus on optimal incoherent strategies for two relevant extreme cases of channel certification. The first one is when the predefined specification is a unitary channel, e.g., a gate in a quantum circuit. In this case, we show that testing whether the black box is described by a fixed unitary operator in dimension $d$ or $\varepsilon$-far from it in the trace norm requires $Θ(d/\varepsilon^2)$ uses of the black box. The second setting we consider is when the predefined specification is a completely depolarizing channel with input dimension $d_{\text{in}}$ and output dimension $d_{\text{out}}$. In this case, we prove that, in the non-adaptive setting, $\tildeΘ(d_{\text{in}}^2d_{\text{out}}^{1.5}/\varepsilon^2)$ uses of the channel are necessary and sufficient to verify whether it is equal to the depolarizing channel or $\varepsilon$-far from it in the diamond norm. Finally, we prove a lower bound of $Ω(d_{\text{in}}^2d_{\text{out}}/\varepsilon^2)$ for this problem in the adaptive setting. Note that the special case $d_{\text{in}} = 1$ corresponds to the well-studied quantum state certification problem.