Determining a noisy quantum channel's classical capacity and entanglement cost generally requires regularization over many channel uses. We remove both regularizations for every qubit-to-qubit channel admitting a pure output. For each such channel, Holevo information, channel entanglement of formation, and parallel ent...
Ziao Tang, Cheng-Kai Zhu, Ge Bai et al.· 1 citation
We determine the preshared entanglement required for spatially separated parties, restricted to local operations and classical communication, to attain globally optimal probabilistic two-copy purification of arbitrary bipartite pure states under depolarizing noise. In every local dimension $d\ge 2$, one shared maximall...
Jia-Yi Zhao, Cheng-Kai Zhu, Xin Wang et al.· 0 citations
Formal verification is becoming increasingly practical for quantum computing, yet the ability of AI agents to construct machine-checkable proofs in this domain remains unmeasured. We introduce Lean-QuantumAlg-Bench and Lean-QIT-Bench, two Lean 4 benchmarks containing 36 and 40 theorem-completion tasks for quantum algor...
Lei Zhang, Yusheng Zhao, Yimeng Cao et al.· 1 citation· ⚡1
Per-matrix singular value decomposition (SVD) truncation is Eckart-Young optimal in the whitened Frobenius norm, but errors from independently compressed matrices compound through the block's nonlinear forward pass. Inspired in part by hierarchical variational optimization in quantum many-body methods, we introduce a t...
Hui-Cheng Zhang, Xi-Yao Feng, Ze-Tong Li et al.· 0 citations
Lean-QIT provides a machine-readable foundation for formal QIT and a compositional knowledge substrate for emerging AI-assisted formalization, automated proof search, and agentic reasoning in quantum information and computation.
