We give a deterministic realization of the finite-dimensional quadratic certificate underlying Collins's mixed-unitary proof of minimum-output-entropy nonadditivity. For every fixed integer $K\ge 2$ and rational $\eta>0$ satisfying $\log K>2(3+\eta)^2$, a deterministic polynomial-time algorithm, for every sufficiently...
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.· 2 citations· ⚡1
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
A three-level chain that widens optimization scope from individual matrices to Transformer blocks to the full model, with improvements only in perplexity and compression fidelity; downstream accuracy remains well below the dense model.
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.
