9 papers
Deterministic Minimum-Output-Entropy Nonadditivity via Haagerup's Inequality and Near-Free Permutation Representations
Guocheng Zhen, Chengkai Zhu, Ranyiliu Chen +1
We give a deterministic realization of the finite-dimensional quadratic certificate underlying Collins's mixed-unitary proof of minimum-output-entropy nonadditivity. For every fixe…
Benchmarking Agents for Proving Theorems in Quantum Algorithms and Quantum Information
Lei Zhang, Yusheng Zhao, Yimeng Cao +10
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.…
Lean-QIT: Towards a Formal Infrastructure for Quantum Information Theory
Chengkai Zhu, Ziao Tang, Guocheng Zhen +6
Quantum information theory (QIT) characterizes the capabilities and fundamental limits of quantum information processing, underpinning quantum communication, computation, and error…
Invariant Measures and Weak-Magic-Injection Asymptotics in Random Monitored Quantum Circuits
Guocheng Zhen, Xuanrong Yang, Chengkai Zhu +2
Monitored quantum circuits combine scrambling with measurement-conditioned state updates, while non-Clifford perturbations inject magic into otherwise stabilizer-compatible dynamic…
Distilling Qubit Unitary Operations: A No-Go Theorem and Minimal Realization
Jiayi Zhao, Yu-Ao Chen, Guocheng Zhen +3
Quantum gates executed on physical hardware are inevitably degraded by environmental noise. While state purification effectively distills static quantum resources, the dynamic exec…
Simulation of Adjoints and Petz Recovery Maps for Unknown Quantum Channels
Chengkai Zhu, Ziao Tang, Guocheng Zhen +3
Transformations of quantum channels, such as the transpose, complex conjugate, and adjoint, are fundamental to quantum information theory. Given access to an unknown channel, a cen…
Structure, Optimality, and Symmetry in Shadow Unitary Inversion
Guocheng Zhen, Yu-Ao Chen, Mingrui Jing +3
Reversing unitary operations is a key task in quantum computing and quantum control. In this work, we introduce and develop the framework of shadow unitary inversion, a relaxed var…
Dual Reinforcement Learning Synergy in Resource Allocation: Emergence of Self-Organized Momentum Strategy
Zhen-Na Zhang, Guo-Zhong Zhen, Li Chen +4
In natural ecosystems and human societies, self-organized resource allocation and policy synergy are ubiquitous and significant. This work focuses on the synergy between Dual Reinf…
Spectral measure of large random Helson matrices
Yanqi Qiu, Guocheng Zhen
We study the limiting spectral measure of large random Helson matrices and large random matrices of certain patterned structures. Given a real random variable $X \in L^{2+ \varepsi…