14 papers
Closed-Form Arbitrary-Gap Rényi Nonadditivity Above Any Positive Order via Direct Products of Free Groups and High-Girth Graphs
Guocheng Zhen, Ranyiliu Chen, Xin Wang
We give a closed-form finite-dimensional construction of quantum channels with real algebraic entries exhibiting arbitrarily large violations of minimum-output Rényi entropy additi…
Collective Quantum State Preparation Is Nonadditive
Lin Zhu, Ranyiliu Chen, Xin Wang +1
Quantum state preparation is a basic primitive of quantum computation and control, but its resource cost is usually analyzed for one target state or under an independent-copy const…
Resource Compatibility in Optimal Quantum Symmetry Testing
Yimeng Cao, Ranyiliu Chen, Chengkai Zhu +1
Can a symmetry be tested optimally without using the quantum resource naturally associated with it? For parallel subgroup-versus-Haar testing, we derive a quantitative representati…
Classical Capacity and Entanglement Cost of the Amplitude Damping Channel
Ziao Tang, Chengkai Zhu, Ge Bai +1
Determining a noisy quantum channel's classical capacity and entanglement cost generally requires regularization over many channel uses. We remove both regularizations for every qu…
Entanglement Cost of Optimal Distributed Quantum State Purification
Jiayi Zhao, Chengkai Zhu, Xin Wang +1
We determine the preshared entanglement required for spatially separated parties, restricted to local operations and classical communication, to attain globally optimal probabilist…
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…
Analytic Qubit Separation between POVMs and Projective Measurements
Lin Zhu, Ranyiliu Chen, Xin Wang +1
Generalized measurements can be implemented projectively after enlarging the Hilbert space, but this dilation changes the available local dimension. We construct a Bell functional…
A Sharp Local-Question Threshold for GHZ-Equatorial Completeness in Four-Player XOR Games
Ziao Tang, Chengkai Zhu, Ge Bai +2
We determine the smallest number of active questions per player at which a four-player binary exclusive-or (XOR) game of commuting-operator value one need not admit a Greenberger--…
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…
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…
Quantifying Unextendibility via Virtual State Extension
Hongshun Yao, Jingu Xie, Xuanqiang Zhao +3
Monogamy of entanglement, which limits how entanglement can be shared among multiple parties, is a fundamental feature underpinning the privacy of quantum communication. In this wo…
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…