arXiv subjects

Hua Nan

Publications and source records attributed to Hua Nan.

4 recordsLinked to original sources

arXiv2026

Geometric Power Capacity of Coherent Ergotropy in Quantum Batteries

We explore coherent ergotropy extraction in quantum batteries from a resource-geometric point of view. For an initial state $\rho$, we quantify the coherent extraction process by the coherent ergotropy $\mathcal{E}_c(\rho)$ and the coherent extraction distance $D_c^{\rm ext}(\rho)$ between the active state $\sigma_\rho$ and the passive state $P_\rho$. This defines the geometric power capacity $\Pi_c(\rho)=\mathcal{E}_c(\rho)/D_c^{\rm ext}(\rho)$, which measures the coherent ergotropy released unit minimal unitary distance. We prove that, for any driving Hamiltonian satisfying $\|V_t\|\leq\nu$, the actual coherent discharging power is bounded by $P_c^{\rm ext}(\rho;V_t)\leq \nu\Pi_c(\rho)$, showing that $\Pi_c(\rho)$ is a capacity under unit driving norm rather than the power of a particular protocol. General bounds on $\Pi_c(\rho)$ are derived by combining relative entropy bounds on coherent ergotropy with geometric bounds on the coherent extraction distance. We also formulate coherence measure induced bounds and protocol-corrected capacities involving the effective speed of a given Hamiltonian. Qubit and qutrit examples demonstrate that $\Pi_c(\rho)$ captures a resource-geometric feature of coherent discharging beyond coherent ergotropy or coherence measures alone.

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arXiv2026

Pre-Channel Entanglement Shaping Achieves Fundamental Superiority over Post-Distillation: A Geometric Entropy Perspective

Traditional entanglement distillation follows a post-processing paradigm, a noisy quantum state, after full transmission through a noisy channel, is treated as a static resource to be purified via LOCC (local operations and classical communication). This work demonstrates a fundamentally different paradigm,pre-channel entanglement shaping (PES) -- actively engineering the system-environment coupling before or during channel transmission -- achieves a level of purification capability that is physically unattainable by any post-distillation protocol. We prove this separation using the framework of geometric entropy (quantum relative entropy to separable states). In post-distillation, the protocol can only select low-entropy sub-ensembles from a fixed mixed state, leaving the global geometric entropy unchanged or increased. In contrast, PES \textit{suppresses the rate of geometric entropy production} during channel evolution, resulting in a final state whose relative entropy of entanglement strictly exceeds the maximum achievable by post-distillation from the same channel. We provide explicit qubit channel examples, numerical simulations (with complete code in Appendix), and a geometric interpretation on the state manifold. Our result establishes pre-channel entanglement shaping as a distinct operational resource class, with immediate implications for quantum repeaters and entanglement-assisted communication. Very recently, Li \textit{et al.} experimentally demonstrated that preprocessing the entangling channel with optimally tailored local unitaries achieves entanglement fidelities unreachable by any postprocessing, revealing an intrinsic temporal asymmetry in entanglement distillation~\cite{Li2025}.

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arXiv2024

Quantum partial coherence measures constructed from Fisher information

Quantum mechanics gives a new breakthrough to the field of parameter estimation. In the realm of quantum metrology, the precision of parameter estimation is limited by the quantum Fisher information. We introduce the measures of partial coherence based on (quantum) Fisher information by taking into account the post-selective non-unitary parametrization process. These partial coherence measures present a clear operational interpretation by directly linking the coherence to the parameter estimation accuracy. Furthermore, we explore the distinctions between our partial coherence measure and the quantum Fisher information within the context of unitary parametrization. We provide an analytical expression for the partial coherence measure of two-qubit states. We elucidate the operational significance of the partial coherence measures by establishing the connections between the partial coherence measures and quantum state discrimination.

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arXiv2024

Uncertainty relation and the constrained quadratic programming

The uncertainty relation is a fundamental concept in quantum theory, plays a pivotal role in various quantum information processing tasks. In this study, we explore the additive uncertainty relation pertaining to two or more observables, in terms of their variance,by utilizing the generalized Gell-Mann representation in qudit systems. We find that the tight state-independent lower bound of the variance sum can be characterized as a quadratic programming problem with nonlinear constraints in optimization theory. As illustrative examples, we derive analytical solutions for these quadratic programming problems in lower-dimensional systems, which align with the state-independent lower bounds. Additionally, we introduce a numerical algorithm tailored for solving these quadratic programming instances, highlighting its efficiency and accuracy. The advantage of our approach lies in its potential ability to simultaneously achieve the optimal value of the quadratic programming problem with nonlinear constraints but also precisely identify the extremal state where this optimal value is attained. This enables us to establish a tight state-independent lower bound for the sum of variances, and further identify the extremal state at which this lower bound is realized.

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