arXiv subjects

Shao-Ming Fei

Publications and source records attributed to Shao-Ming Fei.

At least 19 recordsLinked to original sources

arXiv2026

Estimating the concurrence for quantum states via symmetric measurements

Concurrence is one of the most well-known entanglement measures. We show that, for arbitrary bipartite states, the lower bound of concurrence induced by symmetric measurements is always tighter than the one obtain from realignment. Besides, we derive an extended version of lower bound of concurrence induced by symmetric measurements, which can also be experimentally identified without state tomography, and further present a corresponding lower bound of genuine tripartite entanglement concurrence.

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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 $ρ$, we quantify the coherent extraction process by the coherent ergotropy $\mathcal{E}_c(ρ)$ and the coherent extraction distance $D_c^{\rm ext}(ρ)$ between the active state $σ_ρ$ and the passive state $P_ρ$. This defines the geometric power capacity $Π_c(ρ)=\mathcal{E}_c(ρ)/D_c^{\rm ext}(ρ)$, which measures the coherent ergotropy released unit minimal unitary distance. We prove that, for any driving Hamiltonian satisfying $\|V_t\|\leqν$, the actual coherent discharging power is bounded by $P_c^{\rm ext}(ρ;V_t)\leq νΠ_c(ρ)$, showing that $Π_c(ρ)$ is a capacity under unit driving norm rather than the power of a particular protocol. General bounds on $Π_c(ρ)$ 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 $Π_c(ρ)$ captures a resource-geometric feature of coherent discharging beyond coherent ergotropy or coherence measures alone.

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arXiv2026

Enhancing Quantum Metrology with High-order Fisher Information and Experiments

Fisher information plays a central role in statistics and quantum metrology, providing the basis for the celebrated Cramér-Rao bound. In this work, we introduce a new information measure based on higher-order Fisher information and show that it naturally leads to a generalized uncertainty relation for parameter estimation, which can be regarded as an extension of the Cramér-Rao bound. As an application, we analyze the case of quantum phase estimation with a single qubit and compare our theoretical bounds with the well-known established hierarchical bounds. Finally, we experimentally validate the proposed framework using a photonic platform.

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arXiv2026

Geometric-resource bounds and permutation-averaged success probabilities for the WZP algorithm

Solving linear systems of equations is a fundamental task in machine learning and optimization. In this work, we extend the original WZP algorithm from real symmetric linear systems to complex Hermitian linear systems. We then study the success probability of the modified WZP algorithm from a resource-theoretic perspective. By expressing the postselection success probability as the expectation value of a positive operator, we derive upper and lower bounds of the maximal success probability over separable, incoherent, and real pure states. These bounds further establish connections between the maximal success probability and geometric entanglement, coherence, and imaginarity. We further show that, under permutation averaging, the averaged success probability is an affine function of the coherence fraction, with its dependence determined by the alignment between the success operator and the equal-superposition state. We also investigate the preprocessed WZP algorithm under subgroup-constrained preprocessing. For the two-level family, the optimal success probability is determined by the maximal projection weight onto the orbit of the target projector. Our results provide a unified perspective on the WZP success probability under different operational constraints.

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arXiv2026

Separability criteria and lower bounds of entanglement via realignment

The detection and quantification of quantum entanglement are central problems in quantum information science. Based on the realignment of density matrices and the vectorization of reduced density matrices, we construct a family of enhanced separability criteria for bipartite and multipartite quantum systems. Our criteria recover the previously proposed realignment-based criteria as special cases and detect more entanglement than the earlier ones. Moreover, we derive tighter lower bounds for the concurrence and the convex-roof extended negativity, criteria for detecting the genuine tripartite entanglement, and lower bounds on genuine-multipartite-entanglement concurrence. The advantages of our results are demonstrated with detailed examples.

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arXiv2026

Unitary-accessible coherence-erasure distance: Exact qubit solution and a tight qutrit bound

We introduce the unitary-accessible coherence-erasure distance, which measures the minimum unitary-control cost required to transform a quantum state into an incoherent state without changing its spectrum. The target states are restricted to incoherent states on the same unitary orbit, leading to a geometry different from conventional state-space proximity. We establish inequalities relating orbit-restricted quantum transport, Bures geometry, and the unitary-control distance. These quantities coincide for pure states but can differ for mixed states. For qubits, we derive an exact expression and show that, in the nondegenerate case, the coherence-erasure cost depends on the eigenbasis orientation rather than on the eigenvalues. For nondegenerate qutrits, we reduce the problem to an optimization over the monomial unitary group. We derive the tight universal bound $\arccos[(2\sqrt2-1)/4]$ and construct an explicit eigenbasis that attains it. The resulting distance also determines the minimum coherence-erasure time under bounded unitary driving, giving it a direct operational meaning.

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arXiv2026

Imaginarity as a resource in Shor's algorithm

We investigate the sequential version of Shor's order-finding algorithm from the perspective of the imaginarity of quantum channels. By fixing an eigenbranch of the modular multiplication unitary and a target output path, the process is effectively decomposed into a real diagonal factor and a residual phase channel. We find that for the ideal residual phase channel, the three trace-norm induced imaginarity measures are all equal. On good output paths, a smaller residual imaginarity corresponds to a higher single-block success probability. By combining the branch-wise probabilities, we obtain the exact ideal success probability of the sequential order-finding protocol and derive lower and upper bounds in terms of residual phase-channel imaginarity. We further extend the analysis to noisy residual phase channels, and obtain the lower and upper bounds on the noisy success probability. These results clarify the role of imaginarity of channels in Shor's algorithm and provide a refined perspective on quantum-resource behavior in ideal and noisy sequential quantum algorithms.

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arXiv2026

Characterizing local unitary equivalence of multipartite states by local unitary Bargmann invariants

Local unitary (LU) equivalent states are crucial for understanding the structure of quantum entanglement. We investigate the LU equivalence based on the LU Bargmann invariants (LUBIs). We consider for which states the LUBIs are sufficient to ensure the LU equivalence. We focus on a class of multipartite states with complete local commutativity, called CLC states. We first show that for multipartite CLC states, all the LUBIs are sufficient to ensure the local permutation equivalence, if their single-party marginals are diagonal and non-degenerate. By virtue of the fact that the CLC property remains unchanged under local operations, we verify that the LUBIs are also sufficient to ensure the LU equivalence of multipartite CLC states whose single-party marginals are non-degenerate. Furthermore, when the single-party marginals are degenerate, we propose concrete examples of two-qudit and three-qubit systems, showing that there are states which share all the LUBIs but are not LU equivalent.

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arXiv2026

Quantum speed limits based on quantifiers of quantum-state texture

Quantum speed limits impose intrinsic lower bounds on the shortest time scale for quantum system evolution. As an emerging paradigm in quantum resource theory, quantum-state texture has attracted research interest amid the rapid advancement of quantum theory. Herein, we investigate the interplay between quantum speed limits and quantum-state texture via several canonical quantifiers, including trace distance, state rugosity and Jensen-Shannon divergence. To demonstrate our findings, we analyze the minimum evolution time of physical systems subject to dephasing and dissipative dynamics. For the Jensen-Shannon divergence, we further explore nonunitary dynamics described by completely positive and trace-preserving maps, taking the amplitude damping channel as a typical example. In addition, we explore the tightness of these bounds in the considered dynamical models. Our results reveal that quantum speed limits derived from quantum-state texture capture the fundamental constraints on quantum evolutionary speed, with promising applications in quantum computing, quantum control and quantum metrology.

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arXiv2026

Imaginarity witnessing enhancement via spectral norms of witnesses

Quantum imaginarity is an essential physical resource that underpins key functionalities of modern quantum technologies. We improve imaginarity witnessing via the prior knowledge of imaginarity-witness operators. To this end, we derive a rigorous upper bound on the maximum expectation value of an imaginarity witness operator over the set of all free (real) quantum states, which is given by the spectral norm of the real component of the corresponding witness operator. We demonstrate via detailed examples that this bound substantially improves imaginarity detection. We further classify all imaginarity-witness operators into four distinct families based on this bound. For these four witness classes, we perform a comprehensive analysis of their completeness and finite completeness, the joint detection of shared imaginary quantum states by different witnesses, and the conditions for distinct witnesses to identify identical imaginary states. Our results advance the fundamental understanding of imaginarity detection and offer useful insights for both theoretical studies and experimental implementations of quantum imaginarity.

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arXiv2026

Activate genuine nonlocality from distinguishable sets in tripartite systems

A set of orthogonal quantum states in multipartite systems is of genuine nonlocality if it is locally indistinguishable in every bipartition. If it is locally reducible when the parties are separated, we say that it has genuine nonlocality of type~\uppercase\expandafter{\romannumeral 1}; otherwise, it has genuine nonlocality of type~\uppercase\expandafter{\romannumeral 2}. For a locally distinguishable set without local redundancy, if there exist some orthogonality preserving local measurements such that each outcome leads to a locally indistinguishable set, then we say that it exhibits the activation of nonlocality. We activate type-\uppercase\expandafter{\romannumeral 1} and type-\uppercase\expandafter{\romannumeral 2} genuine nonlocality of orthogonal product state sets in tripartite systems. In particular, we tackle the local irredundancy problem with partial trace operation and $p$-ary numeral systems to significantly simplify the proofs. Our results also address the open question raised by S. Bandyopadhyay \textit{et al.}[\href{https://link.aps.org/doi/10.1103/PhysRevA.104.L050201}{Phys. Rev. A \textbf{104}, L050201 (2021)}]. Furthermore, we observe the activation of hidden genuine nonlocality in multipartite systems, which highlights the applications of nonlocality based on state discrimination in different practical scenarios.

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arXiv2026

Simultaneous estimation of relative phase and coherence in astronomical interferometry

Astronomical interferometry is a cornerstone technique for high-resolution stellar imaging and observational astrophysics, extracting spatial information from the coherence of light collected by separated telescopes. Since the degree of coherence is complex, a genuine imaging task requires the joint recovery of the modulus and the relative phase, instead of independent singleparameter estimations. We investigate the simultaneous estimation of both parameters based on direct interferometry scheme and continuou-svariable quantum teleportation scheme. We find that in simultaneous estimation the direct interferometry scheme consistently yields a lower quantum Cramér-Rao bound, demonstrating its superiority over the continuous-variable quantum teleportation scheme. Furthermore, we establish the conditions under which the classical Cramér-Rao bound for Gaussian measurements saturates the quantum Cramér-Rao bound, identifying heterodyne detection as a near-optimal measurement scheme in the large mean photon number regime. An analysis of transmission loss reveals that the direct interferometry scheme yields superior precision in the short-baseline regime, whereas the continuous-variable quantum teleportation scheme outperforms it at longer baselines.

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arXiv2026

Quantum-state block texture and its quantification

Quantum-state texture (QST) is an emerging quantum resource that has garnered increasing attention amid advances in quantum theory. In this work, we generalize the QST to quantum-state block texture (QSBT). This generalization provides profound operational interpretations for quantifying the advantages of quantum states in quantum information processing. We pioneer an alternative framework for characterizing and quantifying quantum-state block texture, and propose three types of block texture measures. By comparing these QSBT measures, we investigate their distinctions and interrelationships. We demonstrate that the geometric measure serves as an upper bound for the trace distance-based measure. For a specific family of quantum states, we evaluate the values of two trace distance-based measures. Then we sample four sets of data from this family of states, with each set comprising $5\times 10^4, 10^5, 5\times 10^5$ and $10^6 $ samples, respectively, and present the corresponding distributions. Our results reveal that the QSBT measures constructed via different approaches show distinct characteristics, indicating their potential roles in quantifying the block texture of quantum states.

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arXiv2026

Identifying local unitary equivalence based on reduction of quantum states

Local unitary equivalence is central to entanglement quantification and classification. Identifying the local unitary equivalence remains a formidable challenge. We address this problem for a class of quantum states with one highly degenerate eigenvalue and the rest non-degenerate simple eigenvalues that are pivotal to structured resources in quantum resource theory. We introduce a ``reduction" procedure that maps each state to a ``reduced state" by nullifying the highest-multiplicity eigenvalue and prove that the local unitary equivalence of the original states is equivalent to that of their reduced counterparts. For the resulting pure or non-degenerate reduced states, we employ the existing invariants or fixed-point subgroup criteria to establish a complete discrimination framework, although the existing criteria can not directly identify the local unitary equivalence of the original states. We also verify the local unitary equivalence of two families of single-parameterized multipartite mixed states constructed by perturbing absolutely maximally entangled states from distinct combinatorial origins, demonstrating the efficacy and generality of our approach.

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arXiv2026

Monogamy inequalities of entanglement of assistance in $2\otimes 2\otimes d$ systems

The monogamy relations characterize the distribution of quantum correlations among the multipartite quantum systems. We study the monogamy relations of the entanglement of assistance in $2\otimes 2\otimes d$ systems. We present explicitly the relations satisfied by the concurrence, the tangle and the concurrence of assistance, which can be used to derive rigorous monogamy relations. Detailed examples are given to illustrate our results.

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arXiv2026

Entanglement Detection for Two-Qubit and Three-Qubit Pure States via Unitary Transformations and Ancilla State Measurements

Quantum entanglement is the fundamental hallmark of quantum mechanics and a core resource for realizing long-distance quantum communication and scalable linear quantum computing. Accordingly, the precise detection and quantitative quantification of entanglement constitute a foundational and critical problem in quantum information theory. To date, researchers have proposed numerous sufficient conditions for entanglement detection as well as a variety of entanglement measures to characterize the entanglement strength of quantum states; nevertheless, efficient and direct measurement schemes for core entanglement parameters remain underdeveloped. Based on unitary transformations and auxiliary measurements, this paper proposes a set of quantum circuit schemes capable of directly measuring the bipartite concurrence and the tripartite 3-tangle entanglement measure. By introducing auxiliary qubits and constructing specific controlled unitary operations, the proposed scheme maps the analytical expressions of the two entanglement measures onto the measurement probabilities of output states from quantum circuits. It enables efficient and direct quantitative measurement of bipartite and tripartite entanglement without performing full quantum state tomography. This work provides a feasible technical route for the experimental characterization of entanglement properties and lays a groundwork for the practical deployment of multipartite entanglement resources in quantum information processing.

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arXiv2026

Imaginarity as a Resource within Quantum Coherence: Geometric Decomposition and Operational Conversion

We establish a rigorous framework that identifies imaginarity as a fundamental resource inherent in quantum coherence. By means of a geometric decomposition, we partition coherence into distinct imaginarity and residual components, thereby revealing a universal hierarchical relationship among these resources. For bipartite systems, this decomposition provides explicit bounds on the extent to which nonlocal correlations and imaginarity limit local coherence generation. Furthermore, we devise an explicit operational protocol that converts imaginarity into usable coherence, demonstrating the direct interconvertibility of these resources under physically admissible operations. The dynamical evolution under diagonal Hamiltonians is fully characterized, showing that while total coherence is conserved, imaginarity and residual coherence exhibit complementary oscillations. Our results provide a rigorous geometric and operational characterization of imaginarity as a fundamental constituent of quantum coherence, offering concrete insights for resource management in distributed quantum technologies. The geometric framework and theoretical bounds established herein are fully general, while the explicit conversion protocol and dynamical analysis serve as a compelling proof-of-principle demonstration in qubit systems.

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arXiv2026

Quantum Recurrence Plot Algorithm Based on Quantum Principal Component Analysis

Recurrence Plot (RP) is a method employed to analyze the periodicity, chaoticity, and nonlinear characteristics of complex systems. Quantum Principal Component Analysis (QPCA), on the other hand, achieves dimensionality reduction of sample data using density matrices based on quantum circuits. We improve the distance threshold function of the recurrence plot algorithm using a density operator conceptually equivalent to the covariance matrix, integrate it with quantum circuits, and thereby develop a Quantum Recurrence Plot (QRP) algorithm. This algorithm achieves ultra-high efficiency in parallel computing, reduces computational costs, and simultaneously upgrades the traditional grayscale recurrence plot to colored heatmaps, enabling a better revelation of the system's dynamical characteristics.

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