arXiv subjects

Shao-Ming Fei

Publications and source records attributed to Shao-Ming Fei.

At least 55 records · Page 3Linked to original sources

arXiv2025

A new entanglement measure based on the total concurrence

Quantum entanglement is a crucial resource in quantum information processing, advancing quantum technologies. The greater the uncertainty in subsystems' pure states, the stronger the quantum entanglement between them. From the dual form of $q$-concurrence ($q\geq 2$) we introduce the total concurrence. A bona fide measure of quantum entanglement is introduced, the $\mathcal{C}^{t}_q$-concurrence ($q \geq 2$), which is based on the total concurrence. Analytical lower bounds for the $\mathcal{C}^{t}_q$-concurrence are derived. In addition, an analytical expression is derived for the $\mathcal{C}^{t}_q$-concurrence in the cases of isotropic and Werner states. Furthermore, the monogamy relations that the $\mathcal{C}^{t}_q$-concurrence satisfies for qubit systems are examined. Additionally, based on the parameterized $α$-concurrence and its complementary dual, the $\mathcal{C}^{t}_α$-concurrence $(0\leqα\leq\frac{1}{2})$ is also proposed.

quant-ph↗

arXiv2025

Trade-off relations and enhancement protocol of quantum battery capacities in multipartite systems

First, we investigate the trade-off relations of quantum battery capacities in two-qubit system. We find that the sum of subsystem battery capacity is governed by the total system capacity, with this trade-off relation persisting for a class of Hamiltonians, including Ising, XX, XXZ and XXX models. Then building on this relation, we define residual battery capacity for general quantum states and establish coherent/incoherent components of subsystem battery capacity. Furthermore, we introduce the protocol to guide the selection of appropriate incoherent unitary operations for enhancing subsystem battery capacity in specific scenarios, along with a sufficient condition for achieving subsystem capacity gain through unitary operation. Numerical examples validate the feasibility of the incoherent operation protocol. Additionally, for the three-qubit system, we also established a set of theories and results parallel to those for two-qubit case. Finally, we determine the minimum time required to enhance subsystem battery capacity via a single incoherent operation in our protocol. Our findings contribute to the development of quantum battery theory and quantum energy storage systems.

quant-ph↗

arXiv2025

Quantum Separability Criteria Based on Symmetric Measurements

We propose experimentally feasible separability criteria for bipartite systems based on local symmetric measurements. Through detailed examples, we demonstrate that our criteria can detect entanglement more effectively compared to existing counterparts. Furthermore,we demonstrate the potential for our results to be generalized to general multipartite systems.

quant-ph↗

arXiv2025

Generalized product-form monogamy relations in multi-qubit systems

Monogamy of entanglement essentially characterizes the entanglement distributions among the subsystems. Generally it is given by summation-form monogamy inequalities. In this paper, we present the product-form monogamy inequalities satisfied by the $ν$-th ($ν\geq2$) power of the concurrence. We show that they are tighter than the existing ones by detailed example. We then establish tighter product-form monogamy inequalities based on the negativity. We show that they are valid even for high dimensional states to which the well-known CKW inequality is violated.

quant-ph↗

arXiv2025

A note on Schmidt-number witnesses based on symmetric measurements

The Schmidt number is an important kind of characterization of quantum entanglement. Quantum states with higher Schmidt numbers demonstrate significant advantages in various quantum information processing tasks. By deriving a class of k-positive linear maps based on symmetric measurements, we present new Schmidt-number witnesses of class (k + 1). By detailed example, we show that our Schmidt number witnesses identify better the Schmidt number of quantum states in high-dimensional systems. Furthermore, we note that the Fedorov ratio, which coincides with the Schmidt number for pure Gaussian states and provides a close approximation in non-Gaussian cases such as spontaneous parametric down-conversion, serves as an experimentally accessible tool for validating the proposed (k +1)-class Schmidt-number witnesses.

quant-ph↗

arXiv2025

Quantifying nonclassical correlations relative to local channels

Nonclassical correlations are significant physical resources with extensive applications in quantum information processing. We introduce the modified Wigner-Yanase-Dyson skew information of a quantum state relative to a quantum channel, and a quantitative measure of quantum correlations. Their basic properties are explored in detail. Through a specific example, we also compare our correlations measure with the existing one. Moreover, the correlations relative to various channels including the von Neumann measurements, the unitary channels and the twirling channels are analyzed.

quant-ph↗

arXiv2025

Static and dynamic coherence fraction in the Bernstein-Vazirani algorithm

Quantum entanglement and coherence are crucial resources in quantum information theory. In some scenarios, however, it is not necessary to directly estimate entanglement or coherence measures to quantify the capabilities of a state in quantum information processing. Instead, fully entangled fraction and coherence fraction are two alternatives for entanglement and coherence in specific quantum tasks. Here, we establish a link between the coherence fraction and the Bernstein-Vazirani algorithm, which has several potential applications including cryptography and database search. We show that the success probability of the generalized Bernstein-Vazirani algorithm depends only on the coherence fraction of the initial state rather than its entanglement or coherence. Moreover, we discuss the coherence fraction dynamics and establish a relation between the operator's coherence fraction and the algorithm's success probability. Our findings highlight how quantum coherence fraction influences the efficiency of quantum algorithms.

quant-ph↗

arXiv2025

Tightening the entropic uncertainty relations with quantum memory in a multipartite scenario

The quantum uncertainty principle stands as a cornerstone and a distinctive feature of quantum mechanics, setting it apart from classical mechanics. We introduce a tripartite quantum-memory-assisted entropic uncertainty relation, and extend the relation to encompass multiple measurements conducted within multipartite systems. The related lower bounds are shown to be tighter than those formulated by Zhang et al. [Phys. Rev. A 108, 012211 (2023)]. Additionally, we present generalized quantum-memory-assisted entropic uncertainty relations (QMA-EURs) tailored for arbitrary positive-operator-valued measures (POVMs). Finally, we demonstrate the applications of our results to both the relative entropy of unilateral coherence and the quantum key distribution protocols.

quant-ph↗

arXiv2025

Decoding Quantum Search Advantage: The Critical Role of State Properties in Random Walks

Quantum algorithms have demonstrated provable speedups over classical counterparts, yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge. In this work, we decode the quantum search advantage by investigating the critical role of quantum state properties in random-walk-based algorithms. We propose three distinct variants of quantum random-walk search algorithms and derive exact analytical expressions for their success probabilities. These probabilities are fundamentally determined by specific initial state properties: the coherence fraction governs the first algorithm's performance, while entanglement and coherence dominate the outcomes of the second and third algorithms, respectively. We show that increased coherence fraction enhances success probability, but greater entanglement and coherence reduce it in the latter two cases. These findings reveal fundamental insights into harnessing quantum properties for advantage and guide algorithm design. Our searches achieve Grover-like speedups and show significant potential for quantum-enhanced machine learning.

quant-ph↗

arXiv2025

Coherence Fraction in Grover Search Algorithm

The question of which resources drive the advantages in quantum algorithms has long been a fundamental challenge. While entanglement and coherence are critical to many quantum algorithms, our results indicate that they do not fully explain the quantum advantage achieved by the Grover search algorithm. By introducing a generalized Grover search algorithm, we demonstrate that the success probability depends not only on the querying number of oracles but also on the coherence fraction, which quantifies the fidelity between an arbitrary initial quantum state and the equal superposition state. Additionally, we explore the role of the coherence fraction in the quantum minimization algorithm, which offers a framework for solving complex problems in quantum machine learning. These findings offer insights into the origins of quantum advantage and open pathways for the development of new quantum algorithms.

quant-ph↗

arXiv2025

Wave-Particle-Mixedness Relationships Based on lp-norm Coherence

We investigate the relationships among the wave property, particle property and mixedness of quantum states based on the lp-norm coherence. By conforming that the lp-norm coherence is an appropriate measure of wave property and introducing a measure of particle property based on the differences between the maximal l2-norm coherence and the general l2-norm coherence, we present tradeoff relationships among the wave, particle and mixedness of quantum states. For 1<= p <2, we establish two kinds of tradeoffs of the wave, particle and mixedness with respect to the upper and lower bounds of the lp-norm coherence given by the l2-norm coherence. These trade relations give rise to compressive understanding of the intrinsic connections among the wave, particle and mixedness of quantum states, and cover some existing results as particular ones.

quant-ph↗

arXiv2025

Quantum-imaginarity-based quantum speed limit

The quantum speed limit sets a fundamental restriction on the evolution time of quantum systems. We explore the relationship between quantum imaginarity and the quantum speed limit by utilizing measures such as relative entropy, trace distance, and geometric imaginarity. These speed limits define the fundamental constraints on the minimum time necessary for quantum systems to evolve under various dynamical processes. As applications the dephasing dynamics and dissipative dynamics are analyzed in detail. The quantum speed limit in stochastic-approximate transformations is also investigated. Our quantum speed limits provide lower bounds on how fast a physical system evolves to attain or lose certain imaginarity, with potential applications in efficient quantum computation designs, quantum control and quantum sensing.

quant-ph↗

arXiv2025

Quantum Circuit Implementation of Two Matrix Product Operations and Elementary Column Transformations

This paper focuses on quantum algorithms for three key matrix operations: Hadamard (Schur) product, Kronecker (tensor) product, and elementary column transformations each. By designing specific unitary transformations and auxiliary quantum measurement, efficient quantum schemes with circuit diagrams are proposed. Their computational depths are: O(1) for Kronecker product; O(max(m,n)) for Hadamard product (linked to matrix dimensions); and O(m) for elementary column transformations of (2^n X 2^m) matrices (dependent only on column count).Notably, compared to traditional column transformation via matrix transposition and row transformations, this scheme reduces computation steps and quantum gate usage, lowering quantum computing energy costs.

quant-ph↗

arXiv2025

Quantumness near the Schwarzschild black hole based on W-state

We investigate certain quantumness in the vicinity of the Schwarzschild black hole by utilizing the W state. We explore the influence of the Hawking effect on the l_1-norm of quantum coherence, the first-order coherence (FOC), the concurrence-fill (CF) and the global concurrence (GC) in Schwarzschild black hole, for systems with one, two and three physically accessible modes. We conclude that the Hawking effect of the black hole not only disrupts but also enhance the quantum entanglement, while destroying the quantum coherence for systems with three physically accessible modes. For systems with one or two physically accessible modes, the Hawking effect exerts a positive influence on quantum coherence and quantum entanglement. Moreover, we study the influence of both the Hawking effect and environmental noise (AD channels) on l_1-norm of quantum coherence, FOC, CF and GC. It is demonstrated that for systems with three physically accessible modes, the Hawking effect of the black hole disrupts quantum coherence but exerts a positive influence on quantum entanglement under the AD channels.

quant-ph↗

arXiv2025

Classical representation of local Clifford operators

It is known that every (single-qudit) Clifford operator maps the full set of generalized Pauli matrices (GPMs) to itself under unitary conjugation, which is an important quantum operation and plays a crucial role in quantum computation and information. However, in many quantum information processing tasks, it is required that a specific set of GPMs be mapped to another such set under conjugation, instead of the entire set. We formalize this by introducing local Clifford operator, which maps a given $n$-GPM set to another such set under unitary conjugation. We establish necessary and sufficient conditions for such an operator to transform a pair of GPMs, showing that these local Clifford operators admit a classical matrix representation, analogous to the classical (or symplectic) representation of standard (single-qudit) Clifford operators. Furthermore, we demonstrate that any local Clifford operator acting on an $n$-GPM ($n\geq 2$) set can be decomposed into a product of standard Clifford operators and a local Clifford operator acting on a pair of GPMs. This decomposition provides a complete classical characterization of unitary conjugation mappings between $n$-GPM sets. As a key application, we use this framework to address the local unitary equivalence (LU-equivalence) of sets of generalized Bell states (GBSs). We prove that the 31 equivalence classes of $4$-GBS sets in bipartite system $\mathbb{C}^{6}\otimes \mathbb{C}^{6}$ previously identified via Clifford operators are indeed distinct under LU-equivalence, confirming that this classification is complete.

quant-ph↗

arXiv2025

On Sufficient and Necessary Criteria of Multipartite Quantum Entanglement

Based on the generalized Bloch representation, we study the separability and entanglement of arbitrary dimensional multipartite quantum states. Some sufficient and some necessary criteria are presented. For certain states, these criteria together are both sufficient and necessary. Detailed examples show that our criteria are better than some existing ones in identifying separability. Based on these criteria, the largest separable ball around the maximally mixed state for arbitrary multi-qubit systems is found, and it is proved that its radius defined via the $l_1$-norm of the Bloch vector is the constant 1. Furthermore, the criteria in this paper can be implemented experimentally.

quant-ph↗

arXiv2025

Real randomized measurements for analyzing properties of quantum states

Randomized measurements are useful for analyzing quantum systems especially when quantum control is not fully perfect. However, their practical realization typically requires multiple rotations in the complex space due to the adoption of random unitaries. Here, we introduce two simplified randomized measurements that limit rotations in a subspace of the complex space. The first is \textit{real randomized measurements} (RRMs) with orthogonal evolution and real local observables. The second is \textit{partial real randomized measurements} (PRRMs) with orthogonal evolution and imaginary local observables. We show that these measurement protocols exhibit different abilities in capturing correlations of bipartite systems. We explore various applications of RRMs and PRRMs in different quantum information tasks such as characterizing high-dimensional entanglement, quantum imaginarity, and predicting properties of quantum states with classical shadow.

quant-ph↗

arXiv2025

Quantum Algorithms for Matrix Operations Based on Unitary Transformations and Ancillary State Measurements

MQuantum algorithms of matrix operations are of great significance in many fields in science and technology. In this paper, by leveraging multi-qubit Toffoli gates and basic single-qubit operations, the quantum algorithms of matrix operations of row addition, row swapping, trace calculation and transpose are obtained. In particular, the complexities of these quantum algorithms are presented, too.

quant-ph↗