arXiv subjects

Zhong-Xi Shen

Publications and source records attributed to Zhong-Xi Shen.

14 recordsLinked 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.

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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.

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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.

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arXiv2025

Mutually unbiased measurements-induced lower bounds of concurrence

We propose a family of lower bounds for concurrence in quantum systems using mutually unbiased measurements, which prove more effective in entanglement estimation compared to existing methods. Through analytical and numerical examples, we demonstrate that these bounds outperform conventional approaches, particularly in capturing finer entanglement features. Additionally, we introduce separability criterions based on MUMs for arbitrary $d$-dimensional bipartite systems, the research results show that our criterion has more advantages than the existing criteria.

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arXiv2025

Parameterized bipartite entanglement measures and entanglement constraints

In this paper, we propose a novel class of parameterized entanglement measures which are named as $G_ω$-concurrence ($G_ω$C) ($0<ω\leq1$), and demonstrate comprehensively that they satisfy all the necessary axiomatic conditions required for an entanglement measure. Furthermore, we derive an analytical formula relating $G_ω$C to concurrence for the range of $0.85798\leqω\leq1$ within two-qubit systems. Additionally, we prove a new polygamy relation of multiqubit quantum entanglement in terms of $G_ω$-concurrence of assistance ($G_ω$CoA). However, it fails to obey the monogamy relation, but we have demonstrated that the squared $G_ω$-concurrence (S$G_ω$C) does obeys a general monogamy relation in an arbitrary $N$-qubit mixed state. Based on the monogamy properties of S$G_ω$C, we can construct the corresponding multipartite entanglement indicators, which can detect all genuine multiqubit entangled states even in the case of $N$-tangle vanishes. In addition, for multipartite higher-dimensional systems, it is illustrated that S$G_ω$C still has the applicability of the monogamy relation.

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arXiv2025

Monogamy and polygamy for multi-qudit generalized $W$-class states based on concurrence of assistance and Tsallis-$q$ entanglement of assistance

By analyzing the reduced density matrices derived from a generalized $W$-class state under any partition, we present new analytical monogamy inequalities satisfied by the $α$-th ($α\geqγ,~γ\geq2$) power and $β$-th ($0\leqβ\leq\fracγ{2},~γ\geq2$) power of the concurrence of assistance for multi-qudit generalized $W$-class states, which are demonstrated to be tighter than previous studies through detailed examples. Furthermore, using the Tsallis-$q$ entanglement of assistance, we also establish new monogamy and polygamy relations, which are shown to be valid even for multipartite higher-dimensional states that the CKW inequality is violated.

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arXiv2024

Separability criteria based on realignment

The detection of entanglement in a bipartite state is a crucial issue in quantum information science. Based on realignment of density matrices and the vectorization of the reduced density matrices, we introduce a new set of separability criteria. The proposed separability criteria can detect more entanglement than the previous separability criteria. Moreover, we provide new criteria for detecting the genuine tripartite entanglement and lower bounds for the concurrence and convex-roof extended negativity. The advantages of results are demonstrated through detailed examples.

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arXiv2024

Unified monogamy relations for the generalized $W$-class states beyond qubits

The monogamy of entanglement stands as an indispensable feature within multipartite quantum systems. We study monogamy relations with respect to any partitions for the generalized $W$-class (GW) states based on the unified-($q,s$) entanglement (UE). We provide the monogamy relation based on the squared UE for a reduced density matrix of a qudit GW state, as well as tighter monogamy relations based on the $α$th ($α\geq2$) power of UE. Furthermore, for an $n$-qudit system $ABC_1...C_{n-2}$, generalized monogamy relation and upper bound satisfied by the $β$th ($0\leqβ\leq1$) power of UE for the GW states under the partition $AB$ and $C_1...C_{n-2}$ are established. In particular, two partition-dependent residual entanglements for the GW states are analyzed in detail.

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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

Tighter superadditivity relations for $l_{1}$-norm coherence measure

Quantum coherence serves as a crucial physical resource, with its quantification emerging as a focal point in contemporary research. Superadditivity constitutes one of the most fundamental attributes in characterizing the coherence distribution in multipartite quantum systems. In this paper, we provide a way to derive tighter superadditivity inequalities of $l_1$-norm coherence measure for arbitrary multiqubit states. We present a category of superadditivity relations related to the $α$-th ($α\geqslant 2$) power of $l_{1}$-norm coherence $C_{l_{1}}$ under certain conditions. Our results are better than existing ones and are illustrated in detail with examples.

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arXiv2024

General monogamy relations of the $S^{t}$ and $T^{t}_q$-entropy entanglement measures based on dual entropy

Monogamy of entanglement is the fundamental property of quantum systems. By using two new entanglement measures based on dual entropy, the $S^{t}$-entropy entanglement and $T^{t}_q$-entropy entanglement measures, we present the general monogamy relations in multi-qubit quantum systems. We show that these newly derived monogamy inequalities are tighter than the existing ones. Based on these general monogamy relations, we construct the set of multipartite entanglement indicators for $N$-qubit states, which are shown to work well even for the cases that the usual concurrence-based indicators do not work. Detailed examples are presented to illustrate our results.

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arXiv2024

Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA

The monogamy property of entanglement is an intriguing feature of multipartite quantum entanglement. Most entanglement measures satisfying the monogamy inequality are turned out to be convex. Whether nonconvex entanglement measures obeys the monogamy inequalities remains less known at present. As a well known measure of entanglement, the logarithmic negativity is not convex. We elucidate the constraints of multi-qubit entanglement based on the logarithmic convex-roof extended negativity (LCREN) and the logarithmic convex-roof extended negativity of assistance (LCRENoA). Using the Hamming weight derived from the binary vector associated with the distribution of subsystems, we establish monogamy inequalities for multi-qubit entanglement in terms of the $α$th-power ($α\geq 4\ln2$) of LCREN, and polygamy inequalities utilizing the $α$th-power ($0 \leq α\leq 2$) of LCRENoA. We demonstrate that these inequalities give rise to tighter constraints than the existing ones. Furthermore, our monogamy inequalities are shown to remain valid for the high dimensional states that violate the CKW monogamy inequality. Detailed examples are presented to illustrate the effectiveness of our results in characterizing the multipartite entanglement distributions.

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arXiv2023

Tighter monogamy inequalities of multiqubit entanglement

Multipartite entanglement holds great importance in quantum information processing. The distribution of entanglement among subsystems can be characterized by monogamy relations. Based on the $β$th power of concurrence and negativity, we provide two new monogamy inequalities. Through detailed examples, we demonstrate that these inequalities are tighter than previous results.

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arXiv2023

General monogamy and polygamy relations of arbitrary quantum correlations for multipartite systems

Monogamy and polygamy of quantum correlations are the fundamental properties of quantum systems. We study the monogamy and polygamy relations satisfied by any quantum correlations in multipartite quantum systems. General monogamy relations are presented for the $α$th $(0\leqα\leqγ$, $γ\geq2)$ power of quantum correlation, and general polygamy relations are given for the $β$th $(β\geq δ$, $0\leqδ\leq1)$ power of quantum correlation. We show that these newly derived monogamy and polygamy inequalities are tighter than the existing ones. By applying these results to specific quantum correlations such as concurrence and the square of convex-roof extended negativity of assistance (SCRENoA), the corresponding new classes of monogamy and polygamy relations are obtained, which include the existing ones as special cases. Detailed examples are given to illustrate the advantages of our results.

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