arXiv subjects

Xianfei Qi

Publications and source records attributed to Xianfei Qi.

10 recordsLinked to original sources

arXiv2026

Quantifying multilevel coherence and multipartite correlation based on $α$-affinity

Unlike standard quantum coherence, multilevel quantum coherence provides a hierarchical structure that enables a more refined characterization of quantum superposition. In this paper, we investigate multilevel coherence and introduce two $α$-affinity-based indicators to quantify it, both of which satisfy several desirable properties. We further define $α$-affinity-based indicators for multipartite correlation and analyze their properties. Finally, we establish relationships between these multilevel coherence indicators and the multipartite correlation indicators.

quant-ph↗

arXiv2022

A $(k+1)$-partite entanglement measure of $N$-partite quantum states

The concept of \textquotedblleft the permutationally invariant part of a density matrx\textquotedblright constitutes an important tool for entanglement characterization of multiqubit systems. In this paper, we first present $(k+1)$-partite entanglement measure of $N$-partite quantum system, which possesses desirable properties of an entanglement measure. Moreover, we give strong bounds on this measure by considering the permutationally invariant part of a multipartite state. We give two definitions of efficient measurable degree of $(k+1)$-partite entanglement. Finally, several concrete examples are given to illustrate the effectiveness of our results.

quant-ph↗

arXiv2021

Detection of the quantum states containing at most $k-1$ unentangled particles

There are many different classifications of entanglement for multipartite quantum systems, one of which is based on the number of unentangled particles. In this paper, we mainly study the quantum states containing at most $k-1$ unentangled particles and provide several entanglement criteria based on different forms of inequalities which can both identify quantum states containing at most $k-1$ unentangled particles. We show that these criteria are more effective for some states by concrete examples.

quant-ph↗

arXiv2021

Detection of multipartite entanglement via quantum Fisher information

In this paper, we focus on two different kinds of multipartite correlation, $k$-nonseparability and $k$-partite entanglement, both of which can describe the essential characteristics of multipartite entanglement. We propose effective methods to detect $k$-nonseparability and $k$-partite entanglement in terms of quantum Fisher information. We illustrate the significance of our results and show that they identify some $k$-nonseparability and $k$-partite entanglement that cannot be identified by known criteria by several concrete examples.

quant-ph↗

arXiv2020

The verification of a requirement of entanglement measures

The quantification of quantum entanglement is a central issue in quantum information theory. Recently, Gao \emph{et al}. ( \href{http://dx.doi.org/10.1103/PhysRevLett.112.180501}{Phys. Rev. Lett. \textbf{112}, 180501 (2014)}) pointed out that the maximum of entanglement measure of the permutational invariant part of $ρ$ ought to be a lower bound on entanglement measure of the original state $ρ$, and proposed that this argument can be used as an additional requirement for (multipartite) entanglement measures. Whether any individual proposed entanglement measure satisfies the requirement still has to prove. In this work, we show that most known entanglement measures of bipartite quantum systems satisfy the new criterion, include all convex-roof entanglement measures, the relative entropy of entanglement, the negativity, the logarithmic negativity and the logarithmic convex-roof extended negativity. Our results give a refinement in quantifying entanglement and provide new insights into a better understanding of entanglement properties of quantum systems.

quant-ph↗

arXiv2020

Strong superadditivity relations for multiqubit systems

We investigate the distributions of quantum coherence characterized by superadditivity relations in multipartite quantum systems. General superadditivity inequalities based on the $α$th ($α\geqslant 1$) power of $l_1$ norm of coherence are presented for multiqubit states, which include the existing ones as special cases. Our result is shown to be tighter than the existing one by a specific example.

quant-ph↗

arXiv2018

Quantifying the quantumness of ensembles via unitary similarity invariant norms

The quantification of the quantumness of a quantum ensemble has theoretical and practical significance in quantum information theory. We propose herein a class of measures of the quantumness of quantum ensembles using the unitary similarity invariant norms of the commutators of the constituent density operators of an ensemble. Rigorous proof shows that they share desirable properties for a measure of quantumness, such as positivity, unitary invariance, concavity under probabilistic union, convexity under state decomposition, decreasing under coarse graining, and increasing under fine graining. Several specific examples illustrate the applications of these measures of quantumness in studying quantum information.

quant-ph↗

arXiv2017

Measuring Coherence with Entanglement Concurrence

Quantum coherence is a fundamental manifestation of the quantum superposition principle. Recently, Baumgratz \emph{et al}. [Phys. Rev. Lett. \textbf{113}, 140401 (2014)] presented a rigorous framework to quantify coherence from the view of theory of physical resource. Here we propose a new valid quantum coherence measure which is a convex roof measure, for a quantum system of arbitrary dimension, essentially using the generalized Gell-Mann matrices. Rigorous proof shows that the proposed coherence measure fulfills all the requirements dictated by the resource theory of quantum coherence measures. Moreover, strong links between the resource frameworks of coherence concurrence and entanglement concurrence is derived, which shows that any degree of coherence with respect to some reference basis can be converted to entanglement via incoherent operations. Our work provides a clear quantitative and operational connection between coherence and entanglement based on two kinds of concurrence. This new coherence measure, coherence concurrence, may be beneficial to the study of quantum coherence.

quant-ph↗

arXiv2017

Necessary and sufficient product criteria for quantum states via the rank of realignment matrix of density matrix

We present a necessary and sufficient product criterion for bipartite quantum states based on the rank of realignment matrix of density matrix. Then, this approach is generalized to multipartite systems. We first introduce the concept of semiproduct in a similar manner to the semiseparable and prove that semiproduct is equivalent to fully product. Therefore, a quantum state is bipartite product with respect to all possible partitions implies fully product which is different from the case of separability. For pure states, it can easily be seen that several necessary and sufficient separability criteria for multipartite systems are derived as a special case of our results. Several specific examples illustrate that our criteria are convenient and operational.

quant-ph↗

arXiv2017

Lower bounds of concurrence for $N$-qubit systems and the detection of $k$-nonseparability of multipartite quantum systems

Concurrence, as one of entanglement measures, is a useful tool to characterize quantum entanglement in various quantum systems. However, the computation of the concurrence involves difficult optimizations and only for the case of two qubits an exact formula was found. We investigate the concurrence of four-qubit quantum states and derive analytical lower bound of concurrence using the multiqubit monogamy inequality. It is shown that this lower bound is able to improve the existing bounds. This approach can be generalized to arbitrary qubit systems. We present an exact formula of concurrence for some mixed quantum states. For even-qubit states, we derive an improved lower bound of concurrence using a monogamy equality for qubit systems. At the same time, we show that a multipartite state is $k$-nonseparable if the multipartite concurrence is larger than a constant related to the value of $k$, the qudit number and the dimension of the subsystems. Our results can be applied to detect the multipartite $k$-nonseparable states.

quant-ph↗