arXiv subjects

Xiaofei Qi

Publications and source records attributed to Xiaofei Qi.

At least 19 recordsLinked to original sources

arXiv2026

Algebraic Maximal Numerical Range and its preservers of Triple Products on $C^*$-Algebras

Let $\mathcal{A}$ and $\mathcal{B}$ be unital $C^*$-algebras, and let $V_0(a)=\{f(a): f\in\mathcal S(\mathcal A), f(a^*a)=\|a\|^2\}$ be the algebraic maximal numerical range of $a\in\mathcal{A}$, where $\mathcal S(\mathcal A)$ is the set of all states of $\mathcal A$. We study the properties of $V_0(a)$ and characterize surjective maps preserving $V_0$ of triple products. We show that if $\Phi\colon\mathcal{A}\to\mathcal{B}$ satisfies $V_0(\Phi(a)\Phi(b)\Phi(c))=V_0(abc) \text{~for all~} a,b,c\in\mathcal{A},$ then the map $a\mapsto \Phi(1_{\mathcal{A}})^{-1}\Phi(a)$ is a multiplicative bijection. Furthermore, for von Neumann algebras without central summands of type $I_1$ or prime $C^*$-algebras of real rank zero, such preservers are precisely $*$-isomorphisms multiplied by a central element $u\in Z(\mathcal{B})$ with $u^3=1$.

math.OA↗

arXiv2026

Ascent and descent of bounded linear operators

Let $\mathcal B(\mathcal X)$ be the algebra of all bounded linear operators on a real or complex Banach space $\mathcal{X}$ with $\dim\mathcal X \ge 3$. In this paper, we first explore the ascent (descent) of upper triangular block operator matrices and certain special algebraic operators, and then establish characterizations for the ascent (descent) of rank-one and rank-two operators. Based on these results, we characterize features for some special operators by the ascent (descent) of Jordan products. As an application, we give the structure of all maps with range containing all bounded operators of rank at most three preserving the ascent (descent) of operator Jordan product on $\mathcal B(\mathcal X)$.

math.FA↗

arXiv2026

Imaginarity Resource Theory of Gaussian Quantum Channels

Complex numbers play an indispensable role in quantum mechanics and quantum information, as validated by both theoretical analysis and experimental verification. Since quantum information processing inherently relies on quantum channels, the resource theory for quantum channels is equally fundamental to that for quantum states. In this paper, we propose two frameworks for quantifying the imaginarity of Gaussian channels. The first framework regards all real superchannels as free superchannels. Within this setting, we introduce two concrete imaginarity measures for Gaussian channels: I_s^GC based on existing imaginarity measures of Gaussian states, and I_d^GC derived directly from the intrinsic parameters of Gaussian channels, which enjoys high computational simplicity. The second framework adopts only a proper subset of real superchannels as free superchannels. Under this framework, we put forward another imaginarity measure I_c^GC , which is fully determined by the inherent parameters of Gaussian channels and features continuity as well as tractable computation. As a practical application, we employ I_c^GC to investigate the dynamical behavior of Quantum Brownian Motion Gaussian channels throughout the entire evolutionary process.

quant-ph↗

arXiv2025

$k$-Entanglement Measure for Multipartite Systems without Convex-Roof Extensions and its Evaluation

Multipartite entanglement underpins quantum technologies but its study is limited by the lack of universal measures, unified frameworks, and the intractability of convex-roof extensions. We establish an axiomatic framework and introduce the first \emph{true} $k$-entanglement measure, $E_w^{(k,n)}$, which satisfies all axioms, establishes $k$-entanglement as a multipartite quantum resource, avoids convex-roof constructions, and is efficiently computable. A universal algorithm evaluates arbitrary finite-dimensional states, with open-source software covering all partitions of four-qubit systems. Numerical tests certify $k$-entanglement within 200 seconds, consistent with necessary-and-sufficient criteria, tightening bounds and revealing new thresholds. This framework offers a scalable, practical tool for rigorous multipartite entanglement quantification.

quant-ph↗

arXiv2025

Several kinds of Gaussian quantum channels related to Einstein-Podolsky-Rosen steering

Quantum steering is a crucial quantum resource that lies intermediate between entanglement and Bell nonlocality. Gaussian channels, meanwhile, play a foundational role in diverse quantum protocols, secure communication, and related fields. In this paper, we focus on several classes of Gaussian channels associated with quantum steering: Gaussian steering-annihilating channels, Gaussian steering-breaking channels, Gaussian unsteerable channels, and maximal Gaussian unsteerable channels. We give the concepts of these channels, derive the necessary and sufficient conditions for a Gaussian channel to belong to each class, and explore the intrinsic relationships among them. Additionally, since quantifying the steering capability of Gaussian channels in continuous-variable systems requires an understanding of the structure of free superchannels, we also provide a detailed characterization of Gaussian unsteerable superchannels and maximal Gaussian unsteerable superchannels.

quant-ph↗

arXiv2025

Multipartite correlation measures and framework for multipartite quantum resources theory

In recent years, it has been recognized that properties of multipartite physical systems, such as genuine multipartite entanglement, can be considered as important resources for quantum information and other areas of physics. However, the current framework of multipartite quantum resource theory is flawed. In this paper, we propose a more reasonable framework for multipartite quantum resource theory with a particular focus on axiomatic definition for true measures of multipartite quantum correlations (MQC) that regulates how to measure the correlation in part systems (the unification condition) and how to describe the requirement from many-body resource theory that the correlation hold by part system does not exceed that of the entire system (the hierarchy condition). We find that, due to the inherent characteristics of MQCs, the true measures of different MQCs exhibit distinct hierarchy conditions. Based on this framework, we verify that multipartite entanglement, $k$-entanglement, $k$-partite entanglement, multipartite non-PPT, multipartite coherence, multipartite imaginarity, multipartite multi-mode Gaussian non-product correlation, multipartite multi-mode Gaussian imaginarity, and multipartite single-mode Gaussian coherence are all symmetric multipartite quantum resources. We also show that, multipartite steering is an asymmetric multipartite quantum resource. Finally, the monogamy relations for true measures of symmetric MQCs are discussed.

quant-ph↗

arXiv2025

Witnessing nonlocality in quantum network of continuous-variable systems by generalized quasiprobability functions

Gaussian measurements can not be used to witness nonlocality in Gaussian states as well as the network nonlocality in networks of continuous-variable (CV) systems. Thus special non-Gaussian measurements have to be utilized. In the present paper, we first propose a kind of nonlinear Bell-type inequality that is applicable to quantum networks of both finite or infinite dimensional systems. Violation of the inequality will witness the network nonlocality. This inequality allows us to propose a method of the supremum strategy for detecting network nonlocality in CV systems with source states being any multipartite multi-mode Gaussian states according to the configurations of the networks by utilizing non-Gaussian measurements based on generalized quasiprobability functions. The nonlinear Bell-type inequalities for CV networks, which depend solely on the generalized quasiprobability functions of Gaussian states, are straightforward to construct and implement. As illustrations, we propose the corresponding nonlinear Bell-type inequalities for any chain, star, tree-shaped and cyclic networks in CV systems with source states being $(1+1)$-mode Gaussian states. The examples show that this approach works well for witnessing the nonlocality in networks of CV systems. Particularly, a thorough discussion is given for the entanglement swapping network. Our study provide a strong signature for the network nonlocality nature of CV systems and lead to precise recipes for its experimental verification.

quant-ph↗

arXiv2025

Detecting $k$-nonseparability and $k$-partite Entanglement with Generalized Skew Information and Mutually Unbiased Measurements

Multipartite quantum entanglement, as a core quantum resource, is fundamental to the advancement of quantum science and technology. In multipartite quantum systems, there are two kinds of quantum entanglement: $k$-nonseparability and $k$-partite entanglement. In this paper, we propose sufficient criteria for detecting $k$-nonseparability and $k$-partite entanglement by using the generalized Wigner-Yanase skew information and mutually unbiased measurements. Examples are given to demonstrate the detection capability and advantages of these criteria. As an application, an example of recognizing the networks by detecting the depth of quantum networks is given.

quant-ph↗

arXiv2025

An easily computable measure of Gaussian quantum imaginarity

The resource-theoretic frameworks for quantum imaginarity have been developed in recent years. Within these frameworks, many imaginarity measures for finite-dimensional systems have been proposed. However, for imaginarity of Gaussian states in continuous-variable (CV) systems, there are only two known Gaussian imaginarity measures, which exhibit prohibitive computational complexity when applied to multi-mode Gaussian states. In this paper, we propose a computable Gaussian imaginarity measure $\mathcal I^{G_n}$ for $n$-mode Gaussian systems. The value of $\mathcal I^{G_n}$ is simply formulated by the displacement vectors and covariance matrices of Gaussian states. A comparative analysis of $\mathcal{I}^{G_n}$ with existing two Gaussian imaginarity measures indicates that $\mathcal{I}^{G_n}$ can be used to detect imaginarity in any $n$-mode Gaussian states more efficiently. As an application, we study the dynamics behaviour of $(1+1)$-mode Gaussian states in Gaussian Markovian noise environments for two-mode CV system by utilizing ${\mathcal I}^{G_2}$. Moreover, we prove that, ${\mathcal I}^{G_n}$ can induce a quantification of any $m$-multipartite multi-mode CV systems which satisfies all requirements for measures of multipartite multi-mode Gaussian correlations, which unveils that, $n$-mode Gaussian imaginarity can also be regarded as a kind of multipatite multi-mode Gaussian correlation and is a multipartite Gaussian quantum resource.

quant-ph↗

arXiv2024

Gaussian unsteerable channels and computable quantifications of Gaussian steering

The current quantum resource theory for Gaussian steering for continuous-variable systems is flawed and incomplete. Its primary shortcoming stems from an inadequate comprehension of the architecture of Gaussian channels transforming Gaussian unsteerable states into Gaussian unsteerable states, resulting in a restricted selection of free operations. In the present paper, we explore in depth the structure of such $(m+n)$-mode Gaussian channels, and introduce the class of the Gaussian unsteerable channels and the class of maximal Gaussian unsteerable channels, both of them may be chosen as the free operations, which completes the resource theory for Gaussian steering from $A$ to $B$ by Alice's Gaussian measurements. We also propose two quantifications $\mathcal{J}_{j}$ $(j=1,2)$ of $(m+n)$-mode Gaussian steering from $A$ to $B$. The computation of the value of $\mathcal{J}_{j}$ is straightforward and efficient, as it solely relies on the covariance matrices of Gaussian states, eliminating the need for any optimization procedures. Though $\mathcal{J}_{j}$s are not genuine Gaussian steering measures, they have some nice properties such as non-increasing under certain Gaussian unsteerable channels. Additionally, we compare ${\mathcal J}_2$ with the Gaussian steering measure $\mathcal N_3$, which is based on the Uhlmann fidelity, revealing that ${\mathcal J}_2$ is an upper bound of $\mathcal N_3$ at certain class of $(1+1)$-mode Gaussian pure states. As an illustration, we apply $\mathcal J_2$ to discuss the behaviour of Gaussian steering for a special class of $(1+1)$-mode Gaussian states in Markovian environments, which uncovers the intriguing phenomenon of rapid decay in quantum steering.

quant-ph↗

arXiv2022

A computable multipartite multimode Gaussian correlation measure and the monogamy relation for continuous-variable systems

In this paper, a computable multipartite multimode Gaussian quantum correlation measure ${\mathcal M}^{(k)}$ is proposed for any $k$-partite continuous-variable (CV) systems with $k\geq 2$. ${\mathcal M}^{(k)}$ depends only on the covariance matrix of CV states, is invariant under any permutation of subsystems, is a quantification without ancilla problem, nonincreasing under $k$-partite local Gaussian channels (particularly, invariant under $k$-partite local Gaussian unitary operations), vanishes on $k$-partite product states. For a $k$-partite Gaussian state $ρ$, ${\mathcal M}^{(k)}(ρ)=0$ if and only if $ρ$ is a $k$-partite product state. Thus, for the bipartite case, ${\mathcal M}={\mathcal M}^{(2)}$ is an accessible replacement of the Gaussian quantum discord and Gaussian geometric discord. Moreover, ${\mathcal M}^{(k)}$ satisfies the unification condition, hierarchy condition that a multipartite quantum correlation measure should obey. ${\mathcal M}^{(k)}$ is not bipartite like monogamous, but, ${\mathcal M}^{(k)}$ is complete monogamous and tight complete monogamous.

quant-ph↗

arXiv2019

Fidelity based unitary operation-induced quantum correlation for continuous-variable systems

We propose a measure of nonclassical correlation $N_{\mathcal F}^{\mathcal G}$ in terms of local Gaussian unitary operations based on square of the fidelity $\mathcal F$ for bipartite continuous-variable systems. This quantity is easier to calculate or estimate and is a remedy for the local ancilla problem associated with the geometric measurement-induced nonlocality. A simple computation formula of $N_{\mathcal F}^{\mathcal G}$ for any $(1+1)$-mode Gaussian states is presented and an estimation of $N_{\mathcal F}^{\mathcal G}$ for any $(n+m)$-mode Gaussian states is given. For any $(1+1)$-mode Gaussian states, $N_{\mathcal F}^{\mathcal G}$ does not increase after performing a local Gaussian channel on the unmeasured subsystem. Comparing $N_{\mathcal F}^{\mathcal G}(ρ_{AB})$ in scale with other quantum correlations such as Gaussian geometric discord for two-mode symmetric squeezed thermal states reveals that $N_{\mathcal F}^{\mathcal G}$ is much better in detecting quantum correlations of Gaussian states.

quant-ph↗

arXiv2016

Physical origins of ruled surfaces on the reduced density matrices geometry

The reduced density matrices (RDMs) of many-body quantum states form a convex set. The boundary of low dimensional projections of this convex set may exhibit nontrivial geometry such as ruled surfaces. In this paper, we study the physical origins of these ruled surfaces for bosonic systems. The emergence of ruled surfaces was recently proposed as signatures of symmetry-breaking phase. We show that, apart from being signatures of symmetry-breaking, ruled surfaces can also be the consequence of gapless quantum systems by demonstrating an explicit example in terms of a two-mode Ising model. Our analysis was largely simplified by the quantum de Finetti's theorem---in the limit of large system size, these RDMs are the convex set of all the symmetric separable states. To distinguish ruled surfaces originated from gapless systems from those caused by symmetry-breaking, we propose to use the finite size scaling method for the corresponding geometry. This method is then applied to the two-mode XY model, successfully identifying a ruled surface as the consequence of gapless systems.

quant-ph↗

arXiv2015

Coherence convertibility for mixed states

In this paper, by providing a class of coherence measures in finite dimensional systems, a sufficient and necessary condition for the existence of coherence transformations that convert one probability distribution of any pure states into another one is obtained.

quant-ph↗

arXiv2015

Coherence measures and optimal conversion for coherent states

We discuss a general strategy to construct coherence measures. One can build an important class of coherence measures which cover the relative entropy measure for pure states, the $l_1$-norm measure for pure states and the $\alpha$-entropy measure. The optimal conversion of coherent states under incoherent operations is presented which sheds some light on the coherence of a single copy of a pure state.

quant-ph↗

arXiv2014

Lie ring isomorphisms between nest algebras on Banach spaces

Let ${\mathcal N}$ and ${\mathcal M}$ be nests on Banach spaces $X$ and $Y$ over the (real or complex) field $\mathbb F$ and let $\mbox{\rm Alg}{\mathcal N}$ and $\mbox{\rm Alg}{\mathcal M}$ be the associated nest algebras, respectively. It is shown that a map $Φ:{\rm Alg}{\mathcal N}\rightarrow{\rm Alg}{\mathcal M}$ is a Lie ring isomorphism (i.e., $Φ$ is additive, Lie multiplicative and bijective) if and only if $Φ$ has the form $Φ(A) = TAT^{-1} + h(A)I$ for all $A\in \mbox{\rm Alg}{\mathcal N}$ or $Φ(A)=-TA^*T^{-1}+h(A)I$ for all $A\in \mbox{\rm Alg}{\mathcal N}$, where $h$ is an additive functional vanishing on all commutators and $T$ is an invertible bounded linear or conjugate linear operator when $\dim X=\infty$; $T$ is a bijective $τ$-linear transformation for some field automorphism $τ$ of $\mathbb F$ when $\dim X<\infty$.

math.FA↗

arXiv2014

Maps preserving peripheral spectrum of generalized Jordan products of operators

Let $X_1$ and $X_2$ be complex Banach spaces with dimension at least three, $\mathcal{A}_1$ and $\mathcal{A}_2$ be standard operator algebras on $X_1$ and $X_2$, respectively. For $k\geq2$, let $(i_1,...,i_m)$ be a sequence with terms chosen from $\{1,\ldots,k\}$ and assume that at least one of the terms in $(i_1,\ldots,i_m)$ appears exactly once. Define the generalized Jordan product $T_1\circ T_2\circ\cdots\circ T_k=T_{i_1} T_{i_2}\cdots T_{i_m}+T_{i_m}\cdots T_{i_2} T_{i_1}$ on elements in $\mathcal{A}_i$. This includes the usual Jordan product $A_1A_2+A_2A_1$, and the Jordan triple $A_1A_2A_3+A_3A_2A_1$. Let $Φ:\mathcal{A}_1\rightarrow\mathcal{A}_2$ be a map with range containing all operators of rank at most three. It is shown that $Φ$ satisfies that $σ_π(Φ(A_1)\circ\cdots\circΦ(A_k))=σ_π(A_1\circ\cdots\circ A_k)$ for all $A_1, \ldots, A_k$, where $σ_π(A)$ stands for the peripheral spectrum of $A$, if and only if $Φ$ is a Jordan isomorphism multiplied by an $m$th root of unity.

math.FA↗

arXiv2013

Characterizing derivations for any nest algebras on Banach spaces by their behaviors at an injective operator

Let ${\mathcal N}$ be a nest on a complex Banach space $X$ and let $\mbox{ Alg}{\mathcal N}$ be the associated nest algebra. We say that an operator $Z\in \mbox{ Alg}{\mathcal N}$ is an all-derivable point of $\mbox{ Alg}{\mathcal N}$ if every linear map $δ$ from $\mbox{ Alg}{\mathcal N}$ into itself derivable at $Z$ (i.e. $δ$ satisfies $δ(A)B+Aδ(B)=δ(Z)$ for any $A,B \in \mbox{ Alg}{\mathcal N}$ with $AB=Z$) is a derivation. In this paper, it is shown that every injective operator and every operator with dense range in $\mbox{Alg}{\mathcal N}$ are all-derivable points of $\mbox{Alg}{\mathcal N}$ without any additional assumption on the nest.

math.FA↗