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Jinchuan Hou

Publications and source records attributed to Jinchuan Hou.

At least 37 records · Page 2Linked to original sources
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.

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arXiv2022

Approximate separation of quantum gates and separation experiments of CNOT based on Particle Swarm Optimization algorithm

Ying conceived of using two or more small-capacity quantum computers to produce a larger-capacity quantum computing system by quantum parallel programming ([M. S. Ying, Morgan-Kaufmann, 2016]). In doing so, the main obstacle is separating the quantum gates in the whole circuit to produce a tensor product of the local gates. It has been showed that there are few separable multipartite quantum gates, so the approximate separation problem involves finding local quantum gates that approximate a given inseparable gate. We propose and study a problem involving the approximate separation of multipartite gates based on quantum-gate fidelity. For given multipartite and local gates, we conclude that the smaller is the maximal distance between the products of an arbitrary pair of eigenvalues, the greater is their gate fidelity. This provides a criterion for approximate separation. Lastly, we discuss the optimal approximate separation of the CNOT gate.

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arXiv2021

Separation of gates in quantum parallel programming

The number of qubits in current quantum computers is a major restriction on their wider application. To address this issue, Ying conceived of using two or more small-capacity quantum computers to produce a larger-capacity quantum computing system by quantum parallel programming ([M. S. Ying, Morgan-Kaufmann, 2016]). In doing so, the main obstacle is separating the quantum gates in the whole circuit to produce a tensor product of the local gates. In this study, we theoretically analyse the (sufficient and necessary) separability conditions of multipartite quantum gates in finite or infinite dimensional systems. We then conduct separation experiments with n-qubit quantum gates on IBM quantum computers using QSI software.

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arXiv2020

Multiplicative Lie derivation of triangular 3-matrix rings

A map $ϕ$ on an associative ring is called a multiplicative Lie derivation if $ϕ([x,y])=[ϕ(x),y]+[x,ϕ(y)]$ holds for any elements $x,y$, where $[x,y]=xy-yx$ is the Lie product. In the paper, we discuss the multiplicative Lie derivations on the triangular 3-matrix rings $\mathcal T={\mathcal T}_3(\mathcal R_i; \mathcal M_{ij})$. Under the standard assumption $Q_i\mathcal Z(\mathcal T)Q_i=\mathcal Z(Q_i\mathcal T Q_i)$, $i=1,2,3$, we show that every multiplicative Lie derivation $φ:\mathcal T\to\mathcal T$ has the standard form $φ=δ+γ$ with $δ$ a derivation and $γ$ a center valued map vanishing each commutator.

math.RA↗
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.

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arXiv2018

Characterizing the Gaussian coherence-breaking channel and its property with assistant entanglement inputs

In the paper, we give a characterization of arbitrary $n$-mode Gaussian coherence breaking channels (GCBCs) and show the tensor product of a GCBC and arbitrary a Gaussian channel maps all input states into product states. The inclusion relation among GCBCs, Gaussian positive partial transpose channels (GPPTC), entanglement breaking channels (GEBC) and Gaussian classical-quantum channels (GCQC) is displayed. Finally, we prove that Gaussian classical ($χ$-) capacity for the tensor products of GCBCs and arbitrary Gaussian channels is additive.

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arXiv2016

Constructing separable states in infinite-dimensional systems by operator matrices

We introduce a class of states so-called semi-SSPPT (semi super strong positive partial transposition) states in infinite-dimensional bipartite systems by the Cholesky decomposition in terms of operator matrices and show that every semi-SSPPT state is separable. This gives a method of constructing separable states and generalizes the corresponding results in [Phys. Rev. A \textbf{77}, 022113(2008), J. Phys. A: Math. Theor. 45 505303 (2012)]. This criterion is specially convenient to be applied when one of the subsystem is a qubit system.

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arXiv2016

Strong $k$-commutativity preserving maps on 2$\times$2 matrices

Let ${\mathcal M}_2(\mathbb F)$ be the algebra of 2$\times$2 matrices over the real or complex field $\mathbb F$. For a given positive integer $k\geq 1$, the $k$-commutator of $A$ and $B$ is defined by $[A,B]_k=[[A,B]_{k-1},B]$ with $[A,B]_0=A$ and $[A,B]_1=[A,B]=AB-BA$. The main result is shown that a map $Φ: {\mathcal M}_2(\mathbb F)\to {\mathcal M}_2(\mathbb F)$ with range containing all rank one matrices satisfies that $[Φ(A),Φ(B)]_k = [A,B]_k $ for all $A, B\in{\mathcal M}_2(\mathbb F)$ if and only if there exist a functional $h :{\mathcal M}_2(\mathbb F) \rightarrow {\mathbb F}$ and a scalar $λ\in{\mathbb F}$ with $λ^{k+1} = 1$ such that $Φ(A) = λA + h(A)I$ for all $A \in{\mathcal M}_2(\mathbb F)$.

math.RA↗
arXiv2016

Strong $3$-Commutativity Preserving Maps on Standard Operator Algebras

Let $X$ be a Banach space of dimension $\geq 2$ over the real or complex field ${\mathbb F}$ and ${\mathcal A}$ a standard operator algebra in ${\mathcal B}(X)$. A map $Φ:{\mathcal A} \rightarrow {\mathcal A}$ is said to be strong $3$-commutativity preserving if $[Φ(A),Φ(B)]_3 = [A,B]_3$ for all $A, B\in{\mathcal A}$, where $[A,B]_3$ is the 3-commutator of $A,B$ defined by $[A,B]_3=[[[A,B],B],B]$. The main result in this paper is shown that, if $Φ$ is a surjective map on ${\mathcal A}$, then $Φ$ is strong $3$-commutativity preserving if and only if there exist a functional $h :{\mathcal A} \rightarrow {\mathbb F}$ and a scalar $λ\in{\mathbb F}$ with $λ^4 = 1$ such that $Φ(A) = λA + h(A)I$ for all $A \in{\mathcal A}$.

math.FA↗
arXiv2016

Uncertainty relations for any multi observables

Uncertainty relations describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal uncertainty relation for any $k$ observables, of which the formulation depends on the even or odd quality of $k$. This universal uncertainty relation is tight at least for the cases $k=2n$ and $k=3$. For two observables, the uncertainty relation is exactly a simpler reformulation of Schrödinger's uncertainty principle.

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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↗
arXiv2013

Maps preserving peripheral spectrum of generalized products of operators

Let $\mathcal{A}_1$ and $\mathcal{A}_2$ be standard operator algebras on complex Banach spaces $X_1$ 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 product $T_1* T_2*\cdots* T_k=T_{i_1}T_{i_2}\cdots T_{i_m}$ on elements in $\mathcal{A}_i$. Let $Φ:\mathcal{A}_1\rightarrow\mathcal{A}_2$ be a map with the range containing all operators of rank at most two. We show that $Φ$ satisfies that $σ_π(Φ(A_1)*\cdots*Φ(A_k))=σ_π(A_1*\cdots* A_k)$ for all $A_1,\ldots, A_k$, where $σ_π(A)$ stands for the peripheral spectrum of $A$, if and only if $Φ$ is an isomorphism or an anti-isomorphism multiplied by an $m$th root of unity, and the latter case occurs only if the generalized product is quasi-semi Jordan. If $X_1=H$ and $X_2=K$ are complex Hilbert spaces, we characterize also maps preserving the peripheral spectrum of the skew generalized products, and prove that such maps are of the form $A\mapsto cUAU^*$ or $A\mapsto cUA^tU^*$, where $U\in\mathcal{B}(H,K)$ is a unitary operator, $c\in\{1,-1\}$.

math.FA↗
arXiv2013

Criteria of positivity for linear maps constructed from permutation pairs

In this paper, we show that a $D$-type map $Φ_D:M_n\rightarrow M_n$ with $D=(n-2)I_n+P_{π_1}+P_{π_2}$ induced by a pair $\{π_1,π_2\}$ of permutations of $(1,2,..., n)$ is positive if $\{π_1,π_2\}$ has property (C). The property (C) is characterized for $\{π_1,π_2\}$, and an easy criterion is given for the case that $π_1=π^p$ and $π_2=π^q$, where $π$ is the permutation defined by $π(i)=i+1$ mod $n$ and $1\leq p<q\leq n$.

quant-ph↗
arXiv2013

Quantum measurements and maps preserving strict convex combinations and pure states

In this paper, a characterization of maps between quantum states that preserve pure states and strict convex combinations is obtained. Based on this characterization, a structural theorem for maps between multipartite quantum states that preserve separable pure states and strict convex combinations is established. Then these results are applied to characterize injective (local) quantum measurements and answer some conjectures proposed in [J.Phys.A:Math.Theor. 45 (2012) 205305].

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