检索结果-内蒙古大学图书馆

Total, classical, and quantum uncertainty matrices via operator monotone functions

THEORETICAL AND MATHEMATICAL PHYSICS 2024年第2期221卷 1813-1835页

作者： Fan, Yajing Li, Nan Luo, Shunlong North Minzu Univ Res Ctr Math Sch Math & Informat Sci Yinchuan Peoples R China Chinese Acad Sci Acad Math & Syst Sci Beijing Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing Peoples R China

It is important to distinguish between classical information and quantum information in quantum information theory. In this paper, we first extend the concept of metric-adjusted correlation measure and some related measures to non-Hermitian operators, and establish several relations between the metric-adjusted skew information with different operator monotone functions. By employing operator monotone functions, we next introduce three uncertainty matrices generated by channels: the total uncertainty matrix, the classical uncertainty matrix, and the quantum uncertainty matrix. We establish a decomposition of the total uncertainty matrix into classical and quantum parts and further investigate their basic properties. As applications, we employ uncertainty matrices to quantify the decoherence caused by the action of quantum channels on quantum states, and calculate the uncertainty matrices of some typical channels to reveal certain intrinsic features of the corresponding channels. Moreover, we establish several uncertainty relations that improve the traditional Heisenberg uncertainty relations involving variance.

关键词： operator monotone functions metric-adjusted skew information uncertainty quantum channels

来源：评论

学校读者我要写书评

暂无评论

Matrix power means and new characterizations of operator monotone functions

引用

LINEAR & MULTILINEAR ALGEBRA 2023年第18期71卷 2986-2997页

作者： Dinh, Trung Hoa Le, Cong Trinh Nguyen, The Van Vo, Bich Khue Troy Univ Dept Math & Stat Troy AL USA Quy Nhon Univ Dept Math & Stat Quy Nhon Vietnam Univ Illinois Dept Math Urbana IL USA Vietnam Natl Univ Univ Sci Hanoi Vietnam Univ Finance & Mkt Fac Econ & Law Ho Chi Minh City Vietnam Troy Univ Dept Math & Stat Troy AL 36082 USA

For positive definite matrices A and B, the Kubo-Ando matrix power mean is defined as P-mu(p, A, B) = A(1/2)(1 + (A(-1/2)BA(-1/2))(p)/2)(1/p) A(1/2) (p >= 0). In this paper, for 0 <= p <= 1 <= q, we show that if one of the following inequalities f(P-mu(p, A, B)) <= f(P-mu(1, A, B)) <= f(P-mu(q, A, B)) holds for any positive definite matrices A and B, then the function f is operator monotone on (0, infinity). We also study the inverse problem for non-Kubo-Ando matrix power means with the powers 1/2 and 2. As a consequence, we establish new charaterizations of operator monotone functions with the non-Kubo-Ando matrix power means.

关键词： Matrix power mean matrix geometric mean operator monotone functions inverse problems for means Kubo-Ando means

来源：评论

学校读者我要写书评

暂无评论

New characterizations of operator monotone functions

引用

ACTA SCIENTIARUM MATHEMATICARUM 2024年第3-4期90卷 623-636页

作者： Vo, Bich Khue Dinh, Trung Hoa Osaka, Hiroyuki Univ Finance & Mkt Dept Fundamental Sci Ho Chi Minh City Vietnam Troy Univ Dept Math & Stat Troy AL 36072 USA Ritsumeikan Univ Dept Math Sci Kusatsu Shiga 5258577 Japan

In this paper, we establish some new characterizations of operator monotone functions using matrix mean inequalities.

关键词： Kubo-Ando means Scalar means operator monotone functions Mean inequalities

来源：评论

学校读者我要写书评

暂无评论

Upper and Lower Bounds for Noncommutative Perspectives of operator monotone functions: the Case of Second Variable

引用

ACTA MATHEMATICA VIETNAMICA 2022年第2期47卷 581-595页

作者： Dragomir, Silvestru Sever Victoria Univ Coll Engn & Sci Math POB 14428 Melbourne Vic 8001 Australia

Assume that the function f : [0, infinity) -> R is operator monotone in [0, infinity). We can define the perspective P-f (B, A) by setting P-f (B,A) := A(1/2) f(A(-1/2)BA(-1/2))A(1/2), where A, B > 0. In this paper, we show among others that, if sigma >= C >= rho > 0, D > 0, sigma >= Q >= tau > 0 and 0 < n <= D - C <= N for some constants rho, sigma, sigma, tau, n, N, then 0 <= n/N sigma(2)[P-f (sigma, N + sigma) - P-f (tau, sigma)]Q(2). <= P-f(Q, D) - P-f (Q, C) <= N/n tau(2)[P-f(tau, n + rho) - P-f (tau, rho)]Q(2). Applications for the weighted operator geometric mean and the perspective PIn(.+1) (B, A) := A(1/2) In (A(-1/2)BA(-1/2) + 1)A(1/2), A, B > 0 are also provided.

关键词： Noncommutative perspectives Relative operator entropy operator monotone functions

来源：评论

学校读者我要写书评

暂无评论

Lipschitz type inequalities for noncommutative perspectives of operator monotone functions in Hilbert spaces

引用

ADVANCES IN operator THEORY 2021年第2期6卷 1-20页

作者： Dragomir, Silvestru Sever Victoria Univ Coll Engn & Sci Math POB 14428 Melbourne MC 8001 Australia

Assume that f : 1/20;1THORN ! R is a continuous function. We can define the perspective Pf oB;ATHORN by setting Pf oB;ATHORN :1/4 A1=2f A similar to 1=2BA similar to 1=2 similar to similar to A1=2;where A, B[ 0: We show in this paper among others that Pf B;Po THORN similar to P f A;Po THORN similar to similar to similar to similar to similar to kPk2 kB similar to Ak p2 Pf m2;po THORN similar to P f om1;pTHORN m2 similar to m1 similar to similar to if m1 6 1/4 m2;f 0 m p similar to similar to if m1 1/4 m2 1/4 m8>>><>>>: for all A similar to m1[ 0;B similar to m2[ 0 and P similar to p[ 0. If f is operator monotone on 1/20;1THORN, then for all C similar to n1[ 0;D similar to n2[ 0;Q[ q[ 0 we also have

关键词： operator monotone functions Noncommutative perspectives

来源：评论

学校读者我要写书评

暂无评论

Inequalities for generalized derivations of operator monotone functions in norm ideals of compact operators

引用

LINEAR ALGEBRA AND ITS APPLICATIONS 2020年 586卷 43-63页

作者： Jocic, Danko R. Lazarevic, Milan Milosevic, Stefan Univ Belgrade Dept Math Studentski Trg 16POB 550 Belgrade 11000 Serbia

Let Phi be a symmetrically norming (s.n.) function, p >= 2, Phi((p))* to be a dual s.n. function to p-modified s.n. function Phi((p)), A, B, X is an element of B(H), with A and B being normal operators such that AX - XB is an element of C-Phi(H). If both A and B are strictly accretive, then for non-constant Pick function phi is an element of P[0, +infinity) parallel to phi(A)X - X phi(B)parallel to(Phi) <= parallel to root phi'(A*+A/2)(AX - XB)root phi'(B+B*/2)parallel to(Phi). (1) If A and B have Strictly contractive real parts, then 1/2 parallel to root I - vertical bar A* + A/2 vertical bar(2) (log I + A/I - A X - X log I + B/I - B) x root I - vertical bar B + B*/2 vertical bar(2)parallel to(Phi) <= parallel to AX - XB parallel to(Phi). If A is cohyponormal, B is hyponormal and at least one of them is normal, such that AX - XB is an element of C-Phi(p)*(H), then pi/2 parallel to cos A* + A(tan 2A/pi X - X tan 2B/pi) cos B + B*/pi parallel to(Phi(p)*) <= parallel to AX - XB parallel to(Phi(p)*). (2) Inequality (1) generalizes "difference" version of Heinz norm inequality [13, Hilfssatz 3] and mean values norm inequality [21, th. 4.4] for operator monotone functions. Inequality (2) remains valid for all s.n. function Phi if A and B are both (additionally) normal, which extends inequalities in [32, th. 5] and [34, rem. 25] for self-adjoint operators H and K, whence their spectra sigma(H) and sigma(K) are contained in (-pi/2, pi/2), to non necessarily self-adjoint operators A and B. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Inner product type transformers operator monotone functions Q and Q*-norms

来源：评论

学校读者我要写书评

暂无评论

Inequalities for generalized derivations of operator monotone functions in norm ideals of compact operators (vol 586, pg 43, 2020)

引用

LINEAR ALGEBRA AND ITS APPLICATIONS 2020年 599卷 201-204页

作者： Jocic, Danko R. Lazarevic, Milan Milosevic, Stefan Univ Belgrade Dept Math Studentski Trg 16POB 550 Belgrade 11000 Serbia

In this corrigendum note we provide a correct statement and a proof of [3, Th. 2.1] parts (a4'), (a4 ''), (b4'), (b4 ''), as well as a correct statement and a proof for the inequality (34) in [... 详细信息

关键词： Inner product type transformers operator monotone functions Q and Q*-norms

来源：评论

学校读者我要写书评

暂无评论

Some results on strongly operator convex functions and operator monotone functions

引用

LINEAR ALGEBRA AND ITS APPLICATIONS 2018年 553卷 238-251页

作者： Brown, Lawrence G. Uchiyama, Mitsuru Purdue Univ Dept Math W Lafayette IN 47907 USA Shimane Univ Dept Math Matsue Shimane Japan Ritsumeikan Univ Dept Math Kusatsu Japan

This paper concerns three classes of real-valued functions on intervals, operator monotone functions, operator convex functions, and strongly operator convex functions. Strongly operator convex functions were previously treated in [3] and [4], where operator algebraic semicontinuity theory or operator theory were substantially used. In this paper we provide an alternate treatment that uses only operator inequalities (or even just matrix inequalities). We show also that if to is a point in the domain of a continuous function f, then f is operator monotone if and only if (f (t) - f (t(0)) / (t - t(0)) is strongly operator convex. Using this and previously known results, we provide some methods for constructing new functions in one of the three classes from old ones. We also include some discussion of completely monotone functions in this context and some results on the operator convexity or strong operator convexity of phi o f when f is operator convex or strongly operator convex. (C) 2018 Elsevier Inc. All rights reserved.

关键词： operator monotone functions Pick functions Loewner theorem operator convex functions Strongly operator convex functions Completely monotone functions

来源：评论

学校读者我要写书评

暂无评论

New characterizations of operator monotone functions

引用

LINEAR ALGEBRA AND ITS APPLICATIONS 2018年 546卷 169-186页

作者： Trung Hoa Dinh Dumitru, Raluca Franco, Jose A. Ton Duc Thang Univ Inst Computat Sci Div Computat Math & Engn Ho Chi Minh City Vietnam Ton Duc Thang Univ Fac Civil Engn Ho Chi Minh City Vietnam Univ North Florida Dept Math & Stat Jacksonville FL 32224 USA

If sigma is a symmetric mean and f is an operator monotone function on [0, infinity), then f(2(A(-1) + B-1)(-1)) <= f(A sigma B) <= f((A + B)/2). Conversely, Ando and Hiai showed that if f is a function that satisfies either one of these inequalities for all positive operators A and B and a symmetric mean different than the arithmetic and the harmonic mean, then the function is operator monotone. In this paper, we show that the arithmetic and the harmonic means can be replaced by the geometric mean to obtain similar characterizations. Moreover, we give characterizations of operator monotone functions using self-adjoint means and general means subject to a constraint due to Kubo and Ando. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Kubo-Ando means operator monotone functions Symmetric means Self-adjoint means Lattice of functions

来源：评论

学校读者我要写书评

暂无评论

Complete characterization of symmetric Kubo-Ando operator means satisfying Molnár's weak associativity

引用

LINEAR ALGEBRA AND ITS APPLICATIONS 2025年 719卷 158-182页

作者： Grabovsky, Yury Milton, Graeme W. Welters, Aaron Temple Univ Dept Math Philadelphia PA 19122 USA Univ Utah Dept Math Salt Lake City UT 84112 USA Florida Inst Technol Dept Math & Syst Engn Melbourne FL 32901 USA

We provide a complete characterization of a subclass of weakly associative means of positive operators in the class of symmetric Kubo-Ando means. This class, which includes the geometric mean, was first introduced and studied in Moln & aacute;r (2019) [24], where he gives a characterization of this subclass (which we call the Moln & aacute;r class of means) in terms of the properties of their representing operator monotone functions. Moln & aacute;r's paper leaves open the problem of determining if the geometric mean is the only such mean in that subclass. Here we give a negative answer to this question by constructing an order-preserving bijection between this class and a class of real measurable odd periodic functions bounded in absolute value by 1/2. Each member of the latter class defines a Moln & aacute;r mean by an explicit exponential-integral representation. From this we are able to understand the order structure of the Moln & aacute;r class and construct several infinite families of explicit examples of Moln & aacute;r means that are not the geometric mean. Our analysis also shows how to modify Moln & aacute;r's original characterization so that the geometric mean is the only one satisfying the requisite set of properties. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Arithmetic-harmonic-geometric means Kubo-Ando means operator monotone functions Herglotz-Nevanlinna functions Moln & aacute r class of means

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：