曹怀信,博士、教授、博士生导师。1982年1月毕业于陕西师范大学数学系,并留校任教,1987年12月在陕西师范大学数学系获理学硕士学位,1992年12月晋升为副教授,2000年晋升为教授,2000年3月至2003年3月在西安交通大学理学院,师从中国科学院院士徐宗本教授攻读应用数学博士学位,并获理学博士学位。2013年11月-2014年1月在澳大利亚拉筹伯大学访问,2018年11月-2018年12日在台湾(国立)中山大学访问。研究方向为算子论与算子代数、小波分析、量子信息学。
主要从事算子论与算子代数、非线性算子的Lipschitz理论、小波分析、量子信息与量子计算等方面的学术研究。在国内外学术杂志上发表论文150余篇, 主要论文发表于《中国科学》、《Communications in Theoretical Physics》、《Journal of Physics A》、《International Journal of Theoretic Physics》、《Mathematical Analysis and Applications》、《Linear Algebra and its Applications》、《Mathematical Inequalities & Applications》、《Applied and Numerical Harmonic Analysis》、《Acta Mathematica Sinica》、《Journal of Inequalities and Applications》、《Computer Engineering and Applications》、《Chinese Science Bulletin》、《Science China A》、《Science China G》、《Chaos, Solitons & Fractals》、《数学学报》等杂志。近十年来,在SCI与权威期刊上发表研究论文40多篇。参加完成国家自然科学基金2项、教育部优秀青年教师基金1项、主持完成陕西省自然科学基金2项,主持完成国家自然科学基金项目《基于量子信息论的算子论与算子代数研究》(26万元, 2005.1-2008.12), 并参与完成国家自然科学基金项目《量子计算和量子信息中的算子论和算子代数方法》(第二人, 28万元, 2009.1-2011.12),主持国家自然科学基金资助项目《量子态分类与量子绝热逼近中的算子论方法》(No. 11371012, 2014.01-2017.12, 62万元)。 合作完成的科研成果4次获陕西省科技进步奖,主持完成科研成果《泛函分析中若干问题的研究》获2012年陕西省科学技术奖(三等)。2010年11月获宝钢优秀教师奖。中国数学会会员、中国工业与应用数学会员、国际量子结构学会(IQSA)会员。国际开源期刊《Chinese Journal of Mathematics》编委。
提出并研究了C*-代数上的广义迹理论;提示了算子论与小波分析之间的内在联系;给出了Lipschitz-α算子的若干性质;建立了非线性Lipschitz算子的M-谱理论;证明了Riesz函数演算的Lipschitz性质;解决了Lipschitz-算子的延拓问题;提出并研究了非交换Lipschitz-α算子代数;提出了抽象Hilbert空间的中多分辨分析、Reisz小波与正交小波向量的概念;建立了Banach空间上的算子框架理论;建立了C*-代数Mn(A)上矩阵迹的一些不等式;提出了抽象效应代数的分类思想,建立了效应代数的表示理论;提出了复对偶量子计算机的数学模型,建立了广义对偶量子计算机的数学基础;得到了广义量子门可实现的充分必要条件与限制可允许广义量子门的数学基础;发现了量子绝热定理的量化条件及绝热逼近的误差估计;给出了PT-对称量子系统的绝热定理与绝热逼近定理及误差估计;揭示了保持经典量子关联的局部量子信道的一般形式;给出了三体量子态的分类文法;建立了非自伴Hamiltonian的CPT-Frames理论;建立了量子测度与矩阵的对应关系及相应特性;解决了多体量子态的关联分类问题; 建立了ε-近似保正交映射的稳定性与扰动定理;证明了Hilbert空间中有效序列的刻画与扰动定理。
陕西省教学名师,省级《分析学》教学团队、精品资源共享课程《复变函数论》、首批国家级一流课程主持人。
代表性学术论文
[1] Huaixin Cao, Chengyang Zhang, Zhihua Guo, Some measurement-based characterizations of separability of bipartite states, Int. J. Theor. Phys., 2021, 60: 2558-2572.
[2] Mohamed Ismael Ali, Huaixin Cao, Partial steerability and nonlocality of multipartite quantum states, Int. J. Theor. Phys., 2021, 60: 2543-2557.
[3] Yuxing Du, Zhihua Guo, Huaixin Cao, Kanyuan Han, Chuan Yang, Masking quantum information encoded in pure and mixed states, Int. J. Theor. Phys., 2021, 60: 2380-2399.
[4] QiaoWei Zhang, Zhihua Guo, Huaixin Cao, Mathematically proving Bell nonlocality motivated by the GHZ argument, IEEE Access, 2021, 9: 39550-3559.
[5] K. Y. Han, Z. H. Guo, H. X. Cao, Y. X. Du and C. Yang, Quantum multipartite maskers vs. quantum error-correcting codes, EPL, 2020, 131: 30005.
[6] 余雪晴, 肖书, 曹怀信, POVM测量组合的联合可测性及其应用, 中国科学: 物理学 力学 天文学, 2020, 50 070001.
[7] Chengyang Zhang, Zhihua Guo and Huaixin Cao, Symmetry-like relation of relative entropy measure of quantum coherence, Entropy 2020, 22: 297.
[8] Z.Z. Dong, Y. Yang, and H.X. Cao, Detecting Bell nonlocality based on the Hardy paradox, Int. J. Theor. Phys. 2020, 59, 1644-1656.
[9] Y. Yang, H. X. Cao, and Z. J. Zhang, Neural network representations of quantum many-body states, Sci. China-Phys. Mech. Astron. 2020, 63: 210312.
[10] Ying Yang, Huai-Xin Cao, Hui-Xian Meng, Robustness of ʌ-entanglement of multipartite states, Quantum Inf. Pross. 2019, 18: 360.
[11] Ying Yang, Chengyang Zhang and Huaixin Cao, Approximating ground states by neural network quantum states, Entropy, 2019, 21: 82.
[12] Zhihua Guo, Huaixin Cao, Creating quantum correlation from coherence via incoherent quantum operations, J. Phys. A: Math. Theor. 2019, 52: 265301.
[13] 刘洁,杨莹,肖书,曹怀信,三体量子系统中AB→C导引的探测,中国科学: 物理学 力学 天文学, 2019, 49: 120301.
[14] 黄永峰, 曹怀信,王文华,伪自伴量子系统的酉演化与绝热定理, 数学学报,2019,62(3): 469-478.
[15] 肖书, 郭志华, 曹怀信,三体量子系统的量子导引方案,中国科学: 物理学 力学 天文学,2019,49: 010301.
[16] Cao H X, Guo Z H, Characterizing Bell nonlocality and EPR steering, Sci. China-Phys. Mech. Astron., March, 2019,62: 030311.
[17] Chunming Zheng; Zhihua Guo; Huaixin Cao, Generalized steering robustness of quantum states, Int. J. Theor. Phys., 2018, 57: 1787-1801.
[18] Wang W H, Cao H X, Chen Z L, et al. Quantitative conditions for time evolution in terms of the von Neumann equation. Sci China-Phys Mech Astron, 2018, 61: 070312.
[19] Zi-Wei Li, Zhi-Hua Guo, Huai-Xin Cao, Some characterizations of EPR steering, Int. J. Theor. Phys., 2018, 57, 3285-3295.
[20] Ying Yang, Huaixin Cao, Einstein-Podolsky-Rosen steering inequalities and applications, Entropy, 2018, 20: 683.
[21] Ying Yang, Huaixin Cao, Separability criterions of multipartite states, Europ. Phys. J. D, 2018, 72: 143.
[22] Ying Yang, Huai-Xin Cao, Liang Chen, Yongfeng Huang, Λ-Nonlocality of multipartite states and the related nonlocality inequalities, Int. J. Theor. Phys., 2018, 57: 1498-1515
[23] 杨莹, 曹怀信, 构造纠缠目击的一般方法, 物理学报, 2018, 67: 070303
[24] Meng Huixian, Cao Huaixin, Wang Wenhua, Fan Yajing, Chen Liang, A more efficient contextuality distillation protocol, Int. J. Theor. Phys., 2018, 57: 792-803.
[25] H. X. Cao, von Neumann measurement-related matrices, Sci. China-Phys. Mech. Astron. 2017, 60(2): 020332.
[26] J. Li, H.X. Cao, A new generalization of von Neumann relative entropy, Int. J. Theor. Phys., 2017, 56: 3405-3424.
[27] Liang Chen, Huixian Meng, Huaixin Cao, Yongfeng Huang, Ying Yang, A note on markovian quantum dynamics,ANZIAM J., 2017, 58(3-4): 436-445.
[28] Meng Hui-xian, Cao Huai-xin, Wang Wen-hua, Ya-jing Fan, Liang Chen, Quantifying contextuality of empirical models in terms of trace-distance, Int. J. Theor. Phys., 2017, 56: 1807-1830.
[29] Qian Feng, Zhihua Guo, Huaixin Cao, Witness for non-quasi maximally entangled states, Int. J. Theor. Phys., 2016, 55: 5202-5215.
[30] Huixian Meng, Huaixin Cao, Wenhua Wang, Yajing Fan and Liang Chen, Generalized robustness of contextuality, Entropy, 2016, 18: 297.
[31] Yajing Fan, Huaixin Cao, Quantifying correlations via the Wigner-Yanase-Dyson skew information, Int. J. Theor. Phys., 2016, 55: 3833-3858.
[32] Yajing Fan, Huaixin Cao, Huixian Meng, Liang Chen, An uncertainty relation in terms of generalized metric adjusted skew information and correlation measure, Quantum Inf. Process., 2016, 15: 5089-5106.
[33] Zhihua Guo, Huaixin Cao and Shixian Qu, Robustness of quantum correlations against linear noise, J. Phys. A: Math. Theor., 2016, 49: 195301.
[34] H. X. Meng, H. X. Cao, W. H. Wang, L. Chen, and Y. J. Fan, Continuity of the robustness of contextuality of empirical models, Sci. China-Phys. Mech. Astron., 2016, 59: 100311.
[35] H. X. Meng, H. X. Cao and W. H. Wang, The robustness of contextuality and the contextuality cost of empirical models, Sci. China-Phys. Mech. Astron., 2016, 59: 640303.
[36] Ya-Jing Fan, Huai-Xin Cao, Monotonicity of the unified quantum (r, s)-entropy and (r, s)-mutual information, Quantum Inf. Procss., 2015, 14: 4537-4555.
[37] Liang Chen, Huai-Xin Cao, Hui-Xian Meng, Generalized duality quantum computers acting on mixed states, Quantum Inf. Process., 2015, 14: 4351-4360.
[38] Qian Li, Huaixin Cao, Hongke Du, A generalization of Schrödinger’s uncertainty relation described by the Wigner-Yanase skew information, Quantum Inf. Process., 2015, 14: 1513-1522.
[39] Huai-Xin Cao, Zheng-Li Chen, Li Li, Bao-Min Yu, An applicable approximation method and its application,Acta Math. Sci., 2015, 35B: 1189-1202.
[40] Zhihua Guo, Huaixin Cao, Shixian Qu, Structures of three types of local quantum channels based on quantum correlations, Found. Phys., 2015, 45: 355-369.
[41] ZhiHua Guo, HuaiXin Cao, ShiXian Qu,Existence and construction of simultaneous cloning machines for mixed states,Sci. China-Phys., Mech. & Astron., 2015, 58: 040302.
[42] Wenhua Wang, Huaixin Cao, Ling Lu, Baomin Yu, An upper bound for the generalized adiabatic approximation error with a superposition initial state, Sci. China -Phys., Mech.& Astron., 2015, 58: 030001.
[43] Huaixin Cao, Dianhui Wang, Feilong Cao, An adiabatic quantum algorithm and its application to DNA motif model discovery, Information Sciences, 2015, 296: 275-281.
[44] Huaixin Cao, Feilong Cao, Dianhui Wang, Quantum artificial neural networks with applications, Information Sciences, 2015, 290: 1-6.
[45] Guo Z. H., Cao H. X., Qu S. X., Partial correlations in multipartite quantum systems, Information Sciences,2014,289: 262-272.
[46] 杨莹, 曹怀信, 李静, 两类可观测量的Bell不等式, 数学学报, 2014, 57: 473-484
[47] Huaixin Cao, Juncheng Yin, Zhihua Guo, Zhengli Chen, Local Lipschitz-α mappings and applications to sublinear expectations, Acta Math. Sinica, English Series, 2014, 30: 844-860.
[48] Guo Zhihua, Cao Huaixin, Lu Ling, Adiabatic approximation in PT-symmetric quantum mechanics, Sci China-Phys Mech Astron, 2014, 57: 1835-1839.
[49] Yu BaoMin, Cao HuaiXin, Guo ZhiHua, Wang WenHua, Computable upper bounds for the adiabatic approximation errors, Sci China-Phys Mech Astron, 2014, 57: 2031-2038.
[50] Wang WenHua, Guo ZhiHua, Cao HuaiXin, An upper bound for the adiabatic approximation error, Sci China-Phys Mech Astron, 2014, 57: 218-224.
[51] Wang WenHua, Cao HuaiXin, Guo ZhiHua, Yu Bao-Min, Separability of solutions to a Schrodinger equation, Commun. Theor. Phys. 2014, 62: 205-209.
[52] 曹怀信, 郭志华, 陈峥立, 张坤利, 效应代数的表示理论, 中国科学A, 2013, 43: 835-846.
[53] Wu Guochang, Huaixin Cao, Some characterizations of the wave packet frames in higher dimensions, Applied Mechanics and Materials, 2013, 427-429: 1528-1531.
[54] Huai-Xin Cao, Zhi-Hua Guo, Zheng-Li Chen, CPT-Frames for non-Hermitian Hamiltonians, Commun. Theor. Phys. 2013, 60: 328-334.
[55] 张坤利, 曹怀信, 郭志华, 效应代数上态的存在性, 数学学报, 2013, 56: 301-310. I
[56] Wen-Hua Wang, Huai-Xin Cao, An improved multiparty quantum secret sharing with Bell states and Bell measurement, Int. J. Theor. Phys., 2013, 52: 2099-2111.
[57] Huai-Xin Cao, Zhi-Hua Guo, Zheng-Li Chen, Wen-Hua Wang, Quantitative sufficient conditions for adiabatic approximation, Sci China-Phys Mech Astron, 2013, 56: 1401-1407.
[58] Huaixin Cao, Guilu Long, Zhihua Guo, Zhengli Chen, Mathematical theory of generalized duality quantum computers acting on vector-states, Int. J. Theor. Phys., 2013, 52: 1751-1767.
[59] Zhihua Guo and Huaixin Cao, Local quantum channels preserving classical correlations, J. Phys. A: Math. Theor., 2013, 46: 065303.
[60] Zhihua Guo, Huaixin Cao, A classification of correlations of tripartite mixed states, Int. J. Theor. Phys., 2013, 52:1768-1779.
[61] H. X. Cao, Z. L. Chen, Z. H. Guo, F. G. Ren, Complex duality quantum computers acting on pure and mixed states, Sci. China G, 2012, 55(12): 2452-2462.
[62] Zhihua Guo, Huaixin Cao, Zhengli Chen, Distinguishing classical correlations from quantum correlations, J. Phys. A: Math. Theor. 2012, 45: 145301.
[63] Zhihua Guo, Huaixin Cao, Existence and construction of a quantum channel with given inputs and outputs, Chinese Sci Bull., 2012, 57(33):4346-4350.
[64] 银俊成, 曹怀信, C*-代数上完全正映射的刻画, 应用数学, 2012, 25(2): 357-362.
[65] 曹怀信, 陈峥立, 郭志华, 张巧卫,效应代数的表示,中国科学A, 2011, 41: 279-286.
[66] 张邺, 曹怀信, 郭志华, 有限维张量积空间上的强可分算子, 数学学报, 2011, 54: 959-972.
[67] Guo Z H, Cao H X, Chen Z L, Yin Jun-Cheng, Operational properties and matrix representations of quantum measures, Chinese Sci. Bull., 2011, 56: 1671-1678.
出版教材专著
1. 曹怀信, 张建华, 陈峥立, 郭志华,《An Introduction to Complex Analysis》, 科学出版社,2019(普通高等教育“十三五”规划教材);
2. 曹怀信, 张建华, 陈峥立, 郭志华, 《实变函数与泛函分析》,科学出版社,2017(普通高等教育“十三五”规划教材);
3. 曹怀信,郭志华,《小波分析基础》, 科学出版社,2016 ;
4. 曹怀信(总主编),高俊勇(主编),《高等数学》(上、下册),吉林大学出版社,2009。
5. 曹怀信(主编),吴保卫,张建华,张永锋,胡洪平,陈峥立,周焕芹,《实变函数引论》(第二版),陕西师范大学出版总社有限公司,2008;
6. 曹怀信(主编),张建华,陈峥立,魏广生, 郭志华,《泛函分析引论》,陕西师范大学出版总社有限公司,2006;
7. 曹怀信(主编),张建华,陈峥立,任 芳,《An Introduction to Complex Analysis》,陕西师范大学出版总社有限公司,2006。
教育科研项目
1. 国家自然科学基金资助项目: 基于量子信息论的算子论与算子代数研究(10571113, 2006.01-2008.12, 26万), 项目主持人;
2. 国家自然科学基金资助项目: 量子态分类与量子绝热逼近中的算子论方法(11371012, 2014.01-2017.12.30,62万元, 主持人);
3. 国家自然科学基金资助项目: 神经网络量子态的构建及其量子关联性研究(11871318, 2019.01-2022.12,54万元, 主持人)。
教育科研奖励
1. 2020年获陕西省高等教育教学成果奖(二等奖,主持人);
2. 2016年获第十届陕西省高等学校教学名师奖;
3. 2016年被评为陕西省师德先进个人;
4. 2016年获2015年度 明德教师奖;
5. 2015年获陕西省人民政府教学成果奖(二等,第四人);
6. 2010年获宝钢优秀教师奖;
7. 科研成果《泛函分析中若干问题的研究》获2011年陕西高等学校科学技术奖(一等,完成人:曹怀信、张建华、杜鸿科、吴保卫、吉国兴、陈清江、陈峥立) ;
8. 科研成果《泛函分析中若干问题的研究》获2012年陕西省科学技术奖(三等,完成人:曹怀信、张建华、杜鸿科、吴保卫、吉国兴、陈清江、陈峥立);
9. 科研成果《基于算子理论的量子信息理论研究》获2017年陕西高等学校科学技术奖(二等,完成人:曹怀信,郭志华,陈峥立,王文华,张邺)。
讲授课程
本科生:《数学分析》、《复变函数》、《实变函数》
研究生:《泛函分析》、《现代分析》、《量子信息》