Mathematical Research of Quantum Information and Quantum Computing
量子信息与量子计算的数学研究
基本信息
- 批准号:14340028
- 负责人:
- 金额:$ 7.3万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (B)
- 财政年份:2002
- 资助国家:日本
- 起止时间:2002 至 2004
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
1.Heisenberg's uncertainty principle, which gives the trade-off between measurement noise and disturbance, has been reconsidered. Its limitation of the validity has been clarified and the universally valid generalization (universal uncertainty principle) has been established. If any measuring apparatus measures an observable A with noise ε(A) and disturbance η(B) on B, we have the relation ε(A)η(B)+ε(A)σ(B)+σ(A)η(B)≧(1/2)|<[A,B]>|, where σ stands for the standard deviation in the state just before the measurement.2.It has been shown that, if the noise ε(A) and the disturbance η(B) are statistically independent from the initial state of the measured object, we have the original Heisenberg relation ε(A)η(B)≧(1/2)|<[A,B]>|.3.From the universal uncertainty principle, Wigner-Araki-Yanase (WAY), found in 1952 to set a limitation of measurements under conservation law, has been quantitatively generalized to a reciprocal relation between the mean-square-noise of the measurement and the variance of the conserved quantity.4.As a consequence from the universal uncertainty principle, it has been shown that the angular momentum conservation law sets a limitation to the accuracy of quantum gate operations, the accuracy of the CNOT gate controlled by an interaction with n qubit ancilla system is limited with error probability at least 1/(4n^2), and the CNOT controlled by the electro-magnetic field with average photon N is limited with error probability at least 1/(16N).
1.重新考虑了海森堡测不准原理,该原理给出了测量噪声和干扰之间的权衡。澄清了其有效性的局限性,建立了普遍有效的概括(普遍不确定性原理)。如果任何测量仪器测量到一个具有噪声ε(A)和扰动η(B)的可观测A,我们有ε(A)η(B)+ε(A)σ(B)+σ(A)η(B)≧(1/2)|<[A,B]>|的关系式,其中σ表示测量前状态的标准差。结果表明,如果噪声ε(A)和扰动η(B)在统计上与被测物体的初始状态无关,则得到原始海森堡关系ε(A)η(B)≧(1/2)|<[A,B]>|.3。1952年发现的Wigner-Araki-Yanase (WAY)从普遍的测不准原理出发,设定了守恒定律下测量的限制,并将其定量地推广为测量的均方噪声与守恒量的方差之间的反比关系。由普遍不确定性原理可知,角动量守恒定律对量子门操作精度有限制,与n个量子比特辅助系统相互作用控制的CNOT门精度有限制,误差概率至少为1/(4n^2),平均光子n的电磁场控制的CNOT门精度有限制,误差概率至少为1/(16N)。
项目成果
期刊论文数量(217)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
UNCERTAINTY PRINCIPLE FOR QUANTUM INSTRUMENTS AND COMPUTING
- DOI:10.1142/s0219749903000437
- 发表时间:2003-10
- 期刊:
- 影响因子:1.2
- 作者:M. Ozawa
- 通讯作者:M. Ozawa
Universal uncertainty principle and quantum state control under conservation laws
守恒定律下的普遍不确定性原理和量子态控制
- DOI:
- 发表时间:2004
- 期刊:
- 影响因子:0
- 作者:M.Hotta;T.Karasawa;M.Ozawa;M.Ozawa
- 通讯作者:M.Ozawa
Free transportation cost inequalities via random matrix approximation,
通过随机矩阵近似消除运输成本不等式,
- DOI:
- 发表时间:2004
- 期刊:
- 影响因子:0
- 作者:F.Hiai;D.Petz;Y.Ueda
- 通讯作者:Y.Ueda
Computation of Iwasawa invariants
Iwasawa 不变量的计算
- DOI:
- 发表时间:2002
- 期刊:
- 影响因子:0
- 作者:H.Taya;T.Fukuda
- 通讯作者:T.Fukuda
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OZAWA Masanao其他文献
OZAWA Masanao的其他文献
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{{ truncateString('OZAWA Masanao', 18)}}的其他基金
Study of Quantum Foundations and Quantum Set Theory
量子基础和量子集合论研究
- 批准号:
17K19970 - 财政年份:2017
- 资助金额:
$ 7.3万 - 项目类别:
Grant-in-Aid for Challenging Research (Exploratory)
Study of the Probabilistic Interpretation of Quantum Set Theory
量子集合论的概率解释研究
- 批准号:
15K13456 - 财政年份:2015
- 资助金额:
$ 7.3万 - 项目类别:
Grant-in-Aid for Challenging Exploratory Research
Mathematical Studies of Fundamental Principles of Quantum Theory
量子理论基本原理的数学研究
- 批准号:
26247016 - 财政年份:2014
- 资助金额:
$ 7.3万 - 项目类别:
Grant-in-Aid for Scientific Research (A)
Study of Quantum Set Theory Aiming at an Interpretation of Elements of Reality in Quantum Theory
旨在解释量子理论中现实元素的量子集合论研究
- 批准号:
24654021 - 财政年份:2012
- 资助金额:
$ 7.3万 - 项目类别:
Grant-in-Aid for Challenging Exploratory Research
Quantum Set Theory Aiming at Realistic Interpretation of Quantum Theory
量子集合论旨在现实地解释量子理论
- 批准号:
22654013 - 财政年份:2010
- 资助金额:
$ 7.3万 - 项目类别:
Grant-in-Aid for Challenging Exploratory Research
Mathematical study of quantum information
量子信息的数学研究
- 批准号:
21244007 - 财政年份:2009
- 资助金额:
$ 7.3万 - 项目类别:
Grant-in-Aid for Scientific Research (A)
Mathematical Research on Mathematical Models of Quantum Computing
量子计算数学模型的数学研究
- 批准号:
11440028 - 财政年份:1999
- 资助金额:
$ 7.3万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Unitary Representations of Hyperfinite Heisenberg Groups and Their Applications to Quantum Physics
超有限海森堡群的酉表示及其在量子物理中的应用
- 批准号:
08454039 - 财政年份:1996
- 资助金额:
$ 7.3万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
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