Uncertainty principle and quantum Fisher information

被引：0

作者：

Paolo Gibilisco

Tommaso Isola

机构：

[1] Università di Roma “Tor Vergata”,Dipartimento SEFEMEQ and Centro V.Volterra, Facoltà di Economia

[2] Università di Roma “Tor Vergata”,Dipartimento di Matematica

来源：

Annals of the Institute of Statistical Mathematics | 2007年 / 59卷

关键词：

Uncertainty principle; Monotone metrics; Quantum Fisher information; Wigner–Yanase–Dyson information;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

A family of inequalities, related to the uncertainty principle, has been recently proved by S. Luo, Z. Zhang, Q. Zhang, H. Kosaki, K. Yanagi, S. Furuichi and K. Kuriyama. We show that the inequalities have a geometric interpretation in terms of quantum Fisher information. Using this formulation one may naturally ask if this family of inequalities can be further extendend, for example to the RLD quantum Fisher information. We show that this is impossible by producing a family of counterexamples.

引用

页码：147 / 159

页数：12

共 24 条

[1]

Araki H.(1960)Measurement of quantum mechanical operators Physical Review 120 622-626

[2]

Yanase M.M.(1978)Homogeneity of the state space of factors of type Journal of Functional Analysis 28 187-196

[3]

Connes A.(2003)Wigner-Yanase information on quantum state space: the geometric approach Journal of Mathematical Physics 44 3752-3762

[4]

Størmer E.(2004)On the characterisation of paired monotone metrics Annals of the Institute of Statistical Mathematics 56 369-381

[5]

Gibilisco P.(2005)On the monotonicity of scalar curvature in classical and quantum information geometry Journal of Mathematical Physics 46 023501-14

[6]

Isola T.(1982)Interpolation theory and the Wigner–Yanase–Dyson–Lieb concavity Communications in Mathematical Physics, 87 315-329

[7]

Gibilisco P.(2005)Matrix trace inequalities related to uncertainty principle International Journal of Mathematics 6 629-645

[8]

Isola T.(2004)On skew information IEEE Transactions on Information Theory 50 1778-1782

[9]

Gibilisco P.(2004)An informational characterization of Schrödinger’s uncertainty relations Journal of Statistical Physics 114 1557-1576

[10]

Isola T.(2002)Conservation laws, uncertainty relations and quantum limits of measurement Physical Review Letters 88 050402-4

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