Fine-grained uncertainty relations for several quantum measurements

被引：0
作者：
Alexey E. Rastegin
机构：
[1] Irkutsk State University,Department of Theoretical Physics
来源：
Quantum Information Processing | 2015年 / 14卷
关键词：
Uncertainty principle; Spectral norm; State discrimination; Mutually unbiased measurements; Mutually biased bases;
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暂无
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学科分类号：
摘要：
We study fine-grained uncertainty relations for several quantum measurements in a finite-dimensional Hilbert space. The proposed approach is based on the exact calculation or estimation of the spectral norms of corresponding positive matrices. Fine-grained uncertainty relations of the state-independent form are derived for an arbitrary set of mutually unbiased bases. Such relations are extended with a recent notion of mutually unbiased measurements. The case of so-called mutually biased bases is considered in a similar manner. We also discuss a formulation of fine-grained uncertainty relations in the case of generalized measurements. The general approach is then applied to two measurements related to state discrimination. The case of three rank-one projective measurements is further examined in details. In particular, we consider fine-grained uncertainty relations for mutually unbiased bases in three-dimensional Hilbert space.
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页码：783 / 800
页数：17
相关论文
共 106 条
[1]  
Heisenberg W(1927)Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik Zeitschrift für Physik 43 172-198
[2]  
Robertson HP(1929)The uncertainty principle Phys. Rev. 34 163-164
[3]  
Mandilara A(2012)Quantum uncertainty relation saturated by the eigenstates of the harmonic oscillator Phys. Rev. A 86 030102(R)-132
[4]  
Cerf NJ(1975)Uncertainty relations for information entropy in wave mechanics Commun. Math. Phys. 44 129-633
[5]  
Białynicki-Birula I(1983)Uncertainty in quantum measurements Phys. Rev. Lett. 50 631-1106
[6]  
Mycielski J(1988)Generalized entropic uncertainty relations Phys. Rev. Lett. 60 1103-1074
[7]  
Deutsch D(2014)Noise and disturbance in quantum measurements: an information-theoretic approach Phys. Rev. Lett. 112 050401-640
[8]  
Maassen H(2012)Min-entropy uncertainty relation for finite-size cryptography Phys. Rev. A 86 042315-381
[9]  
Uffink JBM(2014)Improved entropic uncertainty relations and information exclusion relations Phys. Rev. A 89 022112-528
[10]  
Buscemi F(2010)Entropic uncertainty relations—a survey New J. Phys. 12 025009-101
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