Universal Uncertainty Relations

被引:147
作者
Friedland, Shmuel [1 ]
Gheorghiu, Vlad [2 ,3 ,4 ]
Gour, Gilad [2 ,3 ]
机构
[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA
[2] Univ Calgary, Inst Quantum Sci & Technol, Calgary, AB T2N 1N4, Canada
[3] Univ Calgary, Dept Math & Stat, Calgary, AB T2N 1N4, Canada
[4] Univ Waterloo, Inst Quantum Comp, Waterloo, ON N2L 3G1, Canada
基金
美国国家科学基金会; 加拿大自然科学与工程研究理事会;
关键词
ENTROPIC UNCERTAINTY; QUANTUM MEASUREMENTS; PRINCIPLE;
D O I
10.1103/PhysRevLett.111.230401
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Uncertainty relations are a distinctive characteristic of quantum theory that impose intrinsic limitations on the precision with which physical properties can be simultaneously determined. The modern work on uncertainty relations employs entropic measures to quantify the lack of knowledge associated with measuring noncommuting observables. However, there is no fundamental reason for using entropies as quantifiers; any functional relation that characterizes the uncertainty of the measurement outcomes defines an uncertainty relation. Starting from a very reasonable assumption of invariance under mere relabeling of the measurement outcomes, we show that Schur-concave functions are the most general uncertainty quantifiers. We then discover a fine-grained uncertainty relation that is given in terms of the majorization order between two probability vectors, significantly extending a majorization-based uncertainty relation first introduced in M. H. Partovi, Phys. Rev. A 84, 052117 (2011). Such a vector-type uncertainty relation generates an infinite family of distinct scalar uncertainty relations via the application of arbitrary uncertainty quantifiers. Our relation is therefore universal and captures the essence of uncertainty in quantum theory.
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页数:5
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