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;
D O I：
暂无
中图分类号：
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
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