期刊
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
卷 55, 期 26, 页码 -出版社
IOP Publishing Ltd
DOI: 10.1088/1751-8121/ac71eb
关键词
incompatibility; commutativity; joint measurability; quantum mea-surements; observables; non-commutativity
资金
- Foundation for Polish Science - European Union under the European Regional Development Fund
The existence of incompatible measurements is an important distinction between quantum mechanics and classical theories, but it is also a necessary ingredient for achieving quantum advantage. To quantify incompatibility, a family of incompatibility measures based on non-commutativity is defined and explored. The basic properties of these measures are investigated, and the pairs achieving the highest incompatibility are fully characterized.
The existence of incompatible measurements, i.e. measurements which cannot be performed simultaneously on a single copy of a quantum state, constitutes an important distinction between quantum mechanics and classical theories. While incompatibility might at first glance seem like an obstacle, it turns to be a necessary ingredient to achieve the so-called quantum advantage in various operational tasks like random access codes or key distribution. To improve our understanding of how to quantify incompatibility of quantum measurements, we define and explore a family of incompatibility measures based on non-commutativity. We investigate some basic properties of these measures, we show that they satisfy some natural information-processing requirements and we fully characterize the pairs which achieve the highest incompatibility (in a fixed dimension). We also consider the behavior of our measures under different types of compositions. Finally, to link our new measures to existing results, we relate them to a robustness-based incompatibility measure and two operational scenarios: random access codes and entropic uncertainty relations.
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