Colloquium: Incompatible measurements in quantum information science

Some measurements in quantum mechanics disturb each other. This has puzzled physicists since the formulation of the theory, but only in recent decades has the incompatibility of measurements been analyzed in depth and detail, using the notion of joint measurability of generalized measurements. In this Colloquium joint measurability and incompatibility are reviewed from the perspective of quantum information science. The Colloquium starts by discussing the basic definitions and concepts. An overview on applications of incompatibility, such as in measurement uncertainty relations, the characterization of quantum correlations, or information processing tasks like quantum state discrimination, is then presented. Finally, emerging directions of research, such as a resource theory of incompatibility as well as other concepts to grasp the nature of measurements in quantum mechanics, are discussed.

Automated summary

The incompatibility of measurements in quantum mechanics has puzzled physicists for a long time. In recent decades, the concept of joint measurability has been used to analyze this issue in depth. This colloquium reviews the basic definitions and concepts of joint measurability and incompatibility and discusses their applications in various areas of quantum information science. It also explores emerging directions of research in understanding the nature of measurements in quantum mechanics, such as a resource theory of incompatibility.