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In this thesis, we consider the properties of measurements in quantum theory and other operational theories. After having introduced the framework of operational theories, we consider a communication scheme based on an experimental…
The problem of deciding whether a set of quantum measurements is jointly measurable is known to be equivalent to determining whether a quantum assemblage is unsteerable. This problem can be formulated as a semidefinite program (SDP).…
Quantum coherence and quantum correlations lie in the center of quantum information science, since they both are considered as fundamental reasons for significant features of quantum mechanics different from classical mechanics. We present…
We introduce a new way of quantifying the degrees of incompatibility of two ob- servables in a probabilistic physical theory and, based on this, a global measure of the degree of incompatibility inherent in such theories, across all…
Measurements in quantum theory can fail to be jointly measurable. Like entanglement, this incompatibility of measurements is necessary but not sufficient for violating Bell inequalities. The (in)compatibility relations among a set of…
The fact that not all measurements can be carried out simultaneously is a peculiar feature of quantum mechanics and responsible for many key phenomena in the theory, such as complementarity or uncertainty relations. For the special case of…
The existence of incompatible measurements, epitomized by Heisenberg's uncertainty principle, is one of the distinctive features of quantum theory. So far, quantum incompatibility has been studied for measurements that test the preparation…
Bohr's principle of complementarity, prohibiting simultaneous access to certain physical properties within a single experimental arrangement, is considered to be a defining feature of quantum mechanics. It is commonly viewed as inducing an…
We propose a class of incompatibility measures for quantum observables based on quantifying the effect of a measurement of one observable on the statistics of the outcomes of another. Specifically, for a pair of observables $A$ and $B$ with…
Incompatible measurements, i.e., measurements that cannot be simultaneously performed, are necessary to observe nonlocal correlations. It is natural to ask, e.g., how incompatible the measurements have to be to achieve a certain violation…
Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of…
How well can multiple incompatible observables be implemented by a single measurement? This is a fundamental problem in quantum mechanics with wide implications for the performance optimization of numerous tasks in quantum information…
Recently a problem concerning the equivalence of joint measurability and coexistence of quantum observables was solved [15]. In this paper we generalize two known joint measurability results from sharp observables to the class of extreme…
The incompatibility of the measurements constraints the achievable precisions in multi-parameter quantum estimation. Understanding the tradeoff induced by such incompatibility is a central topic in quantum metrology. Here we provide an…
Incompatibility of quantum measurements is of fundamental importance in quantum mechanics. It is closely related to many nonclassical phenomena such as Bell nonlocality, quantum uncertainty relations, and quantum steering. We study the…
Three notions of complementarity - operational, probabilistic, and value complementarity - are reanalysed with respect to the question of joint measurements and compared with reference to some examples of canonically conjugate observables.…
A robustness measure for incompatibility of quantum devices in the lines of the robustness of entanglement is proposed. The concept of general robustness measures is first introduced in general convex-geometric settings and these ideas are…
Pivotal within quantum physics, the concept of quantum incompatibility is generally related to algebraic aspects of the formalism, such as commutation relations and unbiasedness of bases. Recently, the concept was identified as a resource…
In many a traditional physics textbook, a quantum measurement is defined as a projective measurement represented by a Hermitian operator. In quantum information theory, however, the concept of a measurement is dealt with in complete…
In this contribution I review rigorous formulations of a variety of limitations of measurability in quantum mechanics. To this end I begin with a brief presentation of the conceptual tools of modern measurement theory. I will make precise…