Related papers: Uses of a Quantum Master Inequality
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative point of view in which…
Quantum mechanics is very odd. It presents both an immensely practical and a deeply troubling conception of the physical world. As such, its uses stretch from optimizing nanoelectronics to examining the very nature of reality. In this…
Recently Kosaki proved an inequality for matrices that can be seen as a kind of new uncertainty principle. Independently, the same result was proved by Yanagi, Furuichi and Kuriyama. The new bound is given in terms of Wigner-Yanase-Dyson…
Quantum theory violates Bell's inequality, but not to the maximum extent that is logically possible. We derive inequalities (generalizations of Cirel'son's inequality) that quantify the upper bound of the violation, both for the standard…
The phenomenon of universality is one of the most striking in many-body physics. Despite having sometimes wildly different microscopic constituents, systems can nonetheless behave in precisely the same way, with only the variable names…
That gravitation can be understood as purely metric phenomenon depends crucially on the validity of a number of hypotheses which are summarised by the Einstein Equivalence Principle, the least well tested part of which being the…
The formalism of quantum mechanics produces spectacular results, but its rules, its parameters are empirical, either deduced from classical physics, or from experimental results rather than from the postulates. Thus, quantum mechanics is…
A formulation of quantum mechanics based on an operational definition of state is presented. This formulation, which includes explicitly the macroscopic systems, assumes the probabilistic interpretation and is nevertheless objective. The…
Since the beginning of quantum mechanics, many puzzling phenomena which distinguish the quantum from the classical world, have appeared such as complementarity, entanglement or contextuality. All of these phenomena are based on the…
Various inequalities (Boole inequality, Chung-Erd\"os inequality, Frechet inequality) for Kolmogorov (classical) probabilities are considered. Quantum counterparts of these inequalities are introduced, which have an extra `quantum…
Quantum data processing inequality bounds the set of bipartite states that can be generated by two far apart parties under local operations; Having access to a bipartite state as a resource, two parties cannot locally transform it to…
The study of measurements in quantum mechanics exposes many of the ways in which the quantum world is different. For example, one of the hallmarks of quantum mechanics is that observables may be incompatible, implying among other things…
Quantum steering is the ability to remotely prepare different quantum states by using entangled pairs as a resource. Very recently, the concept of steering has been quantified with the use of inequalities, leading to substantial…
Gravitation, according to General Relativity, is an attribute of space-time's geometry and hence not a force in the Newtonian sense. This is a consequence of Einstein's equivalence principle, which so far passed all experimental tests with…
The distinction between pure states and mixed states is a kernel ingredient of what is considered to be the standard formulation of quantum mechanics and plays today a kernel role in foundational debates about the meaning of quantum…
In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat…
In the first part of this thesis Bell's theorem is revisited. It points at a difference between the quantum and the classical world. This difference is often behind the advantages of solutions using quantum mechanics. New and more general…
We consider two variants of a quantum-statistical generalization of the Cramer-Rao inequality that establishes an invariant lower bound on the mean square error of a generalized quantum measurement. The proposed complex variant of this…
Validity of just a few physical conditions comprising the Einstein Equivalence Principle (EEP) suffices to ensure that gravity can be understood as space-time geometry. EEP is therefore subject to an ongoing experimental verification, with…
The status of locality in quantum mechanics is analyzed from a nonstandard point of view. It is assumed that quantum states are relative, they depend on and are defined with respect to some bigger physical system which contains the former…