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The Horizon Quantum Mechanics is an approach that allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the (global) formalism and show how it reproduces a gravitationally inspired GUP relation. This results leads to unacceptably large fluctuations in the horizon size of astrophysical black holes if one insists in describing them as (smeared) central singularities. On the other hand, if they are extended systems, like in the corpuscular models, no such issue arises and one can in fact extend the formalism to include asymptotic mass and angular momentum with the harmonic model of rotating corpuscular black holes. The Horizon Quantum Mechanics then shows that, in simple configurations, the appearance of the inner horizon is suppressed and extremal (macroscopic) geometries seem disfavoured. [ABSTRACT FROM AUTHOR]

Often it is assumed that a quantum state or a phase-space distribution must be normalizable. Here it is shown that even if it is not normalizable, one may be able to extract normalized observational probabilities from it. [ABSTRACT FROM AUTHOR]

We clarify the significance of quasiprobability (QP) in quantum mechanics that is relevant in describing physical quantities associated with a transition process. Our basic quantity is Aharonov's weak value, from which the QP can be defined up to a certain ambiguity parameterized by a complex number. Unlike the conventional probability, the QP allows us to treat two noncommuting observables consistently, and this is utilized to embed the QP in Bohmian mechanics such that its equivalence to quantum mechanics becomes more transparent. We also show that, with the help of the QP, Bohmian mechanics can be recognized as an ontological model with a certain type of contextuality. [ABSTRACT FROM AUTHOR]

Following a proposal of Vaidman (Int Stud Philos Sci 12:245-261, ) (in: Zalta EN (ed) The Stanford encyclopaedia of philosophy, ) (in: Ben-Menahem Y, Hemmo M (ed) The probable and the improbable: understanding probability in physics, essays in memory of Itamar Pitowsky, ), Sebens and Carroll (Quantum theory: a two-time success story ), (arXiv preprint ) have argued that in Everettian (i.e. purely unitary) quantum theory, observers are uncertain, before they complete their observation, about which Everettian branch they are on. They argue further that this solves the problem of making sense of probabilities within Everettian quantum theory, even though the theory itself is deterministic. We note some problems with these arguments. [ABSTRACT FROM AUTHOR]