Generalized probabilities in statistical theories

In this review article we present different formal frameworks for the description of generalized probabilities in statistical theories. We discuss the particular cases of probabilities appearing in classical and quantum mechanics, possible generalizations of the approaches of A. N. Kolmogorov and R. T. Cox to non-commutative models, and the approach to generalized probabilities based on convex sets

Generalizing entanglement via informational invariance for arbitrary statistical theories

Given an arbitrary statistical theory, different from quantum mechanics, how to decide which are the nonclassical correlations? We present a formal framework which allows for a definition of nonclassical correlations in such theories, alternative to the current one. This enables one to formulate extrapolations of some important quantum mechanical features via adequate extensions of reciprocal maps relating states of a system with states of its subsystems. These extended maps permit one to generalize i) separability measures to any arbitrary statistical model as well as ii) previous entanglement criteria. The standard definition of entanglement becomes just a particular case of the ensuing, more general notion.Comment: Improved versio

Indistinguishability right from the start in standard quantum mechanics

We discuss a reconstruction of standard quantum mechanics assuming indistinguishability right from the start, by appealing to quasi-set theory. After recalling the fundamental aspects of the construction and introducing some improvements in the original formulation, we extract some conclusions for the interpretation of quantum theory

Generalized coherence vector applied to coherence transformations and quantifiers

One of the main problems in any quantum resource theory is the characterization of the conversions between resources by means of the free operations of the theory. In this work, we advance on this characterization within the quantum coherence resource theory by introducing the generalized coherence vector of an arbitrary quantum state. The generalized coherence vector is a probability vector that can be interpreted as a concave roof extension of the pure states coherence vector. We show that it completely characterizes the notions of being incoherent, as well as being maximally coherent. Moreover, using this notion and the majorization relation, we obtain a necessary condition for the conversion of general quantum states by means of incoherent operations. These results generalize the necessary conditions of conversions for pure states given in the literature, and show that the tools of the majorization lattice are useful also in the general case. Finally, we introduce a family of coherence quantifiers by considering concave and symmetric functions applied to the generalized coherence vector. We compare this proposal with the convex roof measure of coherence and others quantifiers given in the literature.Comment: 21 pages, 2 figures (close to the published version

On the lattice structure of probability spaces in quantum mechanics

Let C be the set of all possible quantum states. We study the convex subsets of C with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models' approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics.Comment: arXiv admin note: substantial text overlap with arXiv:1008.416

Prospects for K+→π+ννˉK^+ \to \pi^+ \nu \bar{ \nu } at CERN in NA62

The NA62 experiment will begin taking data in 2015. Its primary purpose is a 10% measurement of the branching ratio of the ultrarare kaon decay $K^+ \to \pi^+ \nu \bar{ \nu }$, using the decay in flight of kaons in an unseparated beam with momentum 75 GeV/c.The detector and analysis technique are described here.Comment: 8 pages for proceedings of 50 Years of CP

Post-LS3 Experimental Options in ECN3

The Experimental Cavern North 3 (ECN3) is an underground experimental cavern on the CERN Pr\'evessin site. ECN3 currently hosts the NA62 experiment, with a physics programme devoted to rare kaon decays and searches of hidden particles approved until Long Shutdown 3 (LS3). Several options are proposed on the longer term in order to make best use of the worldwide unique potential of the high-intensity/high-energy proton beam extracted from the Super Proton Synchrotron (SPS) in ECN3. The current status of their study by the CERN Physics Beyond Colliders (PBC) Study Group is presented, including considerations on beam requirements and upgrades, detector R&D and construction, schedules and cost, as well as physics potential within the CERN and worldwide landscape.Comment: 113 pages, 39 figure

Workshop summary -- Kaons@CERN 2023

Kaon physics is at a turning point -- while the rare-kaon experiments NA62 and KOTO are in full swing, the end of their lifetime is approaching and the future experimental landscape needs to be defined. With HIKE, KOTO-II and LHCb-Phase-II on the table and under scrutiny, it is a very good moment in time to take stock and contemplate about the opportunities these experiments and theoretical developments provide for particle physics in the coming decade and beyond. This paper provides a compact summary of talks and discussions from the Kaons@CERN 2023 workshop.Comment: 54 pages, Summary of Kaons@CERN 23 workshop, references and clarifications adde