Observability of spontaneous collapse in flavor oscillations and its relation to the CP and CPT symmetries

Spontaneous collapse models aim at solving the measurement problem of quantum mechanics by introducing collapse of wave function as an ontologically objective mechanism that suppresses macroscopic superpositions. In particular, the strength of collapse depends on the mass of the system. Flavor oscillating systems such as neutral mesons feature superpositions of states of different masses and, hence, could be used to test the validity of spontaneous collapse models. Recently, it has been shown that the mass-proportional CSL model causes exponential damping of the neutral meson oscillations which, however, is not strong enough to be observed in the present accelerator facilities. In this Letter, we study how the violation of the $\mathcal{CP}$ symmetry in mixing changes the spontaneous collapse effect on flavor oscillations and its observability.Comment: 8 pages, 1 figur

Infinitesimal and Infinite Numbers as an Approach to Quantum Mechanics

Non-Archimedean mathematics is an approach based on fields which contain infinitesimal and infinite elements. Within this approach, we construct a space of a particular class of generalized functions, ultrafunctions. The space of ultrafunctions can be used as a richer framework for a description of a physical system in quantum mechanics. In this paper, we provide a discussion of the space of ultrafunctions and its advantages in the applications of quantum mechanics, particularly for the Schr\"{o}dinger equation for a Hamiltonian with the delta function potential.Comment: 18 pages, 2 figure

A characterization of singular Schr\"odinger operators on the half-line

We study a class of delta-like perturbations of the Laplacian on the half-line, characterized by Robin boundary conditions at the origin. Using the formalism of nonstandard analysis, we derive a simple connection with a suitable family of Schr\"{o}dinger operators with potentials of very large (infinite) magnitude and very short (infinitesimal) range. As a consequence, we also derive a similar result for point interactions in the Euclidean space $\mathbb{R}^3$, in the case of radial potentials. Moreover, we discuss explicitly our results in the case of potentials that are linear in a neighbourhood of the origin.Comment: 16 page

Ergotropy from indefinite causal orders

We characterize the impact that the application of two consecutive quantum channels or their quantum superposition (thus, without a definite causal order) has on ergotropy, i.e. the maximum work that can be extracted from a system through a cyclic unitary transformation. First of all, we show that commutative channels always lead to a non-negative gain; non-commutative channels, on the other hand, can entail both an increase and a decrease in ergotropy. We then perform a thorough analysis for qubit channels and provide general conditions for achieving a positive gain on the incoherent part of ergotropy. Finally, we extend our results to d-dimensional quantum systems undergoing a pair of completely depolarizing channels.Comment: 8 pages, 2 figure

Measuring incompatibility and clustering quantum observables with a quantum switch

The existence of incompatible observables is a cornerstone of quantum mechanics and a valuable resource in quantum technologies. Here we introduce a measure of incompatibility, called the mutual eigenspace disturbance (MED), which quantifies the amount of disturbance induced by the measurement of a sharp observable on the eigenspaces of another. The MED provides a metric on the space of von Neumann measurements, and can be efficiently estimated by letting the measurement processes act in an indefinite order, using a setup known as the quantum switch, which also allows one to quantify the noncommutativity of arbitrary quantum processes. Thanks to these features, the MED can be used in quantum machine learning tasks. We demonstrate this application by providing an unsupervised algorithm that clusters unknown von Neumann measurements. Our algorithm is robust to noise can be used to identify groups of observers that share approximately the same measurement context.Comment: 14 pages, 2 figure

No-signaling-in-time as a condition for macrorealism: the case of neutrino oscillations

Abstract We consider two necessary and sufficient conditions for macrorealism recently appeared in the literature, known as no-signaling-in-time and arrow-of-time conditions, respectively, and study them in the context of neutrino flavor transitions, within both the plane wave description and the wave packet approach. We then compare the outcome of the above investigation with the implication of various formulations of Leggett–Garg inequalities. In particular, we show that the fulfillment of the addressed conditions for macrorealism in neutrino oscillations implies the fulfillment of the Leggett–Garg inequalities, whereas the converse is not true. Finally, in the framework of wave packet approach, we also prove that, for distances longer than the coherence length, the no-signaling-in-time condition is always violated whilst the Leggett–Garg inequalities are not

The Quantum Internet: Enhancing Classical Internet Services one Qubit at a Time

Nowadays, the classical Internet has mainly envisioned as the underlying communication infrastructure of the Quantum Internet, aimed at providing services such as signaling and coordination messages. However, the interplay between classical and Quantum Internet is complex and its understanding is pivotal for an effective design of the Quantum Internet protocol stack. The aim of the paper is to shed the light on this interplay, by highlighting that such an interplay is indeed bidirectional rather than unidirectional. And the Quantum Internet exhibits the potential of supporting and even enhancing classical Internet functionalities