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Advances in quantum technologies are giving rise to a revolution in the way fundamental physics questions are explored at the empirical level. At the same time, they are the seeds for future disruptive technological applications of quantum physics. Remarkably, a space-based environment may open many new avenues for exploring and employing quantum physics and technologies. Recently, space missions employing quantum technologies for fundamental or applied studies have been proposed and implemented with stunning results. The combination of quantum physics and its space application is the focus of this review: we cover both the fundamental scientific questions that can be tackled with quantum technologies in space and the possible implementation of these technologies for a variety of academic and commercial purposes., peer-reviewed

We derive a general quantum master equation for the dynamics of a scalar bosonic particle interacting with a weak, stochastic and classical external gravitational field. The dynamics predicts decoherence in position, momentum and energy. We show how our master equation reproduces the results present in the literature by taking appropriate limits, thus explaining the apparent contradiction in their dynamical description. Our result is relevant in light of the increasing interest in the low energy quantum-gravity regime., 12 pages. Improved version. Fixed typos. Added Appendices

We consider open quantum systems with factorized initial states, providing the structure of the reduced system dynamics, in terms of environment cumulants. We show that such completely positive (CP) and trace-preserving (TP) maps can be unraveled by linear stochastic Schr\"odinger equations (SSEs) characterized by sets of colored stochastic processes (with $n\mathrm{th}$-order cumulants). We obtain both the conditions such that the SSEs provide CPTP dynamics and those for unraveling an open system dynamics. We then focus on Gaussian non-Markovian unravelings, whose known structure displays a functional derivative. We provide a description that replaces the functional derivative with a recursive operatorial structure. Moreover, for the family of quadratic bosonic Hamiltonians, we are able to provide an explicit operatorial dependence for the unraveling.

We consider a general open system dynamics and we provide a recursive method to derive the associated non-Markovian master equation in a perturbative series. The approach relies on a momenta expansion of the open system evolution. Unlike previous perturbative approaches of this kind, the method presented in this paper provides a recursive definition of each perturbative term. Furthermore, we give an intuitive diagrammatic description of each term of the series, which pro- vides an useful analytical tool to build them and to derive their structure in terms of commutators and anticommutators. We eventually apply our formalism to the evolution of the observables of the reduced system, by showing how the method can be applied to the adjoint master equation, and by developing a diagrammatic description of the associated series., Comment: 9 pages

Starting from an idea of S.L. Adler~\cite{Adler2015}, we develop a novel model of gravity-induced spontaneous wave-function collapse. The collapse is driven by complex stochastic fluctuations of the spacetime metric. After deriving the fundamental equations, we prove the collapse and amplification mechanism, the two most important features of a consistent collapse model. Under reasonable simplifying assumptions, we constrain the strength $\xi$ of the complex metric fluctuations with available experimental data. We show that $\xi\geq 10^{-26}$ in order for the model to guarantee classicality of macro-objects, and at the same time $\xi \leq 10^{-20}$ in order not to contradict experimental evidence. As a comparison, in the recent discovery of gravitational waves in the frequency range 35 to 250 Hz, the (real) metric fluctuations reach a peak of $\xi \sim 10^{-21}$., Comment: 9 pages , 1 figure