We study the entanglement entropy of the quantum trajectories of a free fermion chain under continuous monitoring of local occupation numbers. We propose a simple theory for entanglement entropy evolution from disentangled and highly excited initial states. It is based on generalized hydrodynamics and the quasiparticle pair approach to entanglement in integrable systems. We test several quantitative predictions of the theory against extensive numerics and find good agreement. In particular, the volume law entanglement is destroyed by the presence of arbitrarily weak measurement.

The possibility that a classical space-time and quantum matter cohabit at the deepest level, i.e. the possibility of having a fundamental and not phenomenological semiclassical gravity, is often disregarded for lack of a good candidate theory. The standard semiclassical theory suffers from fundamental inconsistencies (e.g.: Schrödinger cat sources, faster-than-light communication and violation of the Born rule) which can only be ignored in simple typical situations. We harness the power of spontaneous localization models, historically constructed to solve the measurement problem in quantum mechanics, to build a consistent theory of (stochastic) semiclassical gravity in the Newtonian limit. Our model makes quantitative and potentially testable predictions: we recover the Newtonian pair potential up to a short distance cut-off (hence we predict no 1 particle self-interaction) and uncover an additional gravitational decoherence term which depends on the specifics of the underlying spontaneous localization model considered. We hint at a possible program to go past the Newtonian limit, towards a consistent general relativistic semiclassical gravity.

Recent works have proved that semi-classical theories of gravity needed not be fundamentally inconsistent, at least in the Newtonian regime. Using the machinery of continuous measurement theory and feedback, it was shown that one could construct well behaved models of hybrid quantumclassical dynamics at the price of an imposed (non unique) decoherence structure. We introduce a principle of least decoherence (PLD) which allows to naturally single out a unique model from all the available options; up to some unspecified short distance regularization scale. Interestingly, the resulting model is found to coincide with the old -erstwhile only heuristically motivated-proposal of Penrose and one of us for gravity-related spontaneous decoherence and collapse. Finally, this letter suggests that it is in the submillimeter behavior of gravity that new phenomena might be found.Gluing gravity and quantum mechanics in a unified theory has proved to be a discouragingly difficult task. Most efforts have so far been focused on constructing a quantum theory of gravity [1] but the very nature of the gravitational force -classical or quantum-remains unknown. Whereas distinguishing different approaches to quantum gravity might for long remain out of experimental reach, pining down the classical or quantum character of gravity may be doable at low energy. To distinguish a quantum and classical gravitational force, one needs a candidate classical theory. In the Newtonian limit, the standard approach has been to consider the Schrödinger-Newton (SN) equation [2,3], the low energy limit of the fundamentally semi-classical gravity of Møller and Rosenfeld [4,5], as a paradigmatic example. However, the latter is plagued by conceptual complications requiring one to drop, at the very least, the statistical interpretation of quantum states of matter. Interestingly, these foundational problems of SN are not related to relativity but, rather, to the difficulties in constructing consistent hybrid quantum-classical dynamics, a fact that has often been seen as a conclusive proof of the need for quantum gravity [6]. Yet, SN is only one (rather naive) approach: we shall discuss below an alternative while other options [7,8] are available.The conceptual difficulties of hybrid quantum-classical coupling can be solved, without full quantization, provided fluctuations are added to the classical variables [9,10]. The loss of unitarity can then be seen as the necessary price of semi-classical coexistence. For gravity in the Newtonian limit, it means adding a noise term δΦ to the Newtonian potential Φ. These fluctuations are not to be derived from quantum theory (as is e.g. the case in stochastic gravity [11,12]) but are typically posited from heuristic considerations and required to be minimum so long as the hybrid classical-quantum coupling remains consistent. Historically, such considerations [13][14][15] were instrumental in the construction of models of gravityrelated decoherence and collapse [16][17][18][19][20][21][22]. The latter used Gaussian fluct...