Classification of Primary Constraints of Quadratic Non-Metricity Theories of Gravity

We perform the ADM decomposition of a five-parameter family of quadratic non-metricity theories and study their conjugate momenta. After systematically identifying all possible conditions which can be imposed on the parameters such that different sets of primary constraints arise, we find that the five-parametric theory space can be compartmentalized into nine different sectors, based on the presence or absence of primary constraints. This classification allows to dismiss certain classes of theories as unphysical and invites further investigations into the remaining sectors, which may contain phenomenologically interesting modifications of General Relativity.Comment: 8 pages, 3 tables, 1 figur

Experimental investigation on the geometry of GHz states

Nonclassical correlations arising in complex quantum networks are attracting growing interest, both from afundamental perspective and for potential applications in information processing. In particular, in an entanglementswapping scenario a new kind of correlations arise, the so-called nonbilocal correlations that are incompatible withlocal realism augmented with the assumption that the sources of states used in the experiment are independent.In practice, however, bilocality tests impose strict constraints on the experimental setup and in particular to thepresence of shared reference frames between the parties. Here, we experimentally address this point showing thatfalse positive nonbilocal quantum correlations can be observed even though the sources of states are independent.To overcome this problem, we propose and demonstrate a scheme for the violation of bilocality that does notrequire shared reference frames and thus constitutes an important building block for future investigations ofquantum correlations in complex network

Hamiltonian Analysis of f(Q)f(Q) Gravity and the Failure of the Dirac-Bergmann Algorithm for Teleparallel Theories of Gravity

In recent years, $f(Q)$ gravity has enjoyed considerable attention in the literature and important results have been obtained. However, the question of how many physical degrees of freedom the theory propagates -- and how this number may depend on the form of the function $f$ -- has not been answered satisfactorily. In this article we show that a Hamiltonian analysis based on the Dirac-Bergmann algorithm -- one of the standard methods to address this type of question -- fails. We isolate the source of the failure, show that other commonly considered teleparallel theories of gravity are affected by the same problem, and we point out that the number of degrees of freedom obtained in Phys. Rev. D 106 no. 4, (2022) by K. Hu, T. Katsuragawa, and T. Qui (namely eight), based on the Dirac-Bergmann algorithm, is wrong. Using a different approach, we show that the upper bound on the degrees of freedom is seven. Finally, we propose a more promising strategy for settling this important question.Comment: 45 pages, 3 figues, Comments are welcom

Device-independent certification of high-dimensional quantum systems

An important problem in quantum information processing is the certification of the dimension of quantum systems without making assumptions about the devices used to prepare and measure them, that is, in a device-independent manner. A crucial question is whether such certification is experimentally feasible for high-dimensional quantum systems. Here we experimentally witness in a device-independent manner the generation of six-dimensional quantum systems encoded in the orbital angular momentum of single photons and show that the same method can be scaled, at least, up to dimension 13.Comment: REVTeX4, 5 pages, 2 figure

Non-linear extension of non-metricity scalar for MOND

General Relativity enjoys the freedom of different geometrical interpretations in terms of curvature, torsion or non-metricity. Within this geometrical trinity, a simpler geometrical formulation of General Relativity manifests itself in the latter, where gravity is entirely attributed to non-metricity. In this Letter, we consider non-linear extensions of Coincident General Relativity $f(\mathring{\mathbb{Q}})$ for phenomenological applications on both cosmological as well as galactic scales. The theory not only delivers dark energy on large scales but also recovers MOND on galactic scales, together with implications for the early universe cosmology. To the best of our knowledge, this represents the first relativistic, covariant, and ghost-free hybrid-formulation of MOND which recovers both, General Relativity and MOND in the appropriate limits and reconciles expected cosmological behavior. We further illustrate that previous bimetric formulations of MOND generically suffer from ghost instabilities and $f(\mathring{\mathbb{Q}})$ crystalizes as a unique ghost-free theory.Comment: 6 page

Free-space quantum key distribution by rotation-invariant twisted photons

Twisted photons are photons carrying a well-defined nonzero value of orbital angular momentum (OAM). The associated optical wave exhibits a helical shape of the wavefront (hence the name) and an optical vortex at the beam axis. The OAM of light is attracting a growing interest for its potential in photonic applications ranging from particle manipulation, microscopy and nanotechnologies, to fundamental tests of quantum mechanics, classical data multiplexing and quantum communication. Hitherto, however, all results obtained with optical OAM were limited to laboratory scale. Here we report the experimental demonstration of a link for free-space quantum communication with OAM operating over a distance of 210 meters. Our method exploits OAM in combination with optical polarization to encode the information in rotation-invariant photonic states, so as to guarantee full independence of the communication from the local reference frames of the transmitting and receiving units. In particular, we implement quantum key distribution (QKD), a protocol exploiting the features of quantum mechanics to guarantee unconditional security in cryptographic communication, demonstrating error-rate performances that are fully compatible with real-world application requirements. Our results extend previous achievements of OAM-based quantum communication by over two orders of magnitudes in the link scale, providing an important step forward in achieving the vision of a worldwide quantum network