The achievement of quantum supremacy boosted the need for a robust medium of quantum information. In this task, higher-dimensional qudits show remarkable noise tolerance and enhanced security for quantum key distribution applications. However, to exploit the advantages of such states, we need a thorough characterization of their entanglement. Here, we propose a measure of entanglement which can be computed for either pure or mixed states of a $M$-qudit hybrid system. The entanglement measure is based on a distance deriving from an adapted application of the Fubini-Study metric. This measure is invariant under local unitary transformations and has an explicit computable expression that we derive. In the specific case of $M$-qubit systems, the measure assumes the physical interpretation of an obstacle to the minimum distance between infinitesimally close states. Finally, we quantify the robustness of entanglement of a state through the eigenvalue analysis of the metric tensor associated with it.

We show that the quantization ambiguities of loop quantum cosmology, when considered in wider generality, can be used to produce discretionary dynamical behavior. There is an infinite dimensional space of ambiguities which parallels the infinite list of higher curvature corrections in perturbative quantum gravity. There is, however, an ensemble of qualitative consequences which are generic in the sense that they are independent of these ambiguities. Among these, one has well-defined fundamental dynamics across the big bang, as well as extra microscopic quantum degrees of freedom that might be relevant in discussions about unitarity in quantum gravity. We show that, in addition to the well-known bouncing solutions of the effective equations, there are other generic types of solutions for sufficiently soft initial conditions in the matter sector (tunneling solutions) where the scale factor goes through zero and the spacetime orientation is inverted. We also show that, generically, a contracting semiclassical universe branches off at the big bang into a quantum superposition of universes with different quantum numbers. Despite their lack of quantitative predictive power, these models offer a fertile playground for the discussion of qualitative and conceptual issues in quantum gravity.

In this paper, we construct a solvable toy model of the quantum dynamics of the interior of a spherical black hole with falling spherical scalar field excitations. We first argue about how some aspects of the quantum gravity dynamics of realistic black holes emitting Hawking radiation can be modeled using Kantowski–Sachs solutions with a massless scalar field when one focuses on the deep interior region $r\ll M$ (including the singularity). Further, we show that in the $r\ll M$ regime, and in suitable variables, the KS model becomes exactly solvable at both the classical and quantum levels. The quantum dynamics inspired by loop quantum gravity is revisited. We propose a natural polymer quantization where the area a of the orbits of the rotation group is quantized. The polymer (or loop) dynamics is closely related to the Schroedinger dynamics away from the singularity with a form of continuum limit naturally emerging from the polymer treatment. The Dirac observable associated with the mass is quantized and shown to have an infinite degeneracy associated with the so-called $ϵ$-sectors. Suitable continuum superpositions of these are well-defined distributions in the fundamental Hilbert space and satisfy the continuum Schroedinger dynamics.

We explicitly express the Minkowski vacuum of a massless scalar field in terms of the particle notion associated with suitable spherical conformal killing fields. These fields are orthogonal to the light wave fronts originating from a sphere with a radius of $r_H$ in flat spacetime: a bifurcate conformal killing horizon that exhibits semiclassical features similar to those of black hole horizons and Cauchy horizons of spherically symmetric black holes. Our result highlights the quantum aspects of this analogy and extends the well-known decomposition of the Minkowski vacuum in terms of Rindler modes, which are associated with the boost Killing field normal to a pair of null planes in Minkowski spacetime (the basis of the Unruh effect). While some features of our result have been established by the theorems of Kay and Wald in the 1990s—on quantum field theory in stationary spacetimes with bifurcate Killing horizons—the added value we provide here lies in the explicit expression of the vacuum.

We develop the covariant phase space formulation of Weyl-transverse gravity (WTG) in the presence of general timelike and spacelike boundaries. WTG is classically equivalent to General Relativity (GR) but possesses a reduced gauge symmetry consisting of Weyl transformations and transverse diffeomorphisms, together with a fixed background volume form. This structure modifies the variational principle and the definition of conserved quantities relative to GR.We derive the symplectic potential, presymplectic current, and Hamiltonian generators associated with transverse diffeomorphisms, and we identify a set of boundary conditions under which the WTG action is differentiable. These include Dirichlet and Neumann conditions for both the auxiliary Weyl-invariant metric and the dynamical metric, as well as a natural implementation of York boundary conditions, for which WTG exhibits a particularly transparent geometric formulation.We obtain the Noether current and surface charge, clarify the role of the Lagrangian ambiguity related to the cosmological constant, and evaluate the Hamiltonian identity on spacetimes containing a bifurcate Killing horizon. The resulting first-law relation shows that variations of the cosmological constant can contribute nontrivially unless additional physical restrictions are imposed.

We investigate the classical symmetries of the dynamics of the null-dust spherically symmetric Vaidya spacetime. Einstein’s equations for this model can be obtained as equations of motion of a two-dimensional field theory. We discuss the transformations leaving invariant such equations of motion. These are given by two distinct sets, the residual diffeomorphisms coming from general relativity and the generalization of the Schrödinger symmetry, recently found for the static Schwarzschild black holes. Surprisingly, these two sets represent the symmetries of two different action functionals, leading to the same equations of motion, but with different phase spaces.