December 2023

The definition of a quantum system requires a Hilbert space, a way to define the dynamics, and an algebra of observables. The structure of the observable algebra is related to a tensor product decomposition of the Hilbert space and represents the composition of the system by subsystems. It has been remarked that the Hamiltonian may determine this tensor product structure. Here we observe that this fact may lead to questionable consequences in some cases, and does extend to the more general background-independent case, where the Hamiltonian is replaced by a Hamiltonian constraint. These observations reinforces the idea that specifying the observables and the way they interplay with the dynamics, is essential to define a quantum theory. We also reflect on the general role that system decomposition has in the quantum theory.

We provide a covariant framework to study singularity-free Lema^itre-Tolman-Bondi spacetimes with effective corrections motivated by loop quantum gravity. We show that, as in general relativity, physically reasonable energy distributions lead to a contraction of the dust shells. However, quantum-gravity effects eventually stop the collapse, the dust smoothly bounces back, and no gravitational singularity is generated. This model is constructed by deforming the Hamiltonian constraint of general relativity with the condition that the hypersurface deformation algebra is closed. In addition, under the gauge transformations generated by the deformed constraints, the structure function of the algebra changes adequately, so that it can be interpreted as the inverse spatial metric. Therefore, the model is completely covariant in the sense that gauge transformations in phase space simply correspond to coordinate changes in spacetime. However, in the construction of the metric, we point out a specific freedom of considering a conformal factor, which we use to obtain a family of singularity-free spacetimes associated to the modified model.

As fundamental scaling limits start to stifle the evolution of complementary metal–oxide–semiconductor transistor technology, interest in potential alternative computing platforms grows. One such alternative is wave-based computation. In this work, we propose a general string diagrammatic formalism for wave-based computation with phase encoding applicable to a wide range of emerging architectures and technologies, including quantum-dot cellular automata, single-electron circuits, spin torque majority gates, and DNA computing. We demonstrate its applicability for design, analysis, and simplification of Boolean logic circuits using the example of spin-wave circuits.