May 2021

Massive Klein-Gordon theory is quantized on the timelike hypercylinder in Minkowski space. Crucially, not only the propagating, but also the evanescent sector of phase space is included, laying in this way foundations for a quantum scattering theory of fields at finite distance. To achieve this, the novel $alpha$-K”ahler quantization scheme is employed in the framework of general boundary quantum field theory. A potential quantization ambiguity is fixed by stringent requirements, leading to a unitary radial evolution. Formulas for building scattering amplitudes and correlation functions are exhibited. A novel LSZ formula is derived, applicable to scattering at finite distance.

We derive an explicit expression for the transition amplitude from black to white hole horizon at the end of Hawking evaporation using covariant loop quantum gravity.

Symplectic vector spaces are the phase spaces of linear mechanical systems. The symplectic form describes, for example, the relation between position and momentum as well as current and voltage. The category of linear Lagrangian relations between symplectic vector spaces is a symmetric monoidal subcategory of relations which gives a semantics for the evolution — and more generally linear constraints on the evolution — of various physical systems. We give a new presentation of the category of Lagrangian relations over an arbitrary field as a `doubled’ category of linear relations. More precisely, we show that it arises as a variation of Selinger’s CPM construction applied to linear relations, where the covariant orthogonal complement functor plays the role of conjugation. Furthermore, for linear relations over prime fields, this corresponds exactly to the CPM construction for a suitable choice of dagger. We can furthermore extend this construction by a single affine shift operator to obtain a category of affine Lagrangian relations. Using this new presentation, we prove the equivalence of the prop of affine Lagrangian relations with the prop of qudit stabilizer theory in odd prime dimensions. We hence obtain a unified graphical language for several disparate process theories, including electrical circuits, Spekkens’ toy theory, and odd-prime-dimensional stabilizer quantum circuits.

Bell’s theorem is typically understood as the proof that quantum theory is incompatible with local-hidden-variable models. More generally, we can see the violation of a Bell inequality as witnessing the impossibility of explaining quantum correlations with classical causal models. The violation of a Bell inequality, however, does not exclude classical models where some level of measurement dependence is allowed, that is, the choice made by observers can be correlated with the source generating the systems to be measured. Here, we show that the level of measurement dependence can be quantitatively upper bounded if we arrange the Bell test within a network. Furthermore, we also prove that these results can be adapted in order to derive nonlinear Bell inequalities for a large class of causal networks and to identify quantumly realizable correlations that violate them.

One of the most fundamental open problems in physics is the unification of general relativity and quantum theory to a theory of quantum gravity. An aspect that might become relevant in such a theory is that the dynamical nature of causal structure present in general relativity displays quantum uncertainty. This may lead to a phenomenon known as indefinite or quantum causal structure, as captured by the process matriformalism. Due to the generality of that framework, however, for many process matrices there is no clear physical interpretation. A popular approach towards a quantum theory of gravity is the Page-Wootters formalism, which associates to time a Hilbert space structure similar to spatial position. By explicitly introducing a quantum clock, it allows to describe time-evolution of systems via correlations between this clock and said systems encoded in history states. In this paper we combine the process matriframework with a generalization of the Page-Wootters formalism in which one considers several agents, each with their own discrete quantum clock. We describe how to extract process matrices from scenarios involving such agents with quantum clocks, and analyze their properties. The description via a history state with multiple clocks imposes constraints on the implementation of process matrices and on the perspectives of the agents as described via causal reference frames. While it allows for scenarios where different definite causal orders are coherently controlled, we explain why certain noncausal processes might not be implementable within this setting.