December 2021

In this paper we extract from a large-$r$ expansion of the vacuum Einstein’s equations a dynamical system governing the time evolution of an infinity of higher-spin charges. Upon integration, we evaluate the canonical action of these charges on the gravity phase space. The truncation of this action to quadratic order and the associated charge conservation laws yield an infinite tower of soft theorems. We show that the canonical action of the higher spin charges on gravitons in a conformal primary basis, as well as conformally soft gravitons reproduces the higher spin celestial symmetries derived from the operator product expansion. Finally, we give direct evidence that these charges form a canonical representation of a $w_{1+infty}$ loop algebra on the gravitational phase space.

In a recent paper, we vindicated a general entanglement-based witness of non-classicality in hybrid quantum systems. Our vindication refutes a counterexample to the witness, proposed by Hall and Reginatto. These authors recently commented further, claiming to expose “a huge number of errors and misconceptions” in it. However, their comment contains no refutation of our arguments, nor does it expose any error or misconception in them. But it does include a number of misconceptions about the witness of non-classicality. Here we respond to those.

In an ordinary quantum algorithm the gates are applied in a fixed order on the systems. The introduction of indefinite causal structures allows to relathis constraint and control the order of the gates with an additional quantum state. It is known that this quantum-controlled ordering of gates can reduce the query complexity in deciding a property of black-bounitaries with respect to the best algorithm in which the gates are applied in a fixed order. However, all tasks explicitly found so far require unitaries that either act on unbounded dimensional quantum systems in the asymptotic limit (the limiting case of a large number of black-bogates) or act on qubits, but then involve only a few unitaries. Here we introduce tasks (1) for which there is a provable computational advantage of a quantum-controlled ordering of gates in the asymptotic case and (2) that require only qubit gates and are therefore suitable to demonstrate this advantage experimentally. We study their solutions with the quantum-$n$-switch and within the quantum circuit model and find that while the $n$-switch requires to call each gate only once, a causal algorithm has to call at least $2n-1$ gates. Furthermore, the best known solution with a fixed gate ordering calls $O(nlog_2{(n)})$ gates.

Wave-particle duality and entanglement are two fundamental characteristics of quantum mechanics. All previous works on experimental investigations in wave{particle properties of single photons (or single particles in general) show that a well-defined interfeQILab Rometer setting determines a well-defined property of single photons. Here we take a conceptual step forward and control the wave-particle property of single photons with quantum entanglement. By doing so, we experimentally test the complementarity principle in a scenario, in which the setting of the interfeQILab Rometer is not defined at any instance of the experiment, not even in principle. To achieve this goal, we send the photon of interest (S) into a quantum Mach-Zehnder interfeQILab Rometer (MZI), in which the output beam splitter of the MZI is controlled by the quantum state of the second photon (C), who is entangled with a third photon (A). Therefore, the individual quantum state of photon C is undefined, which implements the undefined settings of the MZI for photon S. This is realized by using three cascaded phase-stable interfeQILab Rometers for three photons. There is typically no well-defined setting of the MZI, and thus the very formulation of the wave-particle properties becomes internally inconsistent.

The current theories of quantum physics and general relativity on their own do not allow us to study situations in which the gravitational source is quantum. Here, we propose a strategy to determine the dynamics of objects in the presence of mass configurations in superposition, and hence an indefinite spacetime metric, using quantum reference frame (QRF) transformations. Specifically, we show that, as long as the mass configurations in the different branches are related via relative-distance-preserving transformations, one can use an extension of the current framework of QRFs to change to a frame in which the mass configuration becomes definite. Assuming covariance of dynamical laws under quantum coordinate transformations, this allows to use known physics to determine the dynamics. We apply this procedure to find the motion of a probe particle and the behavior of clocks near the mass configuration, and thus find the time dilation caused by a gravitating object in superposition.

The entanglement entropy of subsystems of typical eigenstates of quantum many-body Hamiltonians has been recently conjectured to be a diagnostic of quantum chaos and integrability. In quantum chaotic systems it has been found to behave as in typical pure states, while in integrable systems it has been found to behave as in typical pure Gaussian states. In this tutorial, we provide a pedagogical introduction to known results about the entanglement entropy of subsystems of typical pure states and of typical pure Gaussian states. They both exhibit a leading term that scales with the volume of the subsystem, when smaller than one half of the volume of the system, but the prefactor of the volume law is fundamentally different. It is constant (and maximal) for typical pure states, and it depends on the ratio between the volume of the subsystem and of the entire system for typical pure Gaussian states. Since particle-number conservation plays an important role in many physical Hamiltonians, we discuss its effect on typical pure states and on typical pure Gaussian states. We prove that while the behavior of the leading volume-law terms does not change qualitatively, the nature of the subleading terms can change. In particular, subleading corrections can appear that depend on the square root of the volume of the subsystem. We unveil the origin of those corrections. Finally, we discuss the connection between the entanglement entropy of typical pure states and analytical results obtained in the context of random matritheory, as well as numerical results obtained for physical Hamiltonians.

We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a “composable constraint encoding”. We show that every composable constraint encoding can be used to construct an equivalent notion of a constrained category in which morphisms are supplemented with the constraints they satisfy. We further describe how to express the compatibility of constraints with additional categorical structures of their targets, such as parallel composition, compactness, and time-symmetry. We present a variety of concrete examples. Some are familiar in the study of quantum protocols and quantum foundations, such as signalling and sectorial constraints; others arise by construction from basic categorical notions. We use the language developed to discuss the notion of intersectability of constraints and the simplifications it allows for when present, and to show that any time-symmetric theory of relational constraints admits a faithful notion of intersection.

We explore the possibility that the connection between spin and statistics in quantum physics is of dynamical origin. We suggest that the gravitational field could provide a fully local mechanism for the phase that arises when fermionic and bosonic particles are exchanged. Our results hold even if the symmetry of space and time is Galilean, thus establishing that special relativity is not needed to explain the existence of spin (although it does motivate the introduction of creation and annihilation of particles, but this is a separate issue). We provide a model for the coupling between a particle of general spin and the gravitational field and discuss it within the context of both the equivalence principle and the Sagnac effect. This leads us to present a new experiment for testing the quantum nature of the gravitational field.