Qiss

We develop a systematic framework to compute the primordial power spectrum up to next-to-next-to-next to leading order (N3LO) in the Hubble-flow parameters for a large class of effective theories of inflation. We assume that the quadratic action for perturbations is characterized by two functions of time, the kinetic amplitude and the speed of sound, that are independent of the Fourier mode $k$. Using the Green’s function method introduced by Stewart $&$ Gong and developed by Auclair $&$ Ringeval, we determine the primordial power spectrum, including its amplitude, spectral indices, their running and running of their running, starting from a given generic action for perturbations. As a check, we reproduce the state-of-the-art results for scalar and the tensor power spectrum of the simplest “vanilla” models of single-field inflation. The framework applies to Weinberg’s effective field theory of inflation (with the condition of no parity violation) and to effective theory of spontaneous de Sitter-symmetry breaking. As a concrete application, we provide the expression for the N3LO power spectrum of $R+R^2$ Starobinsky inflation, without a field redefinition. All expressions are provided in terms of an expansion in one single parameter, the number of inflationary e-foldings $N_*$. Surprisingly we find that, compared to previous leading-order calculations, for $N_* = 55$ the N3LO correction results in a $7%$ decrease of the predicted tensor-to-scalar ratio, in addition to a deviation from the consistency relation. These results provide precise theoretical predictions for the next generation of CMB observations.

Multiphoton indistinguishability is a central resource for quantum enhancement in sensing and computation. Developing and certifying large scale photonic devices requires reliable and accurate characterization of this resource, preferably using methods that are robust against experimental errors. Here, we propose a set of methods for the characterization of multiphoton indistinguishability, based on measurements of bunching and photon number variance. Our methods are robust in a semi-device independent way, in the sense of being effective even when the interferometers are incorrectly dialled. We demonstrate the effectiveness of this approach using an advanced photonic platform comprising a quantum-dot single-photon source and a universal fully-programmable integrated photonic processor. Our results show the practical usefulness of our methods, providing robust certification tools that can be scaled up to larger systems.

In quantum gravity, it has been argued that a proper accounting of the role played by an observer promotes the von Neumann algebra of observables in a given spacetime subregion from Type III to Type II. While this allows for a mathematically precise definition of its entropy, we show that this procedure depends on which observer is employed. We make this precise by considering a setup in which many possible observers are present; by generalising previous approaches, we derive density operators for the subregion relative to different observers (and relative to arbitrary collections of observers), and we compute the associated entropies in a semiclassical regime, as well as in some specific examples that go beyond this regime. We find that the entropies seen by distinct observers can drastically differ. Our work makes extensive use of the formalism of quantum reference frames (QRF); indeed, as we point out, the ‘observers’ considered here and in the previous works are nothing but QRFs. In the process, we demonstrate that the description of physical states and observables invoked by Chandrasekaran et al. [arXiv:2206.10780] is equivalent to the Page-Wootters formalism, leading to the informal slogan “PW=CLPW”. It is our hope that this paper will help motivate a long overdue union between the QRF and quantum gravity communities. Further details will appear in a companion paper.

Trends of genuine entanglement in Haar uniformly generated multimode pure Gaussian states with fixed average energy per mode are explored. A distance-based metric known as the generalized geometric measure (GGM) is used to quantify genuine entanglement. The GGM of a state is defined as its minimum distance from the set of all non-genuinely entangled states. To begin with, we derive an expression for the Haar averaged value of any function defined on the set of energy-constrained states. Subsequently, we investigate states with a large number of modes and provide a closed-form expression for the Haar averaged GGM in terms of the average energy per mode. Furthermore, we demonstrate that typical states closely approximate their Haar averaged GGM value, with deviation probabilities bounded by an exponentially suppressed limit. We then analyze the GGM content of typical states with a finite number of modes and present the distribution of GGM. Our findings indicate that as the number of modes increases, the distribution shifts towards higher entanglement values and becomes more concentrated. We quantify these features by computing the Haar averaged GGM and the standard deviation of the GGM distribution, revealing that the former increases while the latter decreases with the number of modes.

We study extensions of the mappings arising in usual Channel-State duality to the case of Hilbert spaces with a direct sum structure. This setting arises in representations of algebras with centers, which are commonly associated with constraints, and it has many physical applications from quantum many-body theory to holography and quantum gravity. We establish that there is a general relationship between non-separability of the state and the isometric properties of the induced channel. We also provide a generalisation of our approach to algebras of trace-class operators on infinite dimensional Hilbert spaces.

A catalysis state is a quantum state that is used to make some desired operation possible or more efficient, while not being consumed in the process. Recent years have seen catalysis used in state-of-the-art protocols for implementing magic state distillation or small angle phase rotations. In this paper we will see that we can also use catalysis to prove that certain gate sets are computationally universal, and to extend completeness results of graphical languages to larger fragments. In particular, we give a simple proof of the computational universality of the CS+Hadamard gate set using the catalysis of a $T$ gate using a CS gate, which sidesteps the more complicated analytic arguments of the original proof by Kitaev. This then also gives us a simple self-contained proof of the computational universality of Toffoli+Hadamard. Additionally, we show that the phase-free ZH-calculus can be extended to a larger complete fragment, just by using a single catalysis rule (and one scalar rule).

We propose a solution to a classic problem in gravitational physics consisting of defining the spin associated with asymptotically-flat spacetimes. We advocate that the correct asymptotic symmetry algebra to approach this problem is the generalized-BMS algebra $textsf{gbms}$ instead of the BMS algebra used hitherto in the literature for which a notion of spin is generically unavailable. We approach the problem of defining the spin charges from the perspective of coadjoint orbits of $textsf{gbms}$ and construct the complete set of Casimir invariants that determine $textsf{gbms}$ coadjoint orbits, using the notion of vorticity for $textsf{gbms}$. This allows us to introduce spin charges for $textsf{gbms}$ as the generators of area-preserving diffeomorphisms forming its isotropy subalgebra. To elucidate the parallelism between our analysis and the Poincar’e case, we clarify several features of the Poincar’e embedding in $textsf{gbms}$ and reveal the presence of condensate fields associated with the symmetry breaking from $textsf{gbms}$ to Poincar’e. We also introduce the notion of a rest frame available only for this extended algebra. This allows us to construct, from the spin generator, the gravitational analog of the Pauli–Luba’nski pseudo-vector. Finally, we obtain the $textsf{gbms}$ moment map, which we use to construct the gravitational spin charges and gravitational Casimirs from their dual algebra counterparts.

In this note, we provide some categorical perspectives on the relativization construction arising from quantum measurement theory in the presence of symmetries and occupying a central place in the operational approach to quantum reference frames. This construction provides, for any quantum system, a quantum channel from the system’s algebra to the invariant algebra on the composite system also encompassing the chosen reference, contingent upon a choice of the pointer observable. These maps are understood as relativizing observables on systems upon the specification of a quantum reference frame. We begin by extending the construction to systems modelled on subspaces of algebras of operators to then define a functor taking a pair consisting of a reference frame and a system and assigning to them a subspace of relative operators defined in terms of an image of the corresponding relativization map. When a single frame and equivariant channels are considered, the relativization maps can be understood as a natural transformation. Upon fixing a system, the functor provides a novel kind of frame transformation that we call external. Results achieved provide a deeper structural understanding of the framework of interest and point towards its categorification and potential application to local systems of algebraic quantum field theories.

On the one side, the formalism of Global Transformations comes with the claim of capturing any transformation of space that is local, synchronous and deterministic.The claim has been proven for different classes of models such as mesh refinements from computer graphics, Lindenmayer systems from morphogenesis modeling and cellular automata from biological, physical and parallel computation modeling.The Global Transformation formalism achieves this by using category theory for its genericity, and more precisely the notion of Kan extension to determine the global behaviors based on the local ones.On the other side, Causal Graph Dynamics describe the transformation of port graphs in a synchronous and deterministic way and has not yet being tackled.In this paper, we show the precise sense in which the claim of Global Transformations holds for them as well.This is done by showing different ways in which they can be expressed as Kan extensions, each of them highlighting different features of Causal Graph Dynamics.Along the way, this work uncovers the interesting class of Monotonic Causal Graph Dynamics and their universality among General Causal Graph Dynamics.

The Barbero-Immirzi parameter $gamma$ appears as a coupling constant in the spinfoam dynamics of loop quantum gravity and can be understood as a measure of gravitational parity violation via a duality rotation. We investigate an effective field theory for gravity and a scalar field, with dynamics given by a $gamma$-dual action obtained via a duality rotation of a parity-non-violating one. The resulting relation between the coupling constants of parity-even and parity-odd higher-curvature terms is determined by $gamma$, opening the possibility of its measurement in the semiclassical regime. For a choice of $gamma$-dual effective action, we study cosmic inflation and show that the observation of a primordial tensor polarization, together with the tensor tilt and the tensor-to-scalar ratio, provides a measurement of the Barbero-Immirzi parameter and, therefore, of the scale of discreteness of the quantum geometry of space.