Quantum Cramer-Rao bound for a Massless Scalar Field in de Sitter Space

How precisely can we estimate cosmological parameters by performing a quantum measurement on a cosmological quantum state? In quantum estimation theory the variance of an unbiased parameter estimator is bounded from below by the inverse of measurement-dependent Fisher information and ultimately by quantum Fisher information, which is the maximization of the former over all positive operator valued measurements. Such bound is known as the quantum Cramer-Rao bound. We consider the evolution of a massless scalar field with Bunch-Davies vacuum in a spatially flat FLRW spacetime, which results in a two-mode squeezed vacuum out-state for each field wave number mode. We obtain the expressions of the quantum Fisher information as well as the Fisher informations associated to occupation number measurement and power spectrum measurement, and show the specific results of their evoluation for pure de Sitter expansion and de Sitter expansion followed by a radiation-dominated phase as examples. We will discuss these results from the point of view of the quantum-to-classical transition of cosmological perturbations and show quantitatively how this transition and the residual quantum correlations affect the bound on the precision.Comment: 16 pages, published versio

The decoherence and interference of cosmological arrows of time for a de Sitter universe with quantum fluctuations

We consider the superposition of two semiclassical solutions of the Wheeler-DeWitt equation for a de Sitter universe, describing a quantized scalar vacuum propagating in a universe that is contracting in one case and expanding in the other, each identifying a opposite cosmological arrow of time. We discuss the suppression of the interference terms between the two arrows of time due to environment-induced decoherence caused by modes of the scalar vacuum crossing the Hubble horizon. Furthermore, we quantify the effect of the interference on the expectation value of the observable field mode correlations, with respect to an observer that we identify with the spatial geometry

A Wheeler-DeWitt Equation with Time

The equation for canonical gravity produced by Wheeler and DeWitt in the late 1960s still presents difficulties both in terms of its mathematical solution and its physical interpretation. One of these issues is, notoriously, the absence of an explicit time. In this short note, we suggest one simple and straightforward way to avoid this occurrence. We go back to the classical equation that inspired Wheeler and DeWitt (namely, the Hamilton--Jacobi--Einstein equation) and make explicit, before quantization, the presence of a known, classically meaningful notion of time. We do this by allowing Hamilton's principal function to be explicitly dependent on this time locally. This choice results in a Wheeler--DeWitt equation with time. A working solution for the de Sitter minisuperspace is shown

Impacts of radiative corrections on measurements of lepton flavour universality in B→DℓνℓB \to D \ell \nu_{\ell} decays

Radiative corrections to $B \to D \ell \nu_{\ell}$ decays may have an impact on predictions and measurements of the lepton flavour universality observables $\mathcal{R}(D^+)$ and $\mathcal{R}(D^0)$. In this paper, a comparison between recent calculations of the effect of soft-photon corrections on $\mathcal{R}(D^+)$ and $\mathcal{R}(D^0)$, and corrections generated by the widely used package PHOTOS is given. The impact of long-distance Coulomb interactions, which are not simulated in PHOTOS, is discussed. Furthermore, the effect of high-energy photon emission is studied through pseudo-experiments in an LHCb-like environment. It is found that over- or underestimating these emissions can cause a bias on $\mathcal{R}(D)$ as high as 7%. However, this bias depends on individual analyses, and future high precision measurements require an accurate evaluation of these QED corrections.Comment: 8 pages, 21 figures, published by EPJ

Clock Time in Quantum Cosmology

We consider the conditioning of the timeless solution to the Wheeler-DeWitt equation by a predefined matter clock state in the simple scenario of de Sitter universe. The resulting evolution of the geometrodynamical degree of freedom with respect to clock time is characterized by the "Berry connection" of the reduced geometrodynamical space, which relies on the coupling of the clock with the geometry. When the connection vanishes, the standard Schr\"odinger equation is obtained for the geometry with respect to clock time. When one considers environment-induced decoherence in the semi-classical limit, this condition is satisfied and clock time coincides with cosmic time. Explicit results for the conditioned wave functions for minimal clocks made up of two quantum harmonic oscillator eigen-states are shown

Determination of the Cabibbo-Kobayashi-Maskawa matrix element ∣Vcb∣|V_{cb}|

In this review we present and discuss the determination of the magnitude of the Cabibbo-Kobayashi-Maskawa (CKM) matrix parameter $V_{cb}$. The CKM matrix parametrizes the weak charged current interactions of quarks in the Standard Model (SM), and a precise determination of its elements has always been one of the most important targets of particle physics. The precise knowledge of the $|V_{cb}|$ value plays a pivotal role in testing the flavour sector of the SM and in the analyses of the unitarity of the CKM matrix. The SM does not predict the values of the CKM matrix elements, which have to be extracted by experimental data. Given the variety of channels that allow the extraction of $|V_{cb}|$, different theoretical and experimental techniques are mustered for the $|V_{cb}|$ determination. The exertion toward precision represents not only a significant test of our theoretical procedures but a stimulus towards better detection performances. The most precise measurements of $|V_{cb}|$ come from semileptonic decays, that being tree level at the lowest order in the SM are generally considered unaffected by physics beyond the SM. After summarizing the characteristics of the SM that set the frame for the determination of $|V_{cb}|$, we discuss inclusive and exclusive semileptonic $B$ decays. We analyze the $|V_{cb}|$ extraction methods and recent results, detailing both the theoretical and experimental techniques, and, finally, outline future prospects. We also comment on exclusive decays into heavy leptons, on the observables $R(D)$ and $R(D^\ast)$, on decays to excited $D$ meson states and on baryon decays.Comment: Completely revised and updated: latest results (including baryons), details, tables, figures and references added; 77 pages, 19 figures (invited review on J. Phys. G: Nucl. Part. Phys

Testing lepton flavour universality in semileptonic Λb→Λc∗\Lambda_b \to \Lambda_c^* decays

Lepton Flavour Universality tests with semileptonic $\Lambda_b\to\Lambda_c^*$ decays are important to corroborate the present anomalies in the similar ratios $R_{D^{(*)}}$, and can provide complementary constraints on possible origins of these anomalies beyond the Standard Model. In this paper we provide - for the first time - all the necessary theoretical ingredients to perform and interpret measurements of $R_{\Lambda_c^*}$ at the LHCb experiment. For this, we revisit the heavy-quark expansion of the relevant hadronic matrix elements, and provide their expressions to order $\alpha_s$ and $1/m$ accuracy. Moreover, we study the sensitivity to the form factor parameters given the projected size and purity of upcoming and future LHCb datasets of $\Lambda_b\to \Lambda_c^*\mu\bar{\nu}$ decays. We demonstrate explicitly the need to perform a simultaneous fit to both $\Lambda_c^*$ final states. Finally, we provide projections for the uncertainty of $R_{\Lambda_c^*}$ based on the form factor analysis from semimuonic decays and theoretical relations based on the heavy-quark expansion.Comment: 27 pages, 6 figures. v2: Fixed error in subleading IW function, added supplementary information; conclusions unchange

Thermodynamic Reverse Bounds for General Open Quantum Processes

Various quantum thermodynamic bounds are shown to stem from a single tighter and more general inequality, consequence of the operator concavity of the logarithmic function. Such an inequality, which we call the "thermodynamic reverse bound", is compactly expressed as a quantum relative entropy, from which it inherits mathematical properties and meaning. As concrete examples, we apply our bound to evaluate the thermodynamic length for open processes, the heat exchange in erasure processes, and the maximal energy outflow in general quantum evolutions.Comment: v2: added six colorful plots for the heat exchanged in erasure processes, accepted in PRA; v1: 6 pages, two-colum