Estimation of general Hamiltonian parameters via controlled energy measurements

The quantum Cram\'er-Rao theorem states that the quantum Fisher information (QFI) bounds the best achievable precision in the estimation of a quantum parameter $\xi$. This is true, however, under the assumption that the measurement employed to extract information on $\xi$ are regular, i.e. neither its sample space nor its positive-operator valued elements depend on the (true) value of the parameter. A better performance may be achieved by relaxing this assumption. In the case of a general Hamiltonian parameter, i.e. when the parameter enters the system's Hamiltonian in a non-linear way (making the energy eigenstates and eigenvalues $\xi$-dependent), a family of non-regular measurements, referred to as controlled energy measurements, is naturally available. We perform an analytic optimization of their performance, which enables us to compare the optimal controlled energy measurement with the optimal Braunstein-Caves measurement based on the symmetric logarithmic derivative. As the former may outperform the latter, the ultimate quantum bounds for general Hamiltonian parameters are different than those for phase (shift) parameters. We also discuss in detail a realistic implementation of controlled energy measurements based on the quantum phase estimation algorithm and work out a variety of examples to illustrate our results.Comment: revised and enlarged versio

Quantum sensing of curvature

We address the problem of sensing the curvature of a manifold by performing measurements on a particle constrained to the manifold itself. In particular, we consider situations where the dynamics of the particle is quantum mechanical and the manifold is a surface embedded in the three-dimensional Euclidean space. We exploit ideas and tools from quantum estimation theory to quantify the amount of information encoded into a state of the particle, and to seek for optimal probing schemes, able to actually extract this information. Explicit results are found for a free probing particle and in the presence of a magnetic field. We also address precision achievable by position measurement, and show that it provides a nearly optimal detection scheme, at least to estimate the radius of a sphere or a cylinder

Gauged NonAbelian Vortices: Topology and Dynamics of a Coupled 2D-4D Quantum Field Theory

Nonabelian vortices - vortex solutions carrying nonabelian continuous orientational zero modes - have been extensively investigated in the last decade, revealing many interesting features. Typically they occur in a system in the color-flavor locked phase, i.e. systems in which the gauge symmetry is broken by a set of scalar condensates that, however, leave a color-flavor diagonal symmetry intact. Color-flavor locked systems appear to be quite ubiquitous in Nature. Standard QCD at zero temperature exhibits some characteristic features of this sort. They occur in the infrared effective theories of many N=2 supersymmetric theories softly broken to N=1 and may carry important hints about the mechanism responsible for quark confinement. In particular they could shed light on the mysteries of nonabelian monopoles. They are realized in high-density QCD in the color superconductor phase, which may well be realized in the interiors of neutron stars. In the present thesis, a generalization of the standard nonabelian vortex studied in the literature is investigated. In the case of the standard nonabelian vortex, vortices are due to the symmetry breaking G->H, where the residual symmetry group H is realized globally. The low-energy theory is fully higgsed and no massless fields propagate in the 4D bulk around the vortex. At the same time, the existence of an intact nonabelian group H, surviving the symmetry breaking, endows the vortex with nonabelian orientational moduli, describing the orientation of the enclosed flux in group space. Such orientational modes are confined to propagate on the string worldsheet and once excited give rise to finite-energy excitations. The new vortices arise when H is realized locally. In our benchmark model, obtained from the bosonic truncation of an N=2 super Yang-Mills theory, this is achieved through a gauging of the flavor group. As soon as the flavour symmetry is gauged, however, massless fields appear and infrared divergences immediately ensue. The massless gauge bosons of the 4D bulk interact nontrivially with the internal orientational modes supported by the string and change their dynamics dramatically. In addition, with the gauging of the flavor group, all sorts of global effects, reminiscent of the exotic Alice strings, make their appearance. Such global effects, which include a nonabelian version of the Aharonov-Bohm effect and a kind of topological interaction between vortices, are deeply intertwined with the dynamics of the orientational modes

Coarse-grained entanglement classification through orthogonal arrays

Classification of entanglement in multipartite quantum systems is an open problem solved so far only for bipartite systems and for systems composed of three and four qubits. We propose here a coarse-grained classification of entanglement in systems consisting of $N$ subsystems with an arbitrary number of internal levels each, based on properties of orthogonal arrays with $N$ columns. In particular, we investigate in detail a subset of highly entangled pure states which contains all states defining maximum distance separable codes. To illustrate the methods presented, we analyze systems of four and five qubits, as well as heterogeneous tripartite systems consisting of two qubits and one qutrit or one qubit and two qutrits.Comment: 38 pages, 1 figur

Can a Gleason 6 or Less Microfocus of Prostate Cancer

Prostate cancer (PC) remains a cause of death worldwide. Here we investigate whether a single microfocus of PC at the biopsy (graded as Gleason 6 or less, ≤5% occupancy) and the PSA <10 ng/mL can define the archetype of low-risk prostate disease. 4500 consecutive patients were enrolled. Among them, 134 patients with a single micro-focus of PC were followed up, and the parameters influencing the biochemical relapse (BR) were analysed. Out of 134 patients, 94 had clinically significant disease, specifically in 74.26% of the patients with PSA <10 ng/mL. Positive surgical margins and the extracapsular invasion were found in 29.1% and 51.4% patients, respectively. BR was observed in 29.6% of the patients. Cox regression evidenced a correlation between the BR and Gleason grade at the retropubic radical prostatectomy (RRP), capsular invasion, and the presence of positive surgical margins. Multivariate regression analysis showed a statistically significant correlation between the presence of surgical margins at the RRP and BR. Considering a single micro-focus of PC at the biopsy and PSA serum level <10 ng/mL, clinically significant disease was found in 74.26% patients and only positive surgical margins are useful for predicting the BR

Geometry and Dynamics of a Coupled 4D-2D Quantum Field Theory

Geometric and dynamical aspects of a coupled 4D-2D interacting quantum field theory - the gauged nonAbelian vortex - are investigated. The fluctuations of the internal 2D nonAbelian vortex zeromodes excite the massless 4D Yang-Mills modes and in general give rise to divergent energies. This means that the well-known 2D CP(N-1) zeromodes associated with a nonAbelian vortex become nonnormalizable. Moreover, all sorts of global, topological 4D effects such as the nonAbelian Aharonov-Bohm effect come into play. These topological global features and the dynamical properties associated with the fluctuation of the 2D vortex moduli modes are intimately correlated, as shown concretely here in a U(1) x SU(N) x SU(N) model with scalar fields in a bifundamental representation of the two SU(N) factor gauge groups.Comment: Latex, 39 pages, 5 figure