98 research outputs found
Philosophy of mathematics
No full textWe review Linnebo's Philosophy of Mathematics, briefly describing the content of the book.42211311
Time-local optimal control for parameter estimation in the Gaussian regime
No full textInformation about a classical parameter encoded in a quantum state can only decrease if the state undergoes a non-unitary evolution, arising from the interaction with an environment. However, instantaneous control unitaries may be used to mitigate the decrease of information caused by an open dynamics. A possible, locally optimal (in time) choice for such controls is the one that maximises the time-derivative of the quantum Fisher information (QFI) associated with a parameter encoded in an initial state. In this study, we focus on a single bosonic mode subject to a Markovian, thermal master equation, and determine analytically the optimal time-local control of the QFI for its initial squeezing angle (optical phase) and strength. We show that a single initial control operation is already optimal for such cases and quantitatively investigate situations where the o
Does entanglement enhance single-molecule pulsed biphoton spectroscopy?
No full textIt depends. For a single molecule interacting with one mode of a biphoton
probe, we show that the spectroscopic information has three contributions, only
one of which is a genuine two-photon contribution. When all the scattered light
can be measured, solely this contribution exists and can be fully extracted
using unentangled measurements. Furthermore, this two-photon contribution can,
in principle, be matched by an optimised but unentangled single-photon probe.
When the matter system spontaneously emits into inaccessible modes, an
advantage due to entanglement can not be ruled out. In practice, time-frequency
entanglement does enhance spectroscopic performance of the oft-studied
weakly-pumped spontaneous parametric down conversion (PDC) probes. For
two-level systems and coupled dimers, more entangled PDC probes yield more
spectroscopic information, even in the presence of emission into inaccessible
modes. Moreover, simple, unentangled measurements can capture between 60% - 90%
of the spectroscopic information. We thus establish that biphoton spectroscopy
using source-engineered PDC probes and unentangled measurements can provide
tangible quantum enhancement. Our work underscores the intricate role of
entanglement in single-molecule spectroscopy using quantum light.Comment: 18+14 pages, 12+14 figures, 1+0 table
Appunti su Teresa Albarelli Vordoni da Verona, “Alunna privilegiata delle Muse”
No full textIl contributo vuole delineare la figura della poetessa veronese Teresa Albarelli (Verona 1788- Venezia 1868) sposata Vordoni. La figura della poetessa viene ricostruita attraverso documenti d’archivio e testimonianze letterarie che la collocano, a ragione, nel panorama letterario e culturale veneto del primo Ottocento come una figura interessante sia per le produzioni poetiche alla maniera di Gaspare Gozzi, sia per la fitta rete di rapporti che gravitavano intorno a lei
Evaluating the Holevo Cramér-Rao bound for multiparameter quantum metrology
No full textOnly with the simultaneous estimation of multiple parameters are the quantum aspects of metrology fully revealed. This is due to the incompatibility of observables. The fundamental bound for multiparameter quantum estimation is the Holevo Cram´er-Rao bound (HCRB) whose evaluation has so far remained elusive. For finite-dimensional systems we recast its evaluation as a semidefinite program, with reduced size for rank-deficient states. We show that it also satisfies strong duality. We use this result to study phase and loss estimation in optical interferometry and three-dimensional magnetometry with noisy multiqubit systems. For the former, we show that, in some regimes, it is possible to attain the HCRB with the optimal (single-copy) measurement for phase estimation. For the latter, we show a nontrivial interplay between the HCRB and incompatibility and provide numerical evidence that projective single-copy measurements attain the HCRB in the noiseless 2-qubit case
Consistent Partial Matching of Shape Collections via Sparse Modeling
No full textRecent efforts in the area of joint object matching approach the problem by taking as input a set of pairwise maps, which are then jointly optimized across the whole collection so that certain accuracy and consistency criteria are satisfied. One natural requirement is cycle-consistencynamely the fact that map composition should give the same result regardless of the path taken in the shape collection. In this paper, we introduce a novel approach to obtain consistent matches without requiring initial pairwise solutions to be given as input. We do so by optimizing a joint measure of metric distortion directly over the space of cycle-consistent maps; in order to allow for partially similar and extra-class shapes, we formulate the problem as a series of quadratic programs with sparsity-inducing constraints, making our technique a natural candidate for analysing collections with a large presence of outliers. The particular form of the problem allows us to leverage results and tools from the field of evolutionary game theory. This enables a highly efficient optimization procedure which assures accurate and provably consistent solutions in a matter of minutes in collections with hundreds of shapes
A pedagogical introduction to continuously monitored quantum systems and measurement-based feedback
No full textIn this manuscript we present a pedagogical introduction to continuously monitored quantum systems. We
start by giving a simplified derivation of the Markovian master equation in Lindblad form, in the spirit
of collision models and input-output theory, which describes the unconditional dynamics of a continuously
monitored system. The same formalism is then exploited to derive stochastic master equations that describe the
conditional dynamics. We focus on the two most paradigmatic examples of continuous monitoring: continuous
photodetection, leading to a discontinuous dynamics with “quantum jumps”, and continuous homodyne
measurements, leading to a diffusive dynamics. We then present a derivation of feedback master equations that
describe the dynamics (either conditional or unconditional) when the continuous measurement photocurrents
are fed back to the system as a linear driving Hamiltonian, a paradigm known as linear Markovian feedback.
In the second part of the manuscript we focus on continuous-variable Gaussian systems: we first present the
equations for first and second moments describing the dynamics under continuous general-dyne measurements,
and we then discuss in more detail the conditional and unconditional dynamics under Markovian and state-based
feedback
Quantum backflow effect and nonclassicality
No full textThe quantum backflow effect is a counterintuitive behavior of the probability current of a free particle, which may be negative even for states with vanishing negative momentum component. Here, we address the notion of nonclassicality arising from the backflow effect, i.e. from the negativity of the probability current, and analyze its relationships with the notion of nonclassicality based on the negativity of the Wigner function. Our results show that backflow is linked to a different, and in fact more restrictive, notion of nonclassicality, the negativity of the Wigner function being only a necessary prerequisite for its occurrence. This hierarchical structure may be confirmed by looking at the addition of thermal noise, which more easily destroys the negativity of the probability current than the negativity of the Wigner function itself
Probe incompatibility in multiparameter noisy quantum metrology
No full textWe derive fundamental bounds on the maximal achievable precision in multiparameter noisy quantum metrology, valid under the most general entanglement-assisted adaptive strategy, which are tighter than the bounds obtained by a direct use of single-parameter results. This allows us to study the issue of the optimal probe incompatibility in the simultaneous estimation of multiple parameters in generic noisy channels, while so far the issue has been studied mostly in effectively noiseless scenarios (where the Heisenberg scaling is possible). We apply our results to the estimation of both unitary and noise parameters and indicate models where the fundamental probe incompatibility is present. In particular, we show that in lossy multiple-arm interferometry the probe incompatibility is as strong as in the noiseless scenario, reducing the potential advantage of simultaneous estimation to a constant factor. Finally, going beyond the multiparameter estimation paradigm, we introduce the concept of random quantum sensing and show how the tools developed may be applied to multiple-channel discrimination problems. As an illustration, we provide a simple proof of the loss of the quadratic advantage of the time-continuous Grover algorithm in the presence of dephasing or erasure noise
Experimental function estimation from quantum phase measurements
No full textCharacterizing and analyzing a system often requires learning an unknown function, such as the response of a system or the profile of a field. The standard approach is to opportunely sample the function at fiducial points and then interpolate. When the quantity of interest is embodied in physical objects accessible with quantum-enhanced measurements, it becomes relevant to investigate how to transfer this advantage from the individual sampled points to the estimation of the whole function. In this article we report the experimental quantum-enhanced function estimation of the optical response of a liquid crystal. Our results illustrate that optimizing the employment of the resources is not as straightforward as it may appear at a first glance: Quantum advantage becomes substantial only past a sampling density that depends on the interpolation method, and on the function at hand. Our results show how quantum resources should successfully be employed to access the rich information contained in continuous signals
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