49 research outputs found
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
CONTINUOUS MEASUREMENTS AND NONCLASSICALITY AS RESOURCES FOR QUANTUM TECHNOLOGIES
No full textThis PhD thesis contains results about two different main topics.
The first part deals with the application of continuously monitored quantum systems to high precision quantum metrology. A continuous in time measurement on a quantum system is a kind indirect measurement, which only weakly perturbs the system and leaves room for it to evolve under its dynamics. This time-continuous measurement allows one to collect information about some interesting parameter characterizing the dynamics. In this thesis we show how to apply the theory of quantum parameter estimation to continuously monitored quantum systems. In particular, we study the estimation of a magnetic field applied to an ensemble of two level atoms; we show that by continuously monitoring the system we can obtain a quadratic scaling of the precision with the number of atoms, in two different physical settings (dynamically generated entanglement or initial entanglement).
In the second part we study different aspects of nonclassicality of continuous variable quantum systems (bosonic degree of freedoms). They can be described by distributions (in particular, the Wigner function) on a classical phase space, which however can take negative values, the hallmark of nonclassicality. In this context, states with a Gaussian distribution are very useful and very well studied; however, on a fundamental level they must be considered classical. We present several studies connected to the vast topic of non-Gaussian states, starting from an application to parameter estimation, as a link to the first part. We study the relationships between anharmonic Hamiltonians and the nonclassicality of their ground states; we also explore the connection between a quantum effect called `backflow of probability' and the negativity of the Wigner function. We end by showing that quantum operations made out of Gaussian building blocks give rise to a well-defined resource theory of Wigner negativity and non-Gaussianity
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
Universal bounds for quantum metrology in the presence of correlated noise
No full textWe derive fundamental bounds for general quantum metrological models
involving both temporal or spatial correlations (mathematically described by
quantum combs), which may be effectively computed in the limit of a large
number of probes or sensing channels involved. Although the bounds are not
guaranteed to be tight in general, their tightness may be systematically
increased by increasing numerical complexity of the procedure. Interestingly,
this approach yields bounds tighter than the state of the art also for
uncorrelated channels. We apply the bound to study the limits for the most
general adaptive phase estimation models in the presence of temporally
correlated dephasing. We consider dephasing both parallel (no Heisenberg
scaling) and perpendicular (Heisenberg scaling possible) to the signal. In the
former case our new bounds show that negative correlations are beneficial, for
the latter we show evidence that the bounds are tight. We also apply the bounds
to collisional thermometry, i.e. estimation of a parameter of the environment,
showing evidence that entangled probes may provide only a limited advantage
Tensor network approach to sensing quantum light-matter interactions
No full textWe present the fundamental limits to the precision of estimating parameters of a quantum matter system probed by light, even when some of the light is lost. This practically inevitable scenario leads to a tripartite quantum system of matter, and light-detected and lost. Evaluating fundamental information theoretic quantities such as the quantum Fisher information of only the detected light was heretofore impossible. We succeed by expressing the final quantum state of the detected light as a matrix product operator. We apply our method to resonance fluorescence and pulsed spectroscopy. For both, we quantify the sub-optimality of continuous homodyning and photo-counting measurements in parameter estimation. For the latter, we find that single-photon Fock state pulses allow higher precision per photon than pulses of coherent states. Our method should be valuable in studies of quantum light-matter interactions, quantum light spectroscopy, quantum stochastic thermodynamics, and quantum clocks
Enhanced estimation of loss in the presence of Kerr nonlinearity
No full textWe address the characterization of dissipative bosonic channels and show that estimation of the loss rate by Gaussian probes (coherent or squeezed) is improved in the presence of Kerr nonlinearity. In particular, enhancement of precision may be substantial for short interaction time, i.e., for media of moderate size, e.g., biological samples. We analyze in detail the behavior of the quantum Fisher information (QFI), and determine the values of nonlinearity maximizing the QFI as a function of the interaction time and of the parameters of the input signal. We also discuss the precision achievable by photon counting and quadrature measurement and present additional results for truncated, few-photon, probe signals. Finally, we discuss the origin of the precision enhancement, showing that it cannot be linked quantitatively to the non-Gaussianity or the nonclassicality of the interacting probe signal
Pseudomode treatment of strong-coupling quantum thermodynamics
No full textThe treatment of quantum thermodynamic systems beyond weak coupling is of
increasing relevance, yet extremely challenging. The evaluation of
thermodynamic quantities in strong-coupling regimes requires a nonperturbative
knowledge of the bath dynamics, which in turn relies on heavy numerical
simulations. To tame these difficulties, considering thermal bosonic baths
linearly coupled to the open system, we derive expressions for heat, work, and
average system-bath interaction energy that only involve the autocorrelation
function of the bath and two-time expectation values of system operators. We
then exploit the pseudomode approach, which replaces the physical continuous
bosonic bath with a small finite number of damped, possibly interacting, modes,
to numerically evaluate these relevant thermodynamic quantities. We show in
particular that this method allows for an efficient numerical evaluation of
thermodynamic quantities in terms of one-time expectation values of the open
system and the pseudomodes. We apply this framework to the investigation of two
paradigmatic situations. In the first instance, we study the entropy production
for a two-level system coupled to an ohmic bath, simulated via interacting
pseudomodes, allowing for the presence of time-dependent driving. Secondly, we
consider a quantum thermal machine composed of a two-level system interacting
with two thermal baths at different temperatures, showing that an appropriate
sinusoidal modulation of the coupling with the cold bath only is enough to
obtain work extraction.Comment: 23 pages, 5 figure
Simultaneous optical phase and loss estimation revisited : measurement and probe incompatibility
No full textQuantum multiparameter metrology is hindered by incompatibility issues, such as finding a single probe state (probe incompatibility) and a single measurement (measurement incompatibility) optimal for all parameters. The simultaneous estimation of phase shift and loss in a single optical mode is a paradigmatic multiparameter metrological problem in which such tradeoffs are present. We consider two settings: single-mode or two-mode probes (with a reference lossless mode), and for each setting we consider either Gaussian states or arbitrary quantum states of light restricted only by a maximal number of photons allowed. We find numerically that, as the number of photons increases, there are quantum states of light for which probe incompatibility disappears both in the single- and two-mode scenarios. On the other hand, for Gaussian states, probe incompatibility is present in the single-mode case and may be removed only in the two-mode setting thanks to the entanglement with the reference mode. Finally, we provide strong arguments that the fundamental incompatibility aspect of the model is measurement incompatibility, which persists for all the scenarios considered, and unlike probe-incompatibility cannot be overcome even in the large photon number limit
Semiparametric estimation of the Hong-Ou-Mandel profile
No full textWe apply the theory of semiparametric estimation to a Hong-Ou-Mandel interference experiment with a spectrally entangled two-photon state generated by spontaneous parametric down-conversion. Thanks to the semiparametric approach, we can evaluate the Cramér-Rao bound and find an optimal estimator for a particular parameter of interest without assuming perfect knowledge of the two-photon wave function, formally treated as an infinity of nuisance parameters. In particular, we focus on the estimation of the Hermite-Gauss components of the marginal symmetrized wave function, whose Fourier transform governs the shape of the temporal coincidence profile. We show that negativity of these components is an entanglement witness of the two-photon state
