This 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.
This 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.
In the present PhD work, we focus on a specific class of quantum states of light: the non-Gaussian states. These states have the particularity of exhibiting Wigner functions with some negative values. This quantum feature is a necessary condition to perform some quantum computation task; furthermore it is also useful for various other applications, including quantum communication and metrology. Different strategies can be used to generate these states. Here, we start from Gaussian states produced by optical parametric oscillators in the continuous wave regime, (i.e. single-mode and two-mode squeezed vacuum states). The non-Gaussian feature can only be obtained by non-linear phenomena (over-quadratic Hamiltonian). In our case, the non-linearity is induced by photon-counting-based measurements (also called non-Gaussian measurements). This study is mainly divided into two parts. First, the generation of non-classical states associated with two types of qubit encoding: the single-photon state, used for quantum information with discrete variables, and the coherent state superposition (the so-called optical Schrodinger cat state), used for quantum information with continuous variables. These two states have then been used to perform some quantum information protocols. The first one addresses the problem of single-photon entanglement witness, and the other the generation of entanglement between the two encodings (also called hybrid entanglement).
We review some recent results regarding the use of time-continuous measurements for quantum-enhanced metrology. First, we present the underlying quantum estimation framework and elucidate the correct figures of merit to employ. We then report results from two previous works where the system of interest is an ensemble of two-level atoms (qubits) and the quantity to estimate is a magnetic field along a known direction (a frequency). In the first case, we show that, by continuously monitoring the collective spin observable transversal to the encoding Hamiltonian, we get Heisenberg scaling for the achievable precision (i.e., 1 / N for N atoms); this is obtained for an uncorrelated initial state. In the second case, we consider independent noises acting separately on each qubit and we show that the continuous monitoring of all the environmental modes responsible for the noise allows us to restore the Heisenberg scaling of the precision, given an initially entangled GHZ state.
In the present PhD work, we focus on a specific class of quantum states of light: the non-Gaussian states. These states have the particularity of exhibiting Wigner functions with some negative values. This quantum feature is a necessary condition to perform some quantum computation task; furthermore it is also useful for various other applications, including quantum communication and metrology. Different strategies can be used to generate these states. Here, we start from Gaussian states produced by optical parametric oscillators in the continuous wave regime, (i.e. single-mode and two-mode squeezed vacuum states). The non-Gaussian feature can only be obtained by non-linear phenomena (over-quadratic Hamiltonian). In our case, the non-linearity is induced by photon-counting-based measurements (also called non-Gaussian measurements). This study is mainly divided into two parts. First, the generation of non-classical states associated with two types of qubit encoding: the single-photon state, used for quantum information with discrete variables, and the coherent state superposition (the so-called optical Schrödinger cat state), used for quantum information with continuous variables. These two states have then been used to perform some quantum information protocols. The first one addresses the problem of single-photon entanglement witness, and the other the generation of entanglement between the two encodings (also called hybrid entanglement).
The generation of non-Gaussian states of bosonic systems described by continuous quantum degrees of freedom is of interest in a variety of contexts, ranging from quantum foundations to computation and communication. A crucial feature of genuine non-Gaussian states is that they cannot be described in general with a non-negative Wignerquasi-probability distribution. In particular, this feature is equivalent to contextuality and it underpins all attempts at attaining quantum computational advantage in a universal setting. In this thesis, the generation of Wigner-negative states is addressed, pursuing two approaches. First, in an optomechanical-like setting, we develop schemes to generate Wigner-negative states of two massive mechanical systems, in turn correlated such that they also feature entanglement, another genuine quantum hallmark. These schemes are based on driven-dissipative systems where dissipation is properly engineered by taking advantage of linear-and-quadratic optomechanical interactions. We address the robustness of these schemes when uncontrollable noisy channels are included in the dynamics, proving that their resilience is comparable to Gaussian schemes that have already been implemented experimentally. Second, considering in particular circuit QED systems and trapped ions, we propose a method to engineer a set of Hamiltonian evolutions that are universal in terms of single-mode state preparation. This method is based on a driven quantum Rabi model, where the desired evolution is effectively imprinted on a continuous-variable degree of freedom by its interaction with a properly driven two-level system. We demonstrate the universality of such approach by simulating the generation of multi-squeezed and other states, including the celebrated cubic-phase state. We also consider the effect of noise in realistic settings, showing in particular that in systems involving superconducting qubits, the generation of tri-squeezed states --- a universal resource for continuous-variable quantum computation which we prove to display larger Wigner negativities with respect to Fock and cubic-phase states for the same energy --- is within experimental reach.
The use of quantum information in technology promises to supersede the so-called classical devices used nowadays. Understanding what features are inherently non-classical is crucial for reaching better-than-classical performance. This thesis focuses on two nonclassical behaviours: quantum contextuality and Wigner negativity. The former is a notion superseding nonlocality that can be exhibited by quantum systems. To date, it has mostly been studied in discrete-variable scenarios. In those scenarios, contextuality has been shown to be necessary and sufficient for advantages in some cases. On the other hand, negativity of the Wigner function is another unsettling non-classical feature of quantum states that originates from phase-space formulation in continuous-variable quantum optics. Continuous-variable scenarios offer promising candidates for implementing quantum computations. Wigner negativity is known to be a necessary resource for quantum speedup with continuous variables. However contextuality has been little understood and studied in continuous-variable scenarios. We first set out a robust framework for properly treating contextuality in continuous variables. We also quantify contextuality in such scenarios by using tools from infinite-dimensional optimisation theory. Building upon this, we show that Wigner negativity is equivalent to contextuality in continuous variables with respect to Pauli measurements thus establishing a continuous-variable analogue of a celebrated result by Howard et al. We then introduce experimentally-friendly witnesses for Wigner negativity of single mode and multimode quantum states, based on fidelities with Fock states, using again tools from infinite-dimensional optimisation theory. We further extend the range of previously known discrete-variable results linking contextuality and advantage into a new territory of information retrieval.
In this PhD thesis we address the problem of characterizing quantum states and parameters of systems that are of particular interest for quantum technologies. In the first part we consider continuous variable systems and in particular Gaussian states; we address the estimation of quantities characterizing single-mode Gaussian states as the displacement and squeezing parameter and we study the improvement in the parameter estimation by introducing a Kerr nonlinearity. Moreover, we address the discrimination of noisy channels by means of Gaussian states as probe states considering two problems: the detection of a lossy channel against the alternative hypothesis of an ideal lossless channel and the discrimination of two Gaussian noisy channels. In the last part of the thesis, we consider the one dimensional quantum Ising model in a transverse magnetic field. We exploit the recent results about the geometric approach to quantum phase transitions to derive the optimal estimator of the coupling constant of the model at zero and finite temperature in both cases of few spins and in the thermodynamic limit. We also analyze the effects of temperature and the scaling properties of the estimator of the coupling constant. Finally, we consider the discrimination problem for two ground states or two thermal states of the model.