In work arXiv:2111.14700, the scheme of quantum nondemolition measurement of optical quanta which uses a resonantly enhanced Kerr nonlinearity in whispering gallery mode (WGM) optical resonators was analyzed theoretically. Here we show, that by using a squeezed quantum state of the probe mode, it is possible to significantly increase the sensitivity of that scheme.

In this paper, we introduce an emerging quantum machine learning (QML) framework to assist classical deep learning methods for biosignal processing applications. Specifically, we propose a hybrid quantum-classical neural network model that integrates a variational quantum circuit (VQC) into a deep neural network (DNN) for electroencephalogram (EEG), electromyogram (EMG), and electrocorticogram (ECoG) analysis. We demonstrate that the proposed quantum neural network (QNN) achieves state-of-the-art performance while the number of trainable parameters is kept small for VQC.

A generalization of the canonical coherent states of a quantum harmonic oscillator has been performed by requiring the conditions of normalizability, continuity in the label and resolution of the identity operator with a positive weight function. Relying on this approach, in the present scenario coherent states are generalized over the canonical or finite dimensional Fock space of the harmonic oscillator. A class of generalized coherent states is determined such that the distribution of the number of excitations departs from the Poisson statistics according to combinations of stretched exponential decays, power laws and logarithmic forms. The analysis of the Mandel parameter shows that these generalized coherent states exhibit (non-classical) sub-Poissonian or super-Poissonian statistics of the number of excitations for small values of the label, according to determined properties. The statistics is uniquely sub-Poissonian for large values of the label. As particular cases, truncated Wright generalized coherent states exhibit uniquely non-classical properties, differently from the truncated Mittag-Leffler generalized coherent states.

For quantum computers to successfully solve real-world problems, it is necessary to tackle the challenge of noise: the errors which occur in elementary physical components due to unwanted or imperfect interactions. The theory of quantum fault tolerance can provide an answer in the long term, but in the coming era of `NISQ' machines we must seek to mitigate errors rather than completely remove them. This review surveys the diverse methods that have been proposed for quantum error mitigation, assesses their in-principle efficacy, and then describes the hardware demonstrations achieved to date. We identify the commonalities and limitations among the methods, noting how mitigation methods can be chosen according to the primary type of noise present, including algorithmic errors. Open problems in the field are identified and we discuss the prospects for realising mitigation-based devices that can deliver quantum advantage with an impact on science and business.

Complementary information provides fragmented descriptions of quantum systems from different perspectives, and is inaccessible simultaneously. We introduce the notion of \emph{information operator} associated with a measurement set, which allows one to reconstruct (in subspace) arbitrary unknown quantum states from measurement outcomes analytically. Further, we derive from it a universal information tradeoff relation depicting the competitive balance between complementary information extracted from generalized measurements, based on which innovative entropic uncertainty relations are also formulated. Moreover, the unbiasedness of orthonormal bases is naturally captured by the Hilbert-Schmidt norm of the corresponding information operator, it's relationship with the white noise robustness are studied both analytically and numerically.

We examine the fundamental question whether a random discrete structure with the minimal number of restrictions can converge to continuous metric space. We study the geometrical properties such as the dimensionality and the curvature emerging out of the connectivity properties of uniform random graphs. In addition we introduce a simple evolution mechanism for the graph by removing one edge per a fundamental quantum of time from an initially complete graph. We show an exponential growth of the radius of the graph, that ends up in a random structure with emergent approximate spatial dimension $D=3$ and zero curvature, resembling a flat 3D manifold, that could describe the observed space in our universe and some of its geometrical properties. In addition, we introduce a generalized action for graphs based on physical quantities on different subgraph structures that helps to recover the well-known properties of spacetime as described in general relativity, like time dilation due to gravity. Also, we show how various quantum mechanical concepts such as generalized uncertainty principles based on the statistical fluctuations can emerge from random discrete models. Moreover, our approach leads to a unification of space and matter/energy, for which we propose a mass-energy-space equivalence that leads to a way to transform between empty space and matter/energy via the cosmological constant.

We initiate the recently proposed $\boldsymbol{w}$-ensemble one-particle reduced density matrix functional theory ($\boldsymbol{w}$-RDMFT) by deriving the first functional approximations and illustrate how excitation energies can be calculated in practice. For this endeavour, we first study the symmetric Hubbard dimer, constituting the building block of the Hubbard model, for which we execute the Levy-Lieb constrained search. Second, due to the particular suitability of $\boldsymbol{w}$-RDMFT for describing Bose-Einstein condensates, we demonstrate three conceptually different approaches for deriving the universal functional in a homogeneous Bose gas for arbitrary pair interaction in the Bogoliubov regime. Remarkably, in both systems the gradient of the functional is found to diverge repulsively at the boundary of the functional's domain, extending the recently discovered Bose-Einstein condensation force to excited states. Our findings highlight the physical relevance of the generalized exclusion principle for fermionic and bosonic mixed states and the curse of universality in functional theories.

On this PhD thesis we cover the results contained in arXiv:2001.07050, arXiv:2111.10096 and arXiv:2011.02822, while providing further details about their derivations.

In the first two papers, we study the generation and detection of entangled non-Gaussian states of microwave radiation. These states are produced in a new parametric oscillator, built recently within the field of cQED, capable of down-converting a microwave tone into three different tones at once. These three photons share among their magnitudes quantum correlations, in particular genuine entanglement. In this text we refer to it as non-Gaussian because of its manifestation on statistical moments higher than covariances, and we propose a simple and practical criterion for the design of witnesses capable of detecting it: they must be built from higher statistical moments that change through time. Additionally, we speculate on the theoretical implications of the criterion and find suggestive connections to other entanglement classes, such as the paradigmatic nonequivalent GHZ and W three qubit states.

In the third paper, we explore one of the possible applications of quantum technologies: analog simulation of quantum systems. The literature prior to this thesis showcases multiple examples of superconducting circuits capable of mimicking systems in which one must consider both quantum and relativistic phenomena, such as the dynamical Casimir and Unruh effects. This work explores the information that can be obtained through analog simulation, proposing a circuit capable of featuring the internal dynamics of a mirror experiencing a relativistic trajectory, that is, a mirror producing the dynamical Casimir effect.

Mixed quantum-classical spin systems have been proposed in spin chain theory, organic chemistry, and, more recently, spintronics. However, current models of quantum-classical dynamics beyond mean-field approximations typically suffer from long-standing consistency issues, and in some cases invalidate Heisenberg's uncertainty principle. Here, we present a fully Hamiltonian theory of quantum-classical spin dynamics that appears to be the first to ensure an entire series of consistency properties, including positivity of both the classical and quantum densities, and thus Heisenberg's principle. We show how this theory may connect to recent energy-balance considerations in measurement theory and we present its Poisson bracket structure explicitly. After focusing on the simpler case of a classical Bloch vector interacting with a quantum spin observable, we illustrate the extension of the model to systems with several spins, and restore the presence of orbital degrees of freedom.

Light is a precious tool to probe matter, as it captures microscopic and macroscopic information on the system. We here report on the transition from a thermal (classical) to a spontaneous emission (quantum) mechanism for the loss of light coherence from a macroscopic atomic cloud. The coherence is probed by intensity-intensity correlation measurements realized on the light scattered by the atomic sample, and the transition is explored by tuning the balance between thermal coherence loss and spontaneous emission via the pump strength. Our results illustrate the potential of cold atom setups to investigate the classical-to-quantum transition in macroscopic systems.

Quantum sensors and qubits are usually two-level systems (TLS), the quantum analogs of classical bits which assume binary values '0' or '1'. They are useful to the extent to which they can persist in quantum superpositions of '0' and '1' in real environments. However, such TLS are never alone in real materials and devices, and couplings to other degrees of freedom limit the lifetimes - called decoherence times - of the superposition states. Decoherence occurs via two major routes - excitation hopping and fluctuating electromagnetic fields. Common mitigation strategies are based on material improvements, exploitation of clock states which couple only to second rather than first order to external perturbations, and reduction of interactions via extreme dilution of pure materials made from isotopes selected to minimize noise from nuclear spins. We demonstrate that for a dense TLS network in a noisy nuclear spin bath, we can take advantage of interactions to pass from hopping to fluctuation dominance, increasing decoherence times by almost three orders of magnitude. In the dilute rare-earth insulator LiY1-xTbxF4, Tb ions realize TLS characterized by a 30GHz splitting and readily implemented clock states. Dipolar interactions lead to coherent, localized pairs of Tb ions, that decohere due to fluctuating quantum mechanical ring-exchange interaction, sensing the slow dynamics of the surrounding, nearly localized Tb spins. The hopping and fluctuation regimes are sharply distinguished by their Rabi oscillations and the invisible vs. strong effect of classic 'error correcting' microwave pulse sequences. Laying open the decoherence mechanisms at play in a dense, disordered and noisy network of interacting TLS, our work expands the search space for quantum sensors and qubits to include clusters in dense, disordered materials, that can be explored for localization effects.

Quantum reservoir computing is a class of quantum machine learning algorithms involving a reservoir of an echo state network based on a register of qubits, but the dependence of its memory capacity on the hyperparameters is still rather unclear. In order to maximize its accuracy in time--series predictive tasks, we investigate the relation between the memory of the network and the reset rate of the evolution of the quantum reservoir. We benchmark the network performance by three non--linear maps with fading memory on IBM quantum hardware. The memory capacity of the quantum reservoir is maximized for central values of the memory reset rate in the interval [0,1]. As expected, the memory capacity increases approximately linearly with the number of qubits. After optimization of the memory reset rate, the mean squared errors of the predicted outputs in the tasks may decrease by a factor ~1/5 with respect to previous implementations.

Uncloneable encryption, first introduced by Broadbent and Lord (TQC 2020), is a form of encryption producing a quantum ciphertext with the property that if the ciphertext is distributed between two non-communicating parties, they cannot both learn the underlying plaintext even after receiving the decryption key. In this work, we introduce a variant of uncloneable encryption in which several possible decryption keys can decrypt a particular encryption, and the security requirement is that two parties who receive independently generated decryption keys cannot both learn the underlying ciphertext. We show that this variant of uncloneable encryption can be achieved device-independently, i.e., without trusting the quantum states and measurements used in the scheme. Moreover, we show that this variant of uncloneable encryption works just as well as the original definition in constructing private-key quantum money, and that uncloneable bits can be achieved in this variant without using the quantum random oracle model.

We study the fundamental limits of the precision of estimating parameters of a quantum matter system when it is probed by a travelling pulse of quantum light. In particular, we focus on the estimation of the interaction strength between the pulse and a two-level atom, equivalent to the estimation of the dipole moment. Our analysis of single-photon pulses highlights the interplay between the information gained from the photon absorption by the atom, as measured in absorption spectroscopy, and the perturbation to the field temporal mode due to spontaneous emission. Beyond the single-photon regime, we introduce an approximate model to study more general states of light in the limit of short pulses, where spontaneous emission can be neglected. We also show that for a vast class of entangled biphoton states, quantum entanglement provides no fundamental advantage and the same precision can be obtained with a separable state. We conclude by studying the estimation of the electric dipole moment of a sodium atom using quantum light. Our work initiates a quantum information theoretic methodology for developing the theory and practice of quantum light spectroscopy.

The quench dynamics of the Hubbard model in tilted and harmonic potentials is discussed within the semiclassical picture. Applying the fermionic truncated Wigner approximation (fTWA), the dynamics of imbalances for charge and spin degrees of freedom is analyzed and its time evolution is compared with the exact simulations in one-dimensional lattice. Quench from charge or spin density wave is considered. We show that introduction of harmonic and spin-dependent linear potentials sufficiently validates fTWA for longer times. Such an improvement of fTWA is also obtained for the higher order correlations in terms of quantum Fisher information for charge and spin channels. This allows us to discuss the dynamics of larger system sizes and connect our discussion to the recently introduced Stark many-body localization. In particular, we focus on a finite two-dimensional system and show that at intermediate linear potential strength, the addition of a harmonic potential and spin dependence of the tilt, results in subdiffusive dynamics, similar to that of disordered systems. Moreover, for specific values of harmonic potential, we observed phase separation of ergodic and non-ergodic regions in real space. The latter fact is especially important for ultracold atom experiments in which harmonic confinement can be easily imposed, causing a significant change in relaxation times for different lattice locations.

We propose a very simple interpretation of Schroedinger's cat: the cat is in a state that has a well defined value of a property that is complementary to the property "being dead or alive". Hence, because of quantum complementarity, the cat does not possess any definite value for the property of being dead or alive. It is neither dead nor alive. Namely, the cat paradox is explained through quantum complementarity: of many complementary properties, any quantum system can have a well defined value only of one at a time. While this interpretation only uses textbook concepts (the Copenhagen interpretation), apparently it has never explicitly appeared in the literature. We detail how to build an Arduino based simulation of Schroedinger's experiment for science outreach events.

Gases of doubly-dipolar particles, with both magnetic and electric dipole moments, offer intriguing novel possibilities. We show that the interplay between doubly-dipolar interactions, quantum stabilizat\ ion, and external confinement results in a rich ground-state physics of supersolids and incoherent droplet arrays in doubly-dipolar condensates. Our study reveals novel possibilities for engineering quan\ tum droplets and droplet supersolids, including supersolid-supersolid transitions and the realization of supersolid arrays of pancake droplets.

While volume violation of area law has been exhibited in several quantum spin chains, the construction of a corresponding model in higher dimensions, with isotropic terms has been an open problem. Here we construct a 2D frustration free Hamiltonian with maximal violation of the area law. We do so by building a quantum model of random surfaces with color degree of freedom that can be viewed as a collection of colored Dyck paths. The Hamiltonian may be viewed as 2d generalization of the Fredkin spin chain. It's action is shown to be ergodic within the Hilbert subspace of zero fixed Dirichlet boundary condition and positive height function in the bulk and exhibits a non-degenerate ground state. Its entanglement entropy between subsystems is isotropic with respect to the direction of the cut in the thermodynamic limit, and exhibits an entanglement phase transition as the deformation parameter is tuned. The area- and volume-law phases are similar to the one-dimensional model, while the critical point scales as $L\log L$. Similar models can be built in higher dimensions with even softer area violation at the critical point.

This article reviews theoretical and experimental advances in Efimov physics, an array of quantum few-body and many-body phenomena arising for particles interacting via short-range resonant interactions, that is based on the appearance of a scale-invariant three-body attraction theoretically discovered by Vitaly Efimov in 1970. This three-body effect was originally proposed to explain the binding of nuclei such as the triton and the Hoyle state of carbon-12, and later considered as a simple explanation for the existence of some halo nuclei. It was subsequently evidenced in trapped ultra-cold atomic clouds and in diffracted molecular beams of gaseous helium. These experiments revealed that the previously undetermined three-body parameter introduced in the Efimov theory to stabilise the three-body attraction typically scales with the range of atomic interactions. The few- and many-body consequences of the Efimov attraction have been since investigated theoretically, and are expected to be observed in a broader spectrum of physical systems.

It is an open fundamental question how the classical appearance of our environment arises from the underlying quantum many-body theory. We propose that phenomena involved in the quantum-to-classical transition can be probed in collisions of bright solitary waves in Bose- Einstein condensates, where thousands of atoms form a large compound object at ultra cold temperatures. For the experimentally most relevant quasi-1D regime, where integrability is broken through effective three-body interactions, we find that ensembles of solitary waves exhibit complex interplay between phase coherence and entanglement generation in beyond mean-field simulations using the truncated Wigner method: An initial state of two solitons with a well defined relative phase looses that phase coherence in the ensemble, with its single particle two-mode density matrix exhibiting similar dynamics as a decohering two mode superposition. This apparent decoherence is a prerequisite for the formation of entangled superpositions of different atom numbers in a subsequent soliton collision. The necessity for the solitons to first decohere is explained based on the underlying phase-space of the quintic mean field equation. We show elsewhere that superpositions of different atom numbers later further evolve into spatially entangled solitons. Loss of ensemble phase coherence followed by system internal entanglement generation appear in an unusual order in this closed system, compared to a typical open quantum system.