According to quantum mechanics, the informational content of isolated systems does not change in time. However, subadditivity of entropy seems to describe an excess of information when we look at single parts of a composite systems and their correlations. Moreover, the balance between the entropic contributions coming from the various parts is not conserved under unitary transformations. Reasoning on the basic concept of quantum mechanics, we find that in such a picture an important term has been overlooked: the intrinsic quantum information encoded in the coherence of pure states. To fill this gap we are led to define a quantity, that we call coherent entropy, which is necessary to account for the "missing" information and for re-establishing its conservation. Interestingly, the coherent entropy is found to be equal to the information conveyed in the future by quantum states. The perspective outlined in this paper may be of some inspiration in several fields, from foundations of quantum mechanics to black-hole physics.

Two techniques that employ equally spaced trains of optical pulses to map an optical high frequency into a low frequency modulation of the signal that can be detected in real time are compared. The development of phase-stable optical frequency combs has opened up new avenues to metrology and spectroscopy. The ability to generate a series of frequency spikes with precisely controlled separation permits a fast, highly accurate sampling of the material response. Recently, pairs of frequency combs with slightly different repetition rates have been utilized to down-convert material susceptibilities from the optical to microwave regime where they can be recorded in real time. We show how this one-dimensional dual comb technique can be extended to multiple dimensions by using several combs. We demonstrate how nonlinear susceptibilities can be quickly acquired using this technique. In a second class of techniques, sequences of ultrafast mode locked laser pulses are used to recover pathways of interactions contributing to nonlinear susceptibilities by using a photo-acoustic modulation varying along the sequences. We show that these techniques can be viewed as a time-domain analogue of the multiple frequency comb scheme. %We compare the two techniques: in both, an optical high frequency is mapped into a low frequency modulation of the signal that can be detected in real time.

We present a simple $^1$H NMR approach for characterizing intermediate to fast regime molecular motions using $^1$H time-domain NMR at low magnetic field. The method is based on a Goldmann Shen dipolar filter (DF) followed by a Mixed Magic Sandwich Echo (MSE). The dipolar filter suppresses the signals arising from molecular segments presenting sub kHz mobility, so only signals from mobile segments are detected. Thus, the temperature dependence of the signal intensities directly evidences the onset of molecular motions with rates higher than kHz. The DF-MSE signal intensity is described by an analytical function based on the Anderson Weiss theory, from where parameters related to the molecular motion (e.g. correlation times and activation energy) can be estimated when performing experiments as function of the temperature. Furthermore, we propose the use of the Tikhonov regularization for estimating the width of the distribution of correlation times.

Clustering is a powerful machine learning technique that groups "similar" data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of within-the-cluster distances between points. The straightforward approach involves examining all the possible assignments of points to each of the clusters. This approach guarantees the solution will be a global minimum, however the number of possible assignments scales quickly with the number of data points and becomes computationally intractable even for very small datasets. In order to circumvent this issue, cost function minima are found using popular local-search based heuristic approaches such as k-means and hierarchical clustering. Due to their greedy nature, such techniques do not guarantee that a global minimum will be found and can lead to sub-optimal clustering assignments. Other classes of global-search based techniques, such as simulated annealing, tabu search, and genetic algorithms may offer better quality results but can be too time consuming to implement. In this work, we describe how quantum annealing can be used to carry out clustering. We map the clustering objective to a quadratic binary optimization (QUBO) problem and discuss two clustering algorithms which are then implemented on commercially-available quantum annealing hardware, as well as on a purely classical solver "qbsolv." The first algorithm assigns N data points to K clusters, and the second one can be used to perform binary clustering in a hierarchical manner. We present our results in the form of benchmarks against well-known k-means clustering and discuss the advantages and disadvantages of the proposed techniques.

Using the Tridiagonal Representation Approach, we obtain solutions (energy spectrum and corresponding wavefunctions) for a new five-parameter potential box with inverse square singularity at the boundaries.

Quantum emitters are an integral component for a broad range of quantum technologies including quantum communication, quantum repeaters, and linear optical quantum computation. Solid-state color centers are promising candidates for scalable quantum optics operations due to their long coherence time and small inhomogeneous broadening. However, once excited, color centers often decay through phonon-assisted processes, limiting the efficiency of single photon generation and photon mediated entanglement generation. Herein, we demonstrate strong enhancement of spontaneous emission rate of a single silicon-vacancy center in diamond embedded within a monolithic optical cavity, reaching a regime where the excited state lifetime is dominated by spontaneous emission into the cavity mode. We observe a 10-fold lifetime reduction and 42-fold enhancement in emission intensity when the cavity is tuned into resonance with the optical transition of a single silicon-vacancy center, corresponding to a spontaneous emission coupling factor \beta =89%. The cavity enhancement enables us to observe emission competition among different orbital transitions when we selectively couple one transition to the cavity.

The practical implementation of many quantum technologies relies on the development of robust and bright single photon sources that operate at room temperature. The negatively charged silicon-vacancy (SiV-) color center in diamond is a possible candidate for such a single photon source. However, due to the high refraction index mismatch to air, color centers in diamond typically exhibit low photon out-coupling. An additional shortcoming is due to the random localization of native defects in the diamond sample. Here we demonstrate deterministic implantation of Si ions with high conversion efficiency to single SiV- centers, targeted to fabricated nanowires. The co-localization of single SiV- centers with the nanostructures yields a ten times higher light coupling efficiency than for single SiV- centers in bulk diamond. This enhanced photon out-coupling, together with the intrinsic scalability of the SiV- creation method, enables a new class of devices for integrated photonics and quantum science.

We construct an entangled quantum Otto engine based on spin-1/2 systems undergoing Dzyaloshinski-Moriya (DM) interaction within a varying magnetic field. We investigate the influence of the DM interaction on basic thermodynamic quantities, including heat transfer, work done, and efficiency and find that the DM interaction importantly influences the engine's thermodynamics. We obtain an expression for engine efficiency, finding it to yield the same efficiency for antiferromagnetic and ferromagnetic coupling. A new upper bound, nontrivially consistent with the second law of thermodynamics, is derived for engine efficiency in the case of non-zero DM interaction.

In this paper we experimentally demonstrated a broadband microwave scheme suitable for the multiresonator quan- tum memory-interface. The microwave scheme consists of the system of composed mini-resonators strongly inter- acting with a common broadband resonator coupled with the external microwave waveguide. We have implemented the controllable tuning of the mini-resonator frequencies and coupling of the common resonator with the external waveguide for the implementation of the impedance matched quantum storage. The storage of microwave pulses with an efficiency of 16.3% has been shown experimentally at room temperature. The possible properties of the proposed scheme for mini-resonators with high-Q at low temperatures are discussed. The obtained results pave the way for the implementation of superefficient broadband microwave quantum memory-interface.

The conventional method of qubit measurements in circuit QED is employing the dispersive regime of qubit-cavity coupling, which results in an approximated scheme of quantum nondemolition (QND) readout. However, this scheme breaks down owing to the Purcell effect in the case of strong coupling and/or strong measurement drive. To remove the drawbacks of the dispersive readout, a recent proposal by virtue of longitudinal coupling suggests a new scheme to realize fast, high-fidelity and ideal QND readout of qubit state. In the present work, following dispersive readout, we construct the gradual partial-collapse theory for this new measurement scheme, in terms of both the quantum trajectory equation and quantum Bayesian approach. The longitudinal coupling provides as well a convenient method of cavity reset. In combination with the reset procedure, the established theory is expected to be useful for such as measurement-based feedback control and many other quantum applications associated with partial-collapse weak measurements.

Normal--mode splitting is the most evident signature of strong coupling between two interacting subsystems. It occurs when the coupling rate is larger than the dissipative rates of both subsystems. Here we experimentally show that a weakly coupled optomechanical system at room temperature can manifest normal--mode splitting when the pump field fluctuations are anti--squashed by a phase-sensitive feedback loop operating close to its instability threshold, such that the optical cavity exhibits an effectively reduced decay rate. As a consequence, feedback enables a naturally weakly coupled optomechanical device to enter the strong coupling regime. Such a possibility could be useful for the exploitation of optomechanical devices for the transduction, storage and retrieval of classical and quantum signals.

We consider the inverse eigenvalue problem for entanglement witnesses, which asks for a characterization of their possible spectra (or equivalently, of the possible spectra resulting from positive linear maps of matrices). We completely solve this problem in the two-qubit case and we derive a large family of new necessary conditions on the spectra in arbitrary dimensions. We also establish a natural duality relationship with the set of absolutely separable states, and we completely characterize witnesses (i.e., separating hyperplanes) of that set when one of the local dimensions is 2.

The hyperpolarisation of nuclear spins within target molecules is a critical and complex challenge in magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR) spectroscopy. Hyperpolarisation offers enormous gains in signal and spatial resolution which may ultimately lead to the development of molecular MRI and NMR. At present, techniques used to polarise nuclear spins generally require low temperatures and/or high magnetic fields, radio-frequency control fields, or the introduction of catalysts or free-radical mediators. The emergence of room temperature solid-state spin qubits has opened exciting new pathways to circumvent these requirements to achieve direct nuclear spin hyperpolarisation using quantum control. Employing a novel cross-relaxation induced polarisation (CRIP) protocol, we demonstrate the first external nuclear spin hyperpolarisation achieved by a quantum probe, in this case of $^1$H molecular spins in poly(methyl methacrylate). In doing so, we show that a single qubit is capable of increasing the thermal polarisation of $\sim 10^6$ nuclear spins by six orders of magnitude, equivalent to an applied magnetic field of $10^5$\,T. The technique can also be tuned to multiple spin species, which we demonstrate using both \C{13} and $^1$H nuclear spin ensembles. Our results are analysed and interpreted via a detailed theoretical treatment, which is also used to describe how the system can be scaled up to a universal quantum hyperpolarisation platform for the production of macroscopic quantities of contrast agents at high polarisation levels for clinical applications. These results represent a new paradigm for nuclear spin hyperpolarisation for molecular imaging and spectroscopy, and beyond into areas such as materials science and quantum information processing.

We introduce the notion of quantum orthogonal arrays as a generalization of orthogonal arrays. These quantum combinatorial designs naturally induce the concepts of quantum Latin squares, cubes, hypercubes and a notion of orthogonality between them. Furthermore, quantum orthogonal arrays are one-to-one related to $k$-uniform states, i.e., pure states such that every reduction to $k$ parties is maximally mixed. We derive quantum orthogonal arrays having an arbitrary large number of columns and, consequently, infinitely many classes of mutually orthogonal quantum Latin arrangements and absolutely maximally entangled states.

Controlling both the amplitude and phase of the quantum order parameter ({\psi}) in nanostructures is important for next-generation information and communication technologies. The long-range coherence of attractive electrons in superconductors render these materials as a nearly ideal platform for such applications. To-date, control over {\psi} has remained limited to the macroscopic scale, either by adjusting untunable materials properties, such as film thickness, stoichiometry and homogeneity or by tuning external magnetic fields. Yet, although local tuning of {\psi} is desired, the lack of electric resistance in superconductors, which may be advantageous for some technologies hinders convenient voltage-bias tuning. Likewise, challenges related to nanoscale fabrication of superconductors encumber local tunability of {\psi}. Here, we demonstrate local tunability of {\psi}, obtained by patterning with a single lithography step a Nb nano superconducting quantum interference device (nano-SQUID) that is biased at its nano bridges. Our design helped us reveal also unusual electric characteristics-effective zero inductance, which is promising for quantum technologies and nanoscale magnetic sensing. Finally, we accompanied our experimental results by a semi-classical model, which not only is extending the applicability of our devices, but is also useful for describing planar nano-SQUIDs in general.

The family of unitary non-equivalent Weyl-Stratonovich kernels determining the Wigner probability distribution function of an arbitrary N-level quantum system is constructed.

We consider the problem of quantum state certification, where one is given $n$ copies of an unknown $d$-dimensional quantum mixed state $\rho$, and one wants to test whether $\rho$ is equal to some known mixed state $\sigma$ or else is $\epsilon$-far from $\sigma$. The goal is to use notably fewer copies than the $\Omega(d^2)$ needed for full tomography on $\rho$ (i.e., density estimation). We give two robust state certification algorithms: one with respect to fidelity using $n = O(d/\epsilon)$ copies, and one with respect to trace distance using $n = O(d/\epsilon^2)$ copies. The latter algorithm also applies when $\sigma$ is unknown as well. These copy complexities are optimal up to constant factors.

We use the transfer matrix formulation of scattering theory in two-dimensions to treat the scattering problem for a potential of the form $v(x,y)=\zeta\,\delta(ax+by)g(bx-ay)$ where $\zeta,a$, and $b$ are constants, $\delta(x)$ is the Dirac $\delta$ function, and $g$ is a real- or complex-valued function. We map this problem to that of $v(x,y)=\zeta\,\delta(x)g(y)$ and give its exact and analytic solution for the following choices of $g(y)$: i) A linear combination of $\delta$-functions, in which case $v(x,y)$ is a finite linear array of two-dimensional $\delta$-functions; ii) A linear combination of $e^{i\alpha_n y}$ with $\alpha_n$ real; iii) A general periodic function that has the form of a complex Fourier series. In particular we solve the scattering problem for a potential consisting of an infinite linear periodic array of two-dimensional $\delta$-functions. We also prove a general theorem that gives a sufficient condition for different choices of $g(y)$ to produce the same scattering amplitude within specific ranges of values of the wavelength $\lambda$. For example, we show that for arbitrary real and complex parameters, $a$ and $\mathfrak{z}$, the potentials $ \mathfrak{z} \sum_{n=-\infty}^\infty\delta(x)\delta(y-an)$ and $a^{-1}\mathfrak{z}\delta(x)[1+2\cos(2\pi y/a)]$ have the same scattering amplitude for $a< \lambda\leq 2a$.

We study quantum correlations and discord in a bipartite continuous variable hybrid system formed by linear combinations of coherent states $|\alpha\rangle$ and single photon added coherent states (SPACS) of the form $|\psi\rangle_{\text{dp(pa)}}= \mathcal{N}/\sqrt{2} (\hat{a}^\dagger |\alpha\rangle_a |\alpha\rangle_b \pm \hat{b}^\dagger |\alpha\rangle_a |\alpha\rangle_b)$. We stablish a relationship between the quantum discord with a local observable (the quadrature variance for one sub-system) under the influence of scattering and phase fluctuation noise. For the pure states the quantum correlations are characterized by means of measurement induced disturbance (MID) with simultaneous quadrature measurements. In a scenario where homodyne conditional measurements are available we show that the MID provides an easy way to select optimal phases to obtain information of the maximal correlations in the channels. The quantum correlations of these entangled states with channel losses are quantitatively characterized with the quantum discord (QD) with a displaced qubit projector. We observe that as scattering increases, QD decreases monotonically. At the same time for the state $|\psi\rangle_{\text{dp}}$, QD is more resistant to high phase fluctuations when the average photon number $n_0$ is bigger than zero, but if phase fluctuations are low, QD is more resistant if $n_0=0$. For the dp model with scattering, we obtain an analytical expression of the QD as a function of the observable quadrature variance in a local sub-system. This relation allows us to have a way to obtain the degree of QD in the channel by just measuring a local property observable such as the quadrature variance. For the other model this relation still exists but is explored numerically. This relation is an important result that allows to identify quantum processing capabilities in terms of just local observables.

The quantum clock synchronization (QCS) is to measure the time difference among the spatially separated clocks with the principle of quantum mechanics. The first QCS algorithm proposed by Chuang and Jozsa is merely based on two parties, which is further extended and generalized to the multiparty situation by Krco and Paul. They present a multiparty QCS protocol based upon W states that utilizes shared prior entanglement and broadcast of classical information to synchronize spatially separated clocks. Shortly afterwards, Ben-Av and Exman came up with an optimized multiparty QCS using Z state. In this work, we firstly report an implementation of Krco and Ben-AV multiparty QCS algorithm using a four-qubit Nuclear Magnetic Resonance (NMR). The experimental results show a great agreement with the theory and also prove Ben-AV multiparty QCS algorithm more accurate than Krco.