The probability of success of quantum annealing can be improved significantly by pausing the annealer during its dynamics, exploiting thermal relaxation in a controlled fashion. In this paper, we investigate the effect of pausing the quantum annealing of the fully-connected ferromagnetic $ p $-spin model. We numerically show that i) the optimal pausing point is 60\% longer than the avoided crossing time for the analyzed instance, and ii) at the optimal pausing point, we register a 45\% improvement in the probability of success with respect to a quantum annealing with no pauses of the same duration. These results are in line with those observed experimentally for less connected models with the available quantum annealers. The observed improvement for the $ p $-spin model can be up to two orders of magnitude with respect to an isolated quantum dynamics of the same duration.

We study quantum processes, as one parameter families of differentiable completely positive and trace preserving (CPTP) maps. Using different representations of the generator, and the Sylvester criterion for positive semi-definite matrices, we obtain conditions for the divisibility of the process into completely positive (CP-divisibility) and positive (P-divisibility) infinitesimal maps. Both concepts are directly related to the definition of quantum non-Markovianity. For the single qubit case we show that CP- and P-divisibility only depend on the dissipation matrix in the master equation form of the generator. We then discuss three classes of processes where the criteria for the different types of divisibility result in simple geometric inequalities, among these the class of non-unital anisotropic Pauli channels.

We consider an operational restatement of the holographic principle, which we call the principle of asymptotic quantum tasks. Asymptotic quantum tasks are quantum information processing tasks with inputs given and outputs required on points at the boundary of a spacetime. The principle of asymptotic quantum tasks states that tasks which are possible using the bulk dynamics should coincide with tasks that are possible using the boundary. We extract consequences of this principle for holography in the context of asymptotically AdS spacetimes. Among other results we find a novel connection between bulk causal structure and the phase transition in the boundary mutual information. Further, we note a connection between holography and quantum cryptography, where the problem of completing asymptotic quantum tasks has been studied earlier. We study the cryptographic and AdS/CFT approaches to completing asymptotic quantum tasks and consider the efficiency with which they replace bulk classical geometry with boundary entanglement.

We give a technique to reduce the error probability of quantum algorithms that determine whether its input has a specified property of interest. The standard process of reducing this error is statistical processing of the results of multiple independent executions of an algorithm. Denoting by $\rho$ an upper bound of this probability (wlog., assume $\rho \le \frac{1}{2}$), classical techniques require $O(\frac{\rho}{[(1-\rho) - \rho]^2})$ executions to reduce the error to a negligible constant. We investigated when and how quantum algorithmic techniques like amplitude amplification and estimation may reduce the number of executions. On one hand, the former idea does not directly benefit algorithms that can err on both yes and no answers and the number of executions in the latter approach is $O(\frac{1}{(1-\rho) - \rho})$. We propose a novel approach named as {\em Amplitude Separation} that combines both these approaches and achieves $O(\frac{1}{\sqrt{1-\rho} - \sqrt{\rho}})$ executions that betters existing approaches when the errors are high.

In the Multiple-Weight Decision Problem, the input is an $n$-bit Boolean function $f()$ given as a black-box and the objective is to determine the number of $x$ for which $f(x)=1$, denoted as $wt(f)$, given some possible values $\{w_1, \ldots, w_k\}$ for $wt(f)$. When our technique is applied to this problem, we obtain the correct answer, maybe with a negligible error, using $O(\log_2 k \sqrt{2^n})$ calls to $f()$ that shows a quadratic speedup over classical approaches and currently known quantum algorithms.

For a twisted (vortex) Dirac particle in nonuniform electric and magnetic fields, the relativistic Foldy-Wouthuysen Hamiltonian is derived including high order terms describing new effects. The result obtained shows for the first time that a twisted spin-1/2 particle possesses a tensor magnetic polarizability and a measurable (spectroscopic) electric quadrupole moment. We have calculated the former parameter and have evaluated the latter one for a twisted electron. The tensor magnetic polarizability of the twisted electron can be measured in a magnetic storage ring because a beam with an initial orbital tensor polarization acquires a horizontal orbital vector polarization. The electric quadrupole moment is rather large and strongly influences the dynamics of the intrinsic orbital angular momentum. Three different methods of its measurements, freezing the intrinsic orbital angular momentum and two resonance methods, are proposed. The existence of the quadrupole moment of twisted electrons can lead to practical applications.

With the help of quantum key distribution (QKD), two distant peers are able to share information-theoretically secure key bits. Increasing key rate is ultimately significant for the applications of QKD in lossy channel. However, it has proved that there is a fundamental rate-distance limit, named linear bound, which limits the performance of all existing repeaterless protocols and realizations. Surprisingly, a recently proposed protocol, called twin-field (TF) QKD can beat linear bound with no need of quantum repeaters. Here, we present the first implementation of TF-QKD protocol and demonstrate its advantage of beating linear bound at the channel distance of 300 km. In our experiment, a modified TF-QKD protocol which does not assume phase post-selection is considered, and thus higher key rate than the original one is expected. After well controlling the phase evolution of the twin fields travelling hundreds of kilometers of optical fibres, the implemented system achieves high-visibility single-photon interference, and allows stable and high-rate measurement-device-independent QKD. Our experimental demonstration and results confirm the feasibility of the TF-QKD protocol and its prominent superiority in long distance key distribution services.

Inspired by the possibility that generative models based on quantum circuits can provide a useful inductive bias for sequence modeling tasks, we propose an efficient training algorithm for a subset of classically simulable quantum circuit models. The gradient-free algorithm, presented as a sequence of exactly solvable effective models, is a modification of the density matrix renormalization group procedure adapted for learning a probability distribution. The conclusion that circuit-based models offer a useful inductive bias for classical datasets is supported by experimental results on the parity learning problem.

Entanglement contour characterizes the spatial structure of entanglement and quantifies the contribution from the degrees of freedom in any subset of the region $\mathcal{A}$ to the total entanglement entropy $S_{\mathcal{A}}$. Recently in \cite{Wen:2018whg}, the author gave a simple proposal for entanglement contour which involves the entanglement entropies of all the subsets inside $\mathcal{A}$. In this paper we explicitly study this proposal and show it satisfies many rational requirements for entanglement contour. Together with the holographic picture constructed with the modular planes \cite{Wen:2018whg}, we propose the correspondence between bulk geodesic chords and boundary partial entanglement entropies, which can be considered as a finer version of the Ryu-Takayanagi (RT) formula. As an example we calculate the fine correspondence between the points on $\mathcal{A}$ and the points on the RT surface $\mathcal{E}_{\mathcal{A}}$ for the BTZ black hole. We also give a strategy to extract the local modular flow from our entanglement contour proposal.

Recently the bound on the Lyapunov exponent $\lambda_L \le 2\pi T/ \hbar$ in thermal quantum systems was conjectured by Maldacena, Shenker and Stanford. If we naively apply this bound to a system with a fixed Lyapunov exponent $\lambda_L$, it might predict the existence of the lower bound on temperature $T \ge \hbar \lambda_L/ 2\pi $. Particularly, it might mean that chaotic systems cannot be zero temperature quantum mechanically. Even classical dynamical systems, which are deterministic, might exhibit thermal behaviors once we turn on quantum corrections. We elaborate this possibility by investigating semi-classical particle motions near the hyperbolic fixed point and show that indeed quantum corrections may induce energy emission which obeys a Boltzmann distribution. We also argue that this emission is related to acoustic Hawking radiation in quantum fluid. Besides, we discuss when the bound is saturated and show that a particle motion in an inverse harmonic potential and $c=1$ matrix model may saturate the bound although they are integrable.

We present a theoretical study of the optical response of a nonlinear oscillator formed by coupling a metal nanoparticle local surface plasmon resonance to excitonic degrees of freedom in a monolayer transition-metal dichalcogenide. We show that the combined system should exhibit strong anharmonicity in its low-lying states, predicting for example a seven order-of-magnitude increase in nonlinearity relative to a silicon photonic crystal cavity. Arrays of such nanoscale nonlinear oscillators could be used to realize novel optical metamaterials; alternatively, an individual nanoparticle-monolayer construct could be coupled to an optical resonator to mediate efficient input-output coupling to propagating fields.

Hong-Ou-Mandel interference, the fact that identical photons that arrive simultaneously on different input ports of a beam splitter bunch into a common output port, can be used to measure optical delays between different paths. It is generally assumed that great precision in the measurement requires that photons contain many frequencies, i.e., a large bandwidth. Here we challenge this well-known assumption and show that the use of two well-separated frequencies embedded in a quantum entangled state (discrete color entanglement) suffices to achieve great precision. We determine optimum working points using a Fisher Information analysis and demonstrate the experimental feasibility of this approach by detecting thermally-induced delays in an optical fiber. These results will not only prove useful for facilitating the use of quantum interference for quantum sensing, by avoiding some stringent conditions such as the requirement for large bandwidth signals, but also indicate new directions towards harnessing multi-photon interference in general.

Machine learning methods have proved to be useful for the recognition of patterns in statistical data. The measurement outcomes are intrinsically random in quantum physics, however they do have a pattern when the measurements are performed successively on an open quantum system. This pattern is due to the system-environment interaction and contains information about the relaxation rates as well as non-Markovian memory effects. Here we develop a method to extract the information about the unknown environment from a series of single-shot measurements on the system (without resorting to the process tomography). The method is based on embedding the non-Markovian system dynamics into a Markovian dynamics of the system and the effective reservoir of finite dimension. The generator of Markovian embedding is learned by the maximum likelihood estimation. We verify the method by comparing its prediction with an exactly solvable non-Markovian dynamics. The developed algorithm to learn unknown quantum environments enables one to efficiently control and manipulate quantum systems.

We consider a system of interacting bosons in one dimension at a two-body resonance. This system, which is weakly interacting, is known to give rise to effective three-particle interactions, whose dynamics is similar to that of a two-dimensional Bose gas with two-body interactions, and exhibits an identical scale anomaly. We consider the experimentally relevant scenario of a harmonically trapped system. We solve the three-body problem exactly and evaluate the shifts in the frequency of the lowest compressional mode with respect to the dipole mode, and find that the effect of the anomaly is to increase the mode's frequency. We also consider the weak-coupling regime of the trapped many-boson problem and find, within the local density approximation, that the frequency of the lowest compressional mode is also shifted upwards in this limit. Moreover, the anomalous frequency shifts are enhanced by the higher particle number to values that should be observable experimentally.

We demonstrate the experimental realization of a two-qubit M{\o}lmer-S{\o}rensen gate on a magnetic field-insensitive hyperfine transition in $^9$Be$^+$ ions using microwave-near fields emitted by a single microwave conductor embedded in a surface-electrode ion trap. The design of the conductor was optimized to produce a high oscillating magnetic field gradient at the ion position. The measured gate fidelity is determined to be $98.2\pm1.2\,\%$ and is limited by technical imperfections, as is confirmed by a comprehensive numerical error analysis. The conductor design can potentially simplify the implementation of multi-qubit gates and represents a self-contained, scalable module for entangling gates within the quantum CCD architecture for an ion-trap quantum computer.

By filtering out the philosophic component we can be said that the EPR-paper was directed against the straightforward interpretation of the Heisenberg's uncertainty principle or more generally the Bohr's complementarity principle. The latter expresses contextuality of quantum measurements: dependence of measurement's output on the complete experimental arrangement. However, Bell restructured the EPR-argument against complementarity to justify nonlocal theories with hidden variables of the Bohmian mechanics' type. Then this Bell's kind of nonlocality - {\it subquantum nonlocality} - was lifted to the level of quantum theory - up to the terminology {\it "quantum nonlocality"}. The aim of this short note is to explain that Bell's test is simply a special {\it test of local incompatibility of quantum observables}, similar to interference experiments, e.g., the two-slit experiment.

The objective of causal inference is to learn the network of causal relationships holding between a system of variables from the correlations that these variables exhibit; a sub-problem of which is to certify whether or not a given causal hypothesis is compatible with the observed correlations. A particularly challenging setting for causal inference is in the presence of partial information; i.e. when some of the variables are hidden/latent. In this present work, we introduce the possible worlds framework as a method for deciding causal compatibility in this difficult setting. We define a graphical object called an possible worlds diagram, which compactly depicts the set of all possible observations. From this construction, we demonstrate explicitly, using several examples, how to prove causal incompatibility. In fact, we use these constructions to prove causal incompatibility where no other techniques have been able to. Moreover, we prove that the possible worlds framework can be adapted to provide a complete solution to the possibilistic causal compatibility problem. Even more, we also discuss how to exploit graphical symmetries and cross-world consistency constraints in order to implement a hierarchy of necessary compatibility tests that we prove converges to sufficiency.

Satellite quantum communications have rapidly evolved in the past few years, culminating in the proposal, development, and deployment of satellite missions dedicated to quantum key distribution and the realization of fundamental tests of quantum mechanics in space. However, in comparison with the more mature technology based on fiber optics, several challenges are still open, such as the capability of detecting, with high temporal accuracy, single photons coming from orbiting terminals. Satellite laser ranging, commonly used to estimate satellite distance, could also be exploited to overcome this challenge. For example, high repetition rates and a low background noise can be obtained by determining the time-of-flight of faint laser pulses that are retro-reflected by geodynamics satellites and then detected on Earth at the single-photon level. Here we report an experiment with regard to achieving a temporal accuracy of approximately 230 ps in the detection of an optical signal of few photons per pulse reflected by satellites in medium Earth orbit, at a distance exceeding 7500 km, by using commercially available detectors. Lastly, the performance of the Matera Laser Ranging Observatory is evaluated in terms of the detection rate and the signal-to-noise ratio for satellite quantum communications.

The Paradigms introduced in philosophy of science one century ago are shown to be quite more satisfactory of that introduced by Galileo. This is particularly evident in the physics based on Hilbert Spaces and related mathematical structures that we apply in this paper to Quantum Mechanics and to Theory of Images. An exhaustive discussion, that include the algebraic analysis of the operators acting on them, exhibits that the Hilbert Spaces -- that have fixed dimension -- must be generalized to the Rigged Hilbert Spaces that contains right inside spaces with continuous and discrete dimensions. This is the property of Rigged Hilbert Spaces that allows a consistent formal description of the physics we are considering. Theory of Quantum Mechanics and of Images are similar and the fundamental difference between them come from the definition of measure that is outside the theory of the spaces: while in Quantum Mechanics the measure is a probabilistic action, in Images it is a classical functional.

KEYWORDS: Optics, Quantum Mechanics, Rigged Hilbert Spaces, Lie Algebras

We present an analysis of the Frauchiger--Renner Gedankenexperiment from the point of view of the relational interpretation of quantum mechanics. Our analysis indicates that the paradox obtained by Frauchiger and Renner arises from a combination of allowing self-measurement and reasoning about other agent's knowledge in the past without validation by surviving records. A by-product of our analysis is an interaction-free detection scheme for the existence of records from the past.

We generalize the existing finite-size criteria for spectral gaps of frustration-free spin systems to $D>2$ dimensions. We obtain a local gap threshold of $\frac{3}{n}$, independent of $D$, for nearest-neighbor interactions. The $\frac{1}{n}$ scaling persists for arbitrary finite-range interactions in $\mathbb Z^3$. The key observation is that there is more flexibility in Knabe's combinatorial approach if one employs the operator Cauchy-Schwarz inequality.