We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We first prove that contrary to earlier claims, there is no strong nonlocality: a quantum state localized at the center of a well with infinitely high moving walls is not modified by the wall's motion. We then show the existence of a weak form of nonlocality: when a quantum state is extended over the well, the wall's motion induces a current density all over the box instantaneously. We indicate how this current density can in principle be measured by performing weak measurements of the particle's momentum.

The advent of quantum computing processors with possibility to scale beyond experimental capacities magnifies the importance of studying their applications. Combinatorial optimization problems can be one of the promising applications of these new devices. These problems are recurrent in industrial applications and they are in general difficult for classical computing hardware. In this work, we provide a survey of the approaches to solving different types of combinatorial optimization problems, in particular quadratic unconstrained binary optimization (QUBO) problems on a gate model quantum computer. We focus mainly on four different approaches including digitizing the adiabatic quantum computing, global quantum optimization algorithms, the quantum algorithms that approximate the ground state of a general QUBO problem, and quantum sampling. We also discuss the quantum algorithms that are custom designed to solve certain types of QUBO problems.

We first present the exact solutions of the single ring-shaped Coulomb potential and then realize the visualizations of the space probability distribution for a moving particle within the framework of this potential. We illustrate the two-(contour) and three-dimensional (isosurface) visualizations for those specifically given quantum numbers (n, l, m) essentially related to those so-called quasi quantum numbers (n',l',m') through changing the single ring-shaped Coulomb potential parameter b. We find that the space probability distributions (isosurface) of a moving particle for the special case and the usual case are spherical and circular ring-shaped, respectively by considering all variables in spherical coordinates. We also study the features of the relative probability values P of the space probability distributions. As an illustration, by studying the special case of the quantum numbers (n, l, m)=(6, 5, 1) we notice that the space probability distribution for a moving particle will move towards two poles of axis z as the relative probability value P increases. Moreover, we discuss the series expansion of the deformed spherical harmonics through the orthogonal and complete spherical harmonics and find that the principal component decreases gradually and other components will increase as the potential parameter b increases.

This paper is the third part concluding the introduction of the powerful algebra of the pseudo-observables. In this article will be dealt how to treat the time evolution, and, more in general, the transformations, in the framework of the new theory. It will be shown that this requires only minor changes with respect to the Dirac-Jordan transformation theory that can be found in almost any textbook, with some more care about the treatment of the continuous limit. A remarkable difference is also in the introduction of the time reversal, which gives the opportunity to a deeper insight about the Hermitian transposition. In the conclusions, we will examine better the relationship between time evolution and measurement, a very problematic aspect in the framework of the Copenhagen interpretation (and in many others ones). Finally we will present a list of compelling reasons for which the physics community would seriously have to evaluate a switching to the new formalism.

We present a practical scheme for the decomposition of a bipartite mixed state into a sum of direct products of local density matrices, using the technique developed in arXiv:1607.03364. The correlation matrix which characterizes the bipartite entanglement is first decomposed into two matrices composed of the Bloch vectors of local states. And, then we show that the symmetry of Bloch vectors is in consistence with that of the correlation matrix, though the magnitudes of the local Bloch vectors are lower bounded by the correlation matrix. Concrete examples of the separable decomposition for bipartite mixed states are presented for illustration.

Quantum walks provide a powerful demonstration of the effectiveness of the renormalization group (RG), here applied to find a lower bound on the computational complexity of Grover's quantum search algorithms in low-dimensional networks. For these, the RG reveals a competition between Grover's abstract algorithm, i.e., a rotation in Hilbert space, and quantum transport in an actual geometry. It can be characterized in terms of the quantum walk dimension $d^Q_w$ and the spatial (fractal) dimension $d_f$, even when translational invariance is broken. The analysis simultaneously determines the optimal time for a quantum measurement and the probability for successfully pin-pointing the sought-after element in the network. The RG further encompasses an optimization scheme, devised by Tulsi, that allows to tune that probability to certainty. Our RG considers entire families of problems to be studied, thereby establishing a large universality class for quantum search, here verified with extensive simulations.

We derive a Moyal dynamical equation that describes exact time evolution in generic (inhomogeneous) noninteracting spin-chain models. Assuming quasistationarity, we develop a hydrodynamic theory. The question at hand is whether some large-time corrections are captured by higher-order hydrodynamics. We consider in particular the dynamics after that two chains, prepared in different conditions, are joined together. In these situations a light cone, separating regions with macroscopically different properties, emerges from the junction. In free fermionic systems some observables close to the light cone follow a universal behavior, known as Tracy-Widom scaling. Universality means weak dependence on the system's details, so this is the perfect setting where hydrodynamics could emerge. For the transverse-field Ising chain and the XX model, we show that hydrodynamics captures the scaling behavior close to the light cone. On the other hand, our numerical analysis suggests that hydrodynamics fails in more general models, whenever a condition is not satisfied.

We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so called generalized uncertainty principle that is motivated by thought experiments in quantum gravity and string theory and is characterized by a parameter of Planck scale. The corrections are evaluated for small deformation parameters by use of the Gaussian wave function and numerical calculation. As the generalized uncertainty principle has proven to be useful in the study of the quantum nature of black holes, this study would be a step toward introducing an information theory viewpoint to black hole physics.

This progress report covers recent developments in the area of quantum randomness, which is an extraordinarily interdisciplinary area that belongs not only to physics, but also to philosophy, mathematics, computer science, and technology. For this reason the article contains three parts that will be essentially devoted to different aspects of quantum randomness, and even directed, although not restricted, to various audiences: a philosophical part, a physical part, and a technological part. For these reasons the article is written on an elementary level, combining very elementary and non-technical descriptions with a concise review of more advanced results. In this way readers of various provenances will be able to gain while reading the article.

A long standing open problem whether a heat engine with finite power achieves the Carnot efficiency is investigated. We rigorously prove a general trade-off inequality on thermodynamic efficiency and time interval of a cyclic process with quantum heat engines. In a first step, employing the Lieb-Robinson bound we establish an inequality on the change in a local observable caused by an operation far from support of the local observable. This inequality provides a rigorous characterization of the following intuitive picture that most of the energy released from the engine to the cold bath remains near the engine when the cyclic process is finished. Using the above description, we finally prove an upper bound on efficiency with the aid of quantum information geometry. In addition, since our inequality falls down into the conventional second law of thermodynamics in Markovian limit, we adopt a completely different treatment which is developed in the context of classical stochastic processes. Our result generally excludes the possibility of a process with finite speed at the Carnot efficiency in quantum heat engines. In particular, the obtained constraint covers engines evolving with non-Markovian dynamics, which almost all previous studies on this topics fail to address.

A dynamic procedure is established within the generalised Tavis-Cummings model to generate light states with discrete point symmetries, given by the cyclic group ${\cal C}_n$. We consider arbitrary dipolar coupling strengths of the atoms with a one-mode electromagnetic field in a cavity. The method uses mainly the matter-field entanglement properties of the system, which can be extended to any number of $3$-level atoms. An initial state constituted by the superposition of two states with definite total excitation numbers, $\vert \psi \rangle_{M_1}$, and $\vert \psi \rangle_{M_2}$, is considered. It can be generated by the proper selection of the time-of-flight of an atom passing through the cavity. We demonstrate that the resulting Husimi function of the light is invariant under cyclic point transformations of order $n=\vert M_1-M_2\vert$.

Any quantum-confined electronic system coupled to the electromagnetic continuum is subject to radiative decay and renormalization of its energy levels. When coupled to a cavity, these quantities can be strongly modified with respect to their values in vacuum. Generally, this modification can be accurately captured by including only the closest resonant mode of the cavity. In the circuit quantum electrodynamics architecture, where the coupling strengths can be substantial, it is however found that the radiative decay rates are strongly influenced by far off-resonant modes. A multimode calculation accounting for the infinite set of cavity modes leads to divergences unless a cutoff is imposed. It has so far not been identified what the source of divergence is. We show here that unless gauge invariance is respected, any attempt at the calculation of circuit QED quantities is bound to diverge. We then present a theoretical approach to the calculation of a finite spontaneous emission rate and the Lamb shift that is free of cutoff.

Spin qubits hosted in silicon (Si) quantum dots (QD) are attractive due to their exceptionally long coherence times and compatibility with the silicon transistor platform. To achieve electrical control of spins for qubit scalability, recent experiments have utilized gradient magnetic fields from integrated micro-magnets to produce an extrinsic coupling between spin and charge, thereby electrically driving electron spin resonance (ESR). However, spins in silicon QDs experience a complex interplay between spin, charge, and valley degrees of freedom, influenced by the atomic scale details of the confining interface. Here, we report experimental observation of a valley dependent anisotropic spin splitting in a Si QD with an integrated micro-magnet and an external magnetic field. We show by atomistic calculations that the spin-orbit interaction (SOI), which is often ignored in bulk silicon, plays a major role in the measured anisotropy. Moreover, inhomogeneities such as interface steps strongly affect the spin splittings and their valley dependence. This atomic-scale understanding of the intrinsic and extrinsic factors controlling the valley dependent spin properties is a key requirement for successful manipulation of quantum information in Si QDs.

We study the collective optical response of an atomic ensemble confined within a single-mode optical cavity by stochastic electrodynamics simulations that include the effects of atomic position correlations, internal level structure, and spatial variations in cavity coupling strength and atom density. In the limit of low light intensity the simulations exactly reproduce the full quantum field-theoretical description for cold stationary atoms and at higher light intensities we introduce semiclassical approximations to atomic saturation that we compare with the exact solution in the case of two atoms. We find that collective subradiant modes of the atoms, with very narrow linewidths, can be coupled to the cavity field by spatial variation of the atomic transition frequency and resolved at low intensities, and show that they can be specifically driven by tailored transverse pumping beams. We show that the cavity optical response, in particular both the subradiant mode profile and the resonance shift of the cavity mode, can be used as a diagnostic tool for the position correlations of the atoms and hence the atomic quantum many-body phase. The quantum effects are found to be most prominent close to the narrow subradiant mode resonances at high light intensities. Although an optical cavity can generally strongly enhance quantum fluctuations via light confinement, we show that the semiclassical approximation to the stochastic electrodynamics model provides at least a qualitative agreement with the exact optical response outside the subradiant mode resonances even in the presence of significant saturation of the atoms.

We derive quantum trajectories (also known as stochastic master equations) that describe an arbitrary quantum system probed by a propagating wave packet of light prepared in a continuous-mode Fock state. We consider three detection schemes of the output light: photon counting, homodyne detection, and heterodyne detection. We generalize to input field states that are superpositions and or mixtures of Fock states and illustrate the formalism with several examples.

Graph states have been used for quantum error correction by Schlingemann et al. [Phy. Rev. A 2001]. Hypergraph states are generalizations of graph states and they have been used in quantum algorithms. We for the first time demonstrate how hypergraph states can be used for quantum error correction. We also point out that they are more efficient than graph states in the sense that to correct equal number of errors on the same graph topology, suitably defined hypergraph states require less number of gate operations than the corresponding graph states.

We theoretically investigate the dynamics of a spin-qubit periodically driven in both longitudinal and transverse directions by two classical fields respectively a radio-frequency (RF) and a microwave (MW) field operating at phase difference $\phi$. The qubit is simultaneously locally subject to a linearly polarized magnetic field which changes its sign at a degeneracy point in the longitudinal direction and remains constant in the transverse direction. We superimpose the RF and MW signals respectively to the longitudinal and transverse components of the magnetic field. The proposed model may be used to optimize the control of a qubit in quantum devices. The various fields applied are relevant to {\it nearly-decouple} the spin-qubit from its environment, minimize decoherence effects and improve on the coherence time. The study is carried out in the Schr\"odinger and Bloch pictures. We consider the limits of weak and strong longitudinal drives set up by comparing the characteristic time of non-adiabatic transitions with the coherence time of the longitudinal drive. Expressions for populations are compared with numerics and remarkable agreements are observed as both solutions are barely discernible.

Markovian master equations (formally known as quantum dynamical semigroups) can be used to describe the evolution of a quantum state $\rho$ when in contact with a memoryless thermal bath. This approach has had much success in describing the dynamics of real-life open quantum systems in the lab. Such dynamics increase the entropy of the state $\rho$ and the bath until both systems reach thermal equilibrium, at which point entropy production stops. Our main result is to show that the entropy production at time $t$ is bounded by the relative entropy between the original state and the state at time $2t$. The bound puts strong constraints on how quickly a state can thermalise, and we prove that the factor of $2$ is tight. The proof makes use of a key physically relevant property of these dynamical semigroups -- detailed balance, showing that this property is intimately connected with the field of recovery maps from quantum information theory. We envisage that the connections made here between the two fields will have further applications. We also use this connection to show that a similar relation can be derived when the fixed point is not thermal.

Matrix mechanics is developed to describe the bound state spectra in few- and many-electron atoms, ions and molecules. Our method is based on the matrix factorization of many-electron (or many-particle) Coulomb Hamiltonians which are written in hyperspherical coordinates. As follows from the results of our study the bound state spectra of many-electron (or many-particle) Coulomb Hamiltonians always have the `ladder' strucure and this fundamental fact can be used to determine and investigate the bound states in varous few- and many-body Coulomb systems.

It is suggested that the apparently disparate cosmological phenomena attributed to so-called 'dark matter' and 'dark energy' arise from the same fundamental physical process: the emergence, from the quantum level, of spacetime itself. This creation of spacetime results in metric expansion around mass points in addition to the usual curvature due to stress-energy sources of the gravitational field. A recent modification of Einstein's theory of general relativity by Chadwick, Hodgkinson, and McDonald incorporating spacetime expansion around mass points, which accounts well for the observed galactic rotation curves, is adduced in support of the proposal. Recent observational evidence corroborates a prediction of the model that the apparent amount of 'dark matter' increases with the age of the universe. In addition, the proposal leads to the same result for the small but nonvanishing cosmological constant, related to 'dark energy, as that of the causet model of Sorkin et al.