We analyze a simple model of quantum dynamics, which is a discrete-time deterministic version of the Frederickson-Andersen model. We argue that this model is integrable, with a quasiparticle description related to the classical hard-rod gas. Despite the integrability of the model, commutators of physical operators grow as in generic chaotic models, with a diffusively broadening front, and local operators obey the eigenstate thermalization hypothesis (ETH). However, large subsystems violate ETH; as a function of subsystem size, eigenstate entanglement first increases linearly and then saturates at a scale that is parametrically smaller than half the system size.

We discuss the approach toward equilibrium of an isolated quantum system. For a wide class of systems we argue that the time-averaged expectation value of a local operator in any initial state is bounded by the so-called deviation function, which characterizes maximal deviation from the equilibrium for all states with a given value of energy fluctuations. We provide numerical evidence that the bound is approximately saturated by the initial configurations with spatial inhomogeneities at macroscopic level. In this way the deviation function establishes an explicit connection between the macroscopically observed timescales associated with transport and properties of microscopic matrix elements. The form of the deviation function indicates that among the slowest states which saturate the bound there are also those with arbitrarily long equilibration times.

The response part of the exchange-correlation potential of Kohn-Sham density functional theory plays a very important role, for example for the calculation of accurate band gaps and excitation energies. Here we analyze this part of the potential in the limit of infinite interaction in density functional theory, showing that in the one-dimensional case it satisfies a very simple sum rule.

We present a general, second quantization procedure for multi-transverse-spatial mode Gaussian beam dynamics in nonlinear interactions. Previous treatments have focused on the spectral density and angular distribution of spatial modes. Here we go a layer deeper by investigating the complex transverse-spatial mode in each angular-spatial mode. Furthermore, to implement the theory, we simulate four-wave mixing and parametric down-conversion schemes, showing how one can elucidate and tailor the underlying multi-transverse-spatial mode structure along with it's quantum properties.

We propose a technique for robust optomechanical cooling using phase-tailored composite pulse driving with constant amplitude. Our proposal is inspired by coherent control techniques in lossless driven qubits. Using phase-tailored composite pulse sequences, we demonstrate that there exist optimal phases for maximally robust excitation exchange in lossy strongly-driven optomechanical cooling. However, this driving can take the system out of its steady state. For this reason, we use these optimal phases to produce smooth sequences that both maintain the system close to its steady state and optimize the robustness of optomechanical cooling.

We investigate the orthoalgebras of certain non-Boolean models which have a classical realization. Our particular concern will be the partition logics arising from the investigation of the empirical propositional structure of Moore and Mealy type automata.

We study the characterisation of efficient and non-efficient families of Grover's algorithms according to the majorization principle. We develop a geometrical interpretation based on the parameters that appears on these algorithms. Using this interpretation we observe a step-by-step majorization in all efficient Grover's algorithms, whereas the non-efficient Grover's algorithms fail to abide by this majorization principle. These Majorization results are first obtained from numerical calculations. Motivated by these numerical results, we also obtained an analytical demonstration. Finally, the geometrical interpretation found for these parameters is used to obtain additional results of Grover's algorithms that improves our understanding of how they work.

There are two properties that are needed for a classical system to be chaotic: exponential stretching and mixing. Recently, out-of-time order correlators were proposed as a measure of chaos in a wide range of systems. While most of the attention has previously been put on the short time stretching part of chaos, characterized by the Lyapunov exponent, we show for quantum maps that the out-of-time correlator aproaches its stationary value exponentially with a rate determined by the Ruelle-Pollicot resonances. This property constitutes the first clear evidence of the backbone of the time behavior of the out-of-time order correlators for chaotic systems.

This is a brief review on the theoretical interpretation of the Aharonov-Bohm effect, which also contains our new insight into the problem. A particular emphasis is put on the unique role of electron orbital angular momentum, especially viewed from the novel concept of the physical component of the gauge field, which has been extensively discussed in the context of the nucleon spin decomposition problem as well as the photon angular momentum decomposition problem. Practically, we concentrate on the frequently discussed idealized setting of the Aharonov-Bohm effect, i.e. the interference phenomenon of the electron beam passing around the infinitely-long solenoid. One of the most puzzling observations in this Aharonov-Bohm solenoid effect is that the pure-gauge potential outside the solenoid appears to carry non-zero orbital angular momentum. Through the process of tracing its dynamical origin, we try to answer several fundamental questions of the Aharonov-Bohm effect, which includes the question about the reality of the electromagnetic potential, the gauge-invariance issue, and the non-locality interpretation, etc.

Variational quantum algorithms are leading candidates for early applications of near-term quantum computing devices. Borrowing Evolution Strategy methods developed in the context of Reinforcement Learning and Search Gradient Optimization, we show how to apply these methods to quantum circuit optimization in the spirit of hybrid quantum-classical algorithms. These techniques do not rely on direct gradient estimates, gradient circuits or additional ancilla qubits, hence reducing the sampling cost and runtime for large numbers of variational parameters and work even in the limit of single-shot measurements. Additional benefits of the optimizer are its ease of implementation, and the ability to avoid small local optima, making it ideally suitable for optimizing non-convex black-box objective functions. We highlight the efficiency by investigating the behavior of the optimizer on a simple \textsc{Maxcut} example using the Quantum Approximate Optimization Algorithm and compare it to the Goemans-Williamson algorithm.

In multipartite entanglement theory, the partial separability properties have an elegant, yet complicated structure, which boils down in the case when multipartite correlations are considered. In this work, we elaborate this, by giving necessary and sufficient conditions for the existence and uniqueness of the class of a given class-label, by the use of which we work out the structure of the classification for some important particular cases, namely, for the finest classification, for the classification based on k-partitionability and k-producibility, and for the classification based on the atoms of the correlation properties.

Surprising properties of doped Mott insulators are at the heart of many quantum materials, including transition metal oxides and organic materials. The key to unraveling complex phenomena observed in these systems lies in understanding the interplay of spin and charge degrees of freedom. One of the most debated questions concerns the nature of charge carriers in a background of fluctuating spins. To shed new light on this problem, we suggest a simplified model with mixed dimensionality, where holes move through a Mott insulator unidirectionally while spin exchange interactions are two dimensional. By studying individual holes in this system, we find direct evidence for the formation of mesonic bound states of holons and spinons, connected by a string of displaced spins -- a precursor of the spin-charge separation obtained in the 1D limit of the model. Our predictions can be tested using ultracold atoms in a quantum gas microscope, allowing to directly image spinons and holons, and reveal the short-range hidden string order which we predict in this model.

In a recent work, Murmann {\it et. al.} [Phys. Rev. Lett. {\bf114}, 080402 (2015)] have experimentally prepared and manipulated a double-well optical potential containing a pair of Fermi atoms as a possible building block of Hubbard model. Here, we carry out a comparative theoretical study on fermionic vs. bosonic two-site Hubbard models with a pair of interacting atoms in a double-well potential. The fermionic atoms are considered to be of two-component type. We show that, given the same input parameters for both bosonic and fermionic two-site Hubbard models, many of the statistical properties such as the single- and double-occupancy of a site, and the probabilities for the single-particle and pair tunneling are similar in both cases. But, the fluctuation quantities such as number and phase fluctuations are markedly different for the two cases. We treat the bosonic and fermionic phase variables in terms of the quantum mechanical phase operators of bosonic and fermionic matter-waves, respectively. Furthermore, we examine whether it is possible to account for the Feshbach-resonant atom-atom interactions into the models through the finite-ranged model interaction potentials of Jost and Kohn. We briefly discuss the implications of finite as well as long range interactions on two-site atomic Hubbard models.

Quantifying the degree of irreversibility of an open system dynamics represents a problem of both fundamental and applied relevance. Even though a well-known framework exists for thermal baths, the results give diverging results in the limit of zero temperature and are also not readily extended to nonequilibrium reservoirs, such as dephasing baths. Aimed at filling this gap, in this paper we introduce a phase-space-entropy production framework for quantifying the irreversibility of spin systems undergoing Lindblad dynamics. The theory is based on the spin Husimi-Q function and its corresponding phase-space entropy, known as Wehrl entropy. Unlike the von Neumann entropy production rate, we show that in our framework, the Wehrl entropy roduction rate remains valid at any temperature and is also readily extended to arbitrary nonequilibrium baths. As an application, we discuss the irreversibility associated with the interaction of a two-level system with a single-photon pulse, a problem which cannot be treated using the conventional approach.

Electron-positron interactions have been utilized in various fields of science. Here we develop time-dependent multi-component density functional theory to study the coupled electron-positron dynamics from first principles. We prove that there are coupled time-dependent single-particle equations that can provide the electron and positron density dynamics, and derive the formally exact expression for their effective potentials. Introducing the adiabatic local density approximation to time dependent electron-positron correlation, we apply the theory to the dynamics of a positronic lithium hydride molecule under a laser field. We demonstrate the significance of electron-positron dynamical correlation by revealing the complex positron detachment mechanism and the suppression of electronic resonant excitation by the screening effect of the positron.

I provide additional arguments for refuting Vaidmans weak value analysis of the path of a particle in a nested Mach-Zehnder interferometer. The argument uses sequential weak values to supplement my previous analysis according to which even weak measurements disturb the system to such an extent that projector weak values cannot be considered representative for the undisturbed system.

Qubit errors might be avoided by using the quantum Zeno effect to inhibit evolution.

The difficulties encountered up till now in the theory of identifying the spin and orbital angular momentum of the photon stem from the approach of separating the angular momentum of the photon into spin and orbital parts. Here we derive the spin of the photon from a set of two relativistic quantum equations that is equivalent to free-space Maxwell equations, with particular attention paid to the effects of relativistic constraint on the properties of the photon spin. On one hand, we find that the relativistic constraint makes the spin, which appears to be an independent degree of freedom if the relativistic constraint is absent, dependent on the momentum so that no operator for the photon spin exists in position representation. As a result, the notion of local density of the photon spin in position space is physically misleading. On the other hand, we show that the relativistic constraint allows to express the expectation value of the spin as integrals of different integrands over the position space.

We develop a quantum version of the probability estimation framework [arXiv:1709.06159] for randomness generation with quantum side information. We show that most of the properties of probability estimation hold for quantum probability estimation (QPE). This includes asymptotic optimality at constant error and randomness expansion with logarithmic input entropy. QPE is implemented by constructing model-dependent quantum estimation factors (QEFs), which yield statistical confidence upper bounds on data-conditional normalized R\'enyi powers. This leads to conditional min-entropy estimates for randomness generation. The bounds are valid for relevant models of sequences of experimental trials without requiring independent and identical or stationary behavior. QEFs may be adapted to changing conditions during the sequence and trials can be stopped any time, such as when the results so far are satisfactory. QEFs can be constructed from entropy estimators to improve the bounds for conditional min-entropy of classical-quantum states from the entropy accumulation framework [Dupuis, Fawzi and Renner, arXiv:1607.01796]. QEFs are applicable to a larger class of models, including models permitting measurement devices with super-quantum but non-signaling behaviors and semi-device dependent models. The improved bounds are relevant for finite data or error bounds of the form $e^{-\kappa s}$, where $s$ is the number of random bits produced. We give a general construction of entropy estimators based on maximum probability estimators, which exist for many configurations. For the class of $(k,2,2)$ Bell-test configurations we provide schemas for directly optimizing QEFs to overcome the limitations of entropy-estimator-based constructions. We obtain and apply QEFs for examples involving the $(2,2,2)$ Bell-test configuration to demonstrate substantial improvements in finite-data efficiency.

We present a way to realize a multiplex-controlled phase gate of n-1 control qubits simultaneously controlling one target qubit, with n qubits distributed in n different cavities. This multiqubit gate is implemented by using n qutrits (three-level natural or artificial atoms) placed in n different cavities, which are coupled to an auxiliary qutrit. Here, the two logic states of a qubit are represented by the two lowest levels of a qutrit placed in a cavity. We show that this n-qubit controlled phase gate can be realized using only 2n+2 basic operations, i.e., the number of required basic operations only increases linearly with the number n of qubits. Since each basic operation employs the qutrit-cavity or qutrit-pulse resonant interaction, the gate can be fast implemented when the number of qubits is not large. Numerical simulations show that a three-qubit controlled phase gate, which is executed on three qubits distributed in three different cavities, can be high-fidelity implemented by using a circuit QED system. This proposal is quite general and can be applied to a wide range of physical systems, with atoms, NV centers, quantum dots, or various superconducting qutrits distributed in different cavities. Finally, this method can be applied to implement a multiqubit controlled phase gate with atoms using a cavity. A detailed discussion on implementing a three-qubit controlled phase gate with atoms and one cavity is presented.