In quenching a topological phase across phase transition, the dynamical bulk-surface correspondence emerges that the bulk topology of $d$-dimensional ($d$D) phase relates to the nontrivial pattern of quench dynamics emerging on $(d-1)$D subspace, called band inversion surfaces (BISs) in momentum space. Here we report the first experimental observation of the dynamical bulk-surface correspondence through measuring the topological charges in a 2D quantum anomalous Hall model realized in an optical Raman lattice. The system can be quenched with respect to every spin axis by suddenly varying the two-photon detuning or phases of the Raman couplings, in which the topological charges and BISs are measured dynamically by the time-averaged spin textures. We observe that the total charges in the region enclosed by BISs define a dynamical topological invariant, which equals the Chern index of the post-quench band. The topological charges relate to an emergent dynamical field which exhibits nontrivial topology on BIS, rendering the dynamical bulk-surface correspondence. This study opens a new avenue to explore topological phases dynamically.

It is shown that the Fizeau drag can be used to cause nonreciprocity. We propose the use of a nanostructured toroid cavity made of $\chi^{(2)}$ nonlinear materials to achieve nonreciprocal photon blockade (PB) through the Fizeau drag. Under the weak driving condition, we discuss the origins of the PB based on the doubly resonant modes with good spatial overlap at the fundamental and second-harmonic frequencies. We also find that for the fundamental mode, the PB happens when we drive the system from one side but the photon-induced tunneling happens when we drive the system from the other side. However, there is no such phenomenon in the second-harmonic mode. Remarkably, the PB phenomenon occurs with a reasonably small optical nonlinearity thus bringing the system parameters closer to the reasonably achievable realm by the current technology.

Measurement of the branching ratios for $6P_{1/2}$ decays to $6S_{1/2}$ and $5D_{3/2}$ in $^{138}$Ba$^+$ are reported with the decay probability from $6P_{1/2}$ to $5D_{3/2}$ measured to be $p=0.268177\pm(37)_\mathrm{stat}-(20)_\mathrm{sys}$. This result differs from a recent report by $12\sigma$. A detailed account of systematics is given and the likely source of the discrepancy is identified. The new value of the branching ratio is combined with a previous experimental results to give a new estimate of $\tau=7.855(10)\,\mathrm{ns}$ for the $6P_{1/2}$ lifetime. In addition, ratios of matrix elements calculated from theory are combined with experimental results to provide improved theoretical estimates of the $6P_{3/2}$ lifetime and the associated matrix elements.

We present a quantum algorithm for ranking the nodes on a network in their order of importance. The algorithm is based on a directed discrete-time quantum walk, and works on all directed networks. This algorithm can theoretically be applied to the entire internet, and thus can function as a quantum PageRank algorithm. Our analysis shows that the hierarchy of quantum rank matches well with the hierarchy of classical rank for directed tree network and for non-trivial cyclic networks, the hierarchy of quantum ranks do not exactly match to the hierarchy of the classical rank. This highlights the role of quantum interference and fluctuations in networks and the importance of using quantum algorithms to rank nodes in quantum networks. Another application this algorithm can envision is to model the dynamics on networks mimicking the chemical complexes and rank active centers in order of reactivities. Since discrete-time quantum walks are implementable on current quantum processing systems, this algorithm will also be of practical relevance in analysis of quantum architecture.

A conceptual variable is any variable defined by a person or by a group of persons. Such variables may be inaccessible, meaning that they cannot be measured with arbitrary accuracy on the physical system under consideration at any given time. An example may be the spin vector of a particle; another example may be the vector (position, momentum). In this paper, a space of inaccessible conceptual variables is defined, and group actions are defined on this space. Accessible functions are then defined on the same space. Assuming this structure, the basic Hilbert space structure of quantum theory is derived: Operators on a Hilbert space corresponding to the accessible variables are introduced; when these operators have a discrete spectrum, a natural model reduction implies a new model in which the values of the accessible variables are the eigenvalues of the operator. The principle behind this model reduction demands that a group action may also be defined also on the accessible variables; this is possible if the corresponding functions are permissible, a term that is precisely defined. The following recent principle from statistics is assumed: every model reduction should be to an orbit or to a set of orbits of the group. From this derivation, a new interpretation of quantum theory is briefly discussed: I argue that a state vector may be interpreted as connected to a focused question posed to nature together with a definite answer to this question. Further discussion of these topics is provided in a recent book published by the author of this paper.

The interpretation of quantum mechanics has been discussed since this theme first was brought up by Einstein and Bohr. This article describes a proposal for a new foundation of quantum theory, partly drawing upon ideas from statistical inference theory. The approach can be said to have an intuitive basis: The quantum states of a physical system are under certain conditions in one-to-one correspondence with the following: 1. Focus on a concrete question to nature and then 2. Give a definite answer to this question. This foundation implies an epistemic interpretation, depending upon the observer, but the objective world is restored when all observers agree on their observations on some variables. The article contains a survey of parts of the authors books on epistemic processes, which give more details about the theory. At the same time, the article extends some of the discussion in the books, and at places makes it more precise.

To begin with, some of the conundrums concerning Quantum Mechanics and its interpretation(s) are recalled. Subsequently, a sketch of the "ETH-Approach to Quantum Mechanics" is presented. This approach yields a logically coherent quantum theory of "events" featured by physical systems and of direct or projective measurements of physical quantities, without the need to invoke "observers". It enables one to determine the stochastic time evolution of states of physical systems. We also briefly comment on the quantum theory of indirect or weak measurements, which is much easier to understand and more highly developed than the theory of direct (projective) measurements. A relativistic form of the ETH-Approach will be presented in a separate paper.

By using the non-Markovian master equation, we investigate the effect of the cavity and the environment on the quantum Fisher information (QFI) of an atom qubit system in a dissipation cavity. We obtain the formulae of QFI for two different initial states and analyze the effect of the atom-cavity coupling and the cavity-reservoir coupling on the QFI. The results show that the dynamic behavior of the QFI is obviously dependent on the initial atomic states, the atom-cavity coupling and the cavity-reservoir coupling. The stronger the atom-cavity coupling, the quicker the QFI oscillates and the slower the QFI reduces. Especially, the QFI will tend to a stable value not zero if the atom-cavity coupling is large enough. On the other hand, the smaller the cavity-reservoir coupling, the stronger the non-Markovian effect, the slower the QFI decay. In other words, choosing the best parameter can improve the accuracy of parameter estimation. In addition, the physical explanation of the dynamic behavior of the QFI is given by means of the QFI flow.

The dynamics evolutions of discord and entanglement of two atoms in two independent Lorentzian reservoirs at zero or finite temperature have been investigated by using the time-convolutionless master-equation method. Our results show that, when both the non-Markovian effect and the detuning are present simultaneously, due to the memory and feedback effect of the non-Markovian reservoirs, the discord and the entanglement can be effectively protected even at nonzero temperature by increasing the non-Markovian effect and the detuning. The discord and the entanglement have different robustness for different initial states and their robustness may changes under certain conditions. Nonzero temperature can accelerate the decays of discord and entanglement and induce the entanglement sudden death.

The states of three-qubit systems split into two inequivalent types of genuine tripartite entanglement, namely the Greenberger-Horne-Zeilinger (GHZ) type and the $W$-type. A state belongs to one of these classes can be stochastically transformed only into a state within the same class by local operations and classical communications. We provide local quantum operations, consisting of the most general two-outcome measurement operators, for the deterministic transformations of three-qubit pure states in which the initial and the target states are in the same class. We explore these transformations, originally having the standard GHZ and the standard $W$ states, under the local measurement operators carried out by a single party and $p$ ($p=2,3$) parties (successively). We find a notable result that the standard GHZ state cannot be deterministically transformed to a GHZ-type state in which its all bipartite entanglements are nonzero, i.e., a transformation can be achieved with unit probability when the target state has at least one vanishing bipartite concurrence.

Prominent among the many fascinating properties of graphene are its surprising electronic transport characteristics which are commonly studied theoretically and numerically within the Landauer-B\"uttiker formalism. Here a device is characterized by its scattering properties to and from reservoirs connected by perfect semi-infinite leads, and transport quantities are derived from the scattering matrix. In many respects, however, the device becomes a `black box' as one only analyses what goes in and out. Here we use the Husimi function as a complementary tool for understanding transport in graphene nanodevices. It is a phase space representation of the scattering wavefunctions that allows to link the scattering matrix to a more semiclassical and intuitive description and gain additional insight in to the transport process. In this article we demonstrate the benefits of the Husimi approach by analysing \emph{Klein tunneling} and \emph{intervalley scattering} in two simple graphene nanostructures.

We show that the simple model of an ordered one-dimensional non-interacting system with power-law hopping has extremely interesting transport properties. We restrict ourselves to the case where the power-law decay exponent $\alpha>1$, so that the thermodynamic limit is well-defined. We explore the quantum phase-diagram of this model in terms of the zero temperature Drude weight, which can be analytically calculated. Most interestingly, we reveal that for $1>\alpha>2$, there is a phase where the Drude weight diverges as filling fraction goes to zero. Thus, in this regime, counter intuitively, reducing number of particles increases transport and is maximum for a sub-extensive number of particles. This behavior is immune to adding interactions. Measurement of persistent current due to a flux through a mesoscopic ring with power-law hopping will give an experimental signature of this phase. This behavior survives up to a finite temperature for a finite system. At higher temperatures, a crossover is seen. The maximum persistent current shows a power-law decay at high temperatures. This is in contrast with short ranged systems, where the persistent current decays exponentially with temperature.

We derive a quasiclassical expression for the density of states (DOS) of an arbitrary, ultracold, N-atom collision complex, for a general potential energy surface (PES). We establish the accuracy of our quasiclassical method by comparing to exact quantum results for the K$_2$-Rb and NaK-NaK system, with isotropic model PESs. Next, we calculate the DOS for an accurate NaK-NaK PES to be 0.248 $\mu$K$^{-1}$, with an associated Rice-Ramsperger-Kassel-Marcus (RRKM) sticking time of 11.9 $\mu$s. We extrapolate the DOS and sticking times to all other polar bialkali-bialkali collision complexes by scaling with atomic masses, equilibrium bond lengths, dissociation energies and dispersion coefficients. The sticking times calculated here are two to three orders of magnitude shorter than those reported by Mayle et al. [Phys. Rev. A 85, 062712 (2012)]. We find that the sticking-amplified three-body loss mechanism is not likely the cause of the losses observed in the experiments.

Quantum Random Access Codes (QRACs) are key tools for a variety of protocols in quantum information theory. These are commonly studied in prepare-and-measure scenarios in which a sender prepares states and a receiver measures them. Here, we consider a three-party prepare-transform-measure scenario in which the simplest QRAC is implemented twice in sequence based on the same physical system. We derive optimal trade-off relations between the two QRACs. We apply our results to construct semi-device independent self-tests of quantum instruments, i.e. measurement channels with both a classical and quantum output. Finally, we show how sequential QRACs enable inference of upper and lower bounds on the sharpness parameter of a quantum instrument.

We propose a method for learning a quantum probabilistic model of a perceptron. By considering a cross entropy between two density matrices we can learn a model that takes noisy output labels into account while learning. A multitude of proposals already exist that aim to utilize the curious properties of quantum systems to build a quantum perceptron, but these proposals rely on a classical cost function for the optimization procedure. We demonstrate the usage of a quantum equivalent of the classical log-likelihood, which allows for a quantum model and training procedure. We show that this allows us to better capture noisyness in data compared to a classical perceptron. By considering entangled qubits we can learn nonlinear separation boundaries, such as XOR.

The quantum dynamics of isolated systems under quench condition exhibits a variety of interesting features depending on the integrable/chaotic nature of system. We study the exact dynamics of trivially integrable system of harmonic chains under a multiple quench protocol. Out of time ordered correlator of two Hermitian operators at large time displays scrambling in the thermodynamic limit. In this limit, the entanglement entropy and the central component of momentum distribution both saturate to a steady state value. We also show that reduced density matrix assumes the diagonal form long after multiple quenches for large system size. These exact results involving infinite dimensional Hilbert space are indicative of local thermal behaviour for a trivially integrable harmonic chain.

This paper posits the existence of, and finds a candidate for, a variable change that allows quantum mechanics to be interpreted as quantum geometry. The Bohr model of the Hydrogen atom is thought of in terms of an indeterministic electron position and a deterministic metric and the motivation for this paper is to try to change variables to have a deterministic position and momentum for the electron and nucleus but with an indeterministic (quantum) metric that reproduces the physics of the Bohr model. This mapping is achieved by allowing the metric in the Hamiltonian to be different to the metric in the space-time distance element and then representing the two metrics with vierbeins and assuming they are canonically conjugate variables. Effectively, the usual Schr\"odinger space-time variables have been re-interpreted as four of the potentially sixteen parameters of the metric tensor vierbein in the distance element while the metric tensor vierbein in the Hamiltonian is an operator expressible as first-order derivatives in these variables or vice versa. I then argue that this reproduces observed quantum physics at the sub-atomic level by demonstrating the energy spectrum of electron orbitals is exactly the same as the usual relativistic Bohr model for the Hydrogen atom in a certain limit. Next, by introducing a single dimensionless running coupling that shows up in the analogous place as, but in addition to, Planck's constant in the commutator definition I argue that this allows massive objects to couple to the physical space-time geometry but not massless ones - no matter coupling value. This claim is based on a fit to the Schwarzschild metric with a few simple assumptions and thus obtaining an effective theory of how the quantum geometries at nearby space-time points couple to one another. This demonstrates that this coupling constant is related to Newton's gravitational constant.

Multimode photon-subtraction provides an experimentally feasible option to construct large non-Gaussian quantum states in continuous-variable quantum optics. The non-Gaussian features of the state can lead towards the more exotic aspects of quantum theory, such as negativity of the Wigner function. However, the pay-off for states with such delicate quantum properties is their sensitivity to decoherence. In this paper, we present a general model that treats the most important source of decoherence in a purely optical setting: losses. We use the framework of open quantum systems and master equations to describe losses in n-photon-subtracted multimode states, where each photon can be subtracted in an arbitrary mode. As a main result, we find that mode-dependent losses and photon-subtraction generally do not commute. In particular, the losses do not only reduce the purity of the state, they also change the modal structure of its non-Gaussian features. We then conduct a detailed study of single-photon subtraction from a multimode Gaussian state, which is a setting that lies within the reach of present-day experiments.

The three-qubit Toffoli gate plays an important role in quantum error correction and complex quantum algorithms such as Shor's factoring algorithm, motivating the search for efficient implementations of this gate. Here we introduce a Toffoli gate suitable for exchange-coupled electron spin qubits in silicon quantum dot arrays. Our protocol is a natural extension of a previously demonstrated resonantly driven CNOT gate for silicon spin qubits. It is based on a single exchange pulse combined with a resonant microwave drive, with an operation time on the order of 100 ns and fidelity exceeding 99%. We analyze the impact of calibration errors and 1/f noise on the gate fidelity and compare the gate performance to Toffoli gates synthesized from two-qubit gates. Our approach is readily generalized to other controlled three-qubit gates such as the Deutsch and Fredkin gates.

We consider distributed sensing of non-local quantities. We introduce quantum enhanced protocols to directly measure any (scalar) field with a specific spatial dependence by placing sensors at appropriate positions and preparing a spatially distributed entangled quantum state. Our scheme has optimal Heisenberg scaling and is completely unaffected by noise on other processes with different spatial dependence than the signal. We consider both Fisher and Bayesian scenarios, and design states and settings to achieve optimal scaling. We explicitly demonstrate how to measure coefficients of spatial Taylor and Fourier series, and show that our approach can offer an exponential advantage as compared to strategies that do not make use of entanglement between different sites.