Fisher information quantifies how well we can detect small changes in a parameter. According to the parameter that we focus on, the Fisher information presents different quantum phenomena. Here we investigate quantum interference of two particles in a two-wave mixing operation. Due to the symmetry of the two-wave mixing operation, we construct the Fisher information only by counting the number of particles in one of the output modes. When we focus on an input state parameter, we cannot discriminate particle species, i.e., boson and fermion, but can observe Hong-Ou-Mandel effect. When we focus on a parameter of the two-wave mixing operation, on the other hand, we can discriminate the particle species and extend it to detect two-particle entanglement scenario.

We investigate dissipative extensions of the Su-Schrieffer-Heeger model with regard to different approaches of modeling dissipation. In doing so, we use two distinct frameworks to describe the gain and loss of particles, one uses Lindblad operators within the scope of Lindblad master equations, the other uses complex potentials as an effective description of dissipation. The reservoirs are chosen in such a way that the non-Hermitian complex potentials are $\mathcal{PT}$-symmetric. From the effective theory we extract a state which has similar properties as the non-equilibrium steady state following from Lindblad master equations with respect to lattice site occupation. We find considerable similarities in the spectra of the effective Hamiltonian and the corresponding Liouvillean. Further, we generalize the concept of the Zak phase to the dissipative scenario in terms of the Lindblad description and relate it to the topological phases of the underlying Hermitian Hamiltonian.

Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this paper, assuming that our usual inference procedure makes sense for every set of logical propositions represented in terms of commuting projectors on a given Hilbert space, we extend the logical interpretation to quantum mechanics and derive the Born rule. Our result implies that, from the epistemological viewpoints, we can regard quantum mechanics as a natural extension of the classical probability.

In this paper we studied approximate solutions of the radial Schr\"odinger equation with the attractive Gaussian potential. We used asymptotic iteration method and variational method in order to obtain energy eigenvalues for any $n$ and $l$ quantum numbers. Our results are in good agreement with the other studies.

We present a theoretical proposal of a tunable charge qubit, hosted in triple quantum dots. The manipulation is solely performed by changing the heights of the two potential barriers between the three dots, while the energy of all three dots are fixed. We have found that when the relative height of the two barriers are changed, the direction of the axis of rotation in performing single-qubit gates can be varied. On the other hand, the corresponding rotation speed can be tuned by raising or lowering the two barriers at the same time. Our proposal therefore allows for tunability of both the rotation axis and rotating speed for a charge qubit via all-electrical control, which may facilitate realization of quantum algorithms in these devices.

The error in estimating the separation of a pair of incoherent sources from radiation emitted by them and subsequently captured by an imager is fundamentally bounded below by the inverse of the corresponding quantum Fisher information (QFI) matrix. We calculate the QFI for estimating the full three-dimensional (3D) pair separation vector, extending previous work on pair separation in one and two dimensions. We also show that the pair-separation QFI is, in fact, identical to source localization QFI, which underscores the fundamental importance of photon-state localization in determining the ultimate estimation-theoretic bound for both problems. We also propose general coherent-projection bases that can attain the QFI in two special cases. We present simulations of an approximate experimental realization of such quantum limited pair superresolution using the Zernike basis, confirming the achievability of the QFI bounds.

I consider the role of detection noise in quantum-enhanced metrology in collective spin systems, and derive a fundamental bound for the maximum obtainable sensitivity for a given level of added detection noise. I then present an interaction-based readout utilising the commonly used one-axis twisting scheme that approaches this bound for states generated via several commonly considered methods of generating quantum enhancement, such as one-axis twisting, two-axis counter-twisting, twist-and-turn squeezing, quantum non-demolition measurements, and adiabatically scanning through a quantum phase transition. I demonstrate that this method performs significantly better than other recently proposed interaction-based readouts. These results may help provide improved sensitivity for quantum sensing devices in the presence of unavoidable detection noise.

We theoretically analyze the errors in one- and two-qubit gates in SiMOS and Si/SiGe spin qubit experiments, and present a pulse sequence which can suppress the errors in exchange coupling due to charge noise using ideal local rotations. In practice, the overall fidelity of the pulse sequence will be limited only by the quality of the single-qubit gates available: the C-phase infidelity comes out to be $\approx 2.5 \times$ the infidelity of the single-qubit operations. Based on experimental data, we model the errors and show that C-phase gate infidelities can be suppressed by two orders in magnitude.

Our pulse sequence is simple and we expect an experimental implementation would be relatively straightforward. We also evaluate the performance of this gate against $1/f$ noise. Assuming a soft ultraviolet cutoff, we show that the pulse sequence designed for quasistatic noise still performs well when the cutoff occurs below $\sim 1$MHz given fast enough one-qubit Rabi frequencies, suppressing the infidelity by an order of magnitude compared to the existing direct adiabatic protocol. We also analyze the effects of nonadiabaticity during finite rise periods, and find that adiabaticity is not a limitation for the current values of exchange coupling.

Mesoscopic spin ensembles coupled to a cavity offer the exciting prospect of observing complex nonclassical phenomena that pool the microscopic features from a few spins with those of macroscopic spin ensembles. Here, we demonstrate how the collective interactions in an ensemble of as many as hundred spins can be harnessed to obtain a periodic pulse train of nonclassical light. To unravel the full quantum dynamics and photon statistics, we develop a time-adaptive variational renormalization group method that accurately captures the underlying Lindbladian dynamics of the mesoscopic spin-cavity system.

We investigate magnetically tunable Feshbach resonances between ultracold europium atoms and between europium and alkali-metal atoms using multichannel quantum scattering calculations. For ultracold gases of europium atoms both homonuclear $^{153}$Eu+$^{153}$Eu and heteronuclear $^{151}$Eu+$^{153}$Eu systems are studied. Calculations for mixtures of europium and alkali-metal atoms are carried out for prototype systems of $^{153}$Eu+$^{87}$Rb and $^{153}$Eu+$^7$Li. We analyze the prospects for the control of scattering properties, observation of quantum chaotic behavior, and magnetoassociation into ultracold polar and paramagnetic molecules. We show that favorable resonances can be expected at experimentally feasible magnetic field strengths below 1000$\,$G for all investigated atomic combinations. For Eu atoms, a rich spectrum of resonances is expected as a result of the competition between relatively weak short-range spin-exchange and strong long-range magnetic dipole-dipole interactions, where the dipolar interaction induces measurable resonances. A high density of resonances is expected at magnetic field strengths below 200$\,$G without pronounced quantum chaos signatures. The present results may be useful for the realization and application of dipolar atomic and molecular quantum gases based on europium atoms in many-body physics.

The "trilobite" type of molecule, predicted in 2000 and observed experimentally in 2015, arises when a Rydberg electron exerts a weak attractive force on a neutral ground state atom. Such molecules have bond lengths exceeding 100 nm. The ultra-long-range chemical bond between the two atoms is a nonperturbative linear combination of the many degenerate electronic states associated with high principal quantum numbers, and the resulting electron probability distribution closely resembles a fossil trilobite from antiquity. We show how to coherently engineer this same long-range orbital through a sequence of electric and magnetic field pulses even when the ground state atom is not present, and propose several methods to observe the resulting orbital. The existence of such a ghost chemical bond in which an electron reaches out from one atom to a nonexistent second atom is a consequence of the high level degeneracy.

The quantum phase-space dynamics driven by hyperbolic P\"oschl-Teller (PT) potentials is investigated in the context of the Weyl-Wigner quantum mechanics. The obtained Wigner functions for quantum superpositions of ground and first-excited states exhibit some non-classical and non-linear patterns which are theoretically tested and quantified according to a non-gaussian continuous variable framework. It comprises the computation of quantifiers of non-classicality for an anharmonic two-level system where non-Liouvillian features are identified through the phase-space portrait of quantum fluctuations. In particular, the associated non-gaussian profiles are quantified by measures of {\em kurtosis} and {\em negative entropy}. As expected from the PT {\em quasi}-harmonic profile, our results suggest that quantum wells can work as an experimental platform that approaches the gaussian behavior in the investigation of the interplay between classical and quantum scenarios. Furthermore, it is also verified that the Wigner representation admits the construction of a two-particle bipartite quantum system of continuous variables, $A$ and $B$, identified by $\sum_{i,j=0,1}^{i\neq j}\vert i_{_A}\rangle\otimes\vert j_{_B}\rangle$, which are shown to be separable under gaussian and non-gaussian continuous variable criteria.

Spin-orbit coupling fundamentally alters spin qubits, opening pathways to improve the scalability of quantum computers via long distance coupling mediated by electric fields, photons, or phonons. It also allows for new engineered hybrid and topological quantum systems. However, spin qubits with intrinsic spin-orbit coupling are not yet viable for quantum technologies due to their short ($\sim1~\mu$s) coherence times $T_2$, while qubits with long $T_2$ have weak spin-orbit coupling making qubit coupling short-ranged and challenging for scale-up. Here we show that an intrinsic spin-orbit coupled "generalised spin" with total angular momentum $J=\tfrac{3}{2}$, which is defined by holes bound to boron dopant atoms in strained $^{28}\mathrm{Si}$, has $T_2$ rivalling the electron spins of donors and quantum dots in $^{28}\mathrm{Si}$. Using pulsed electron paramagnetic resonance, we obtain $0.9~\mathrm{ms}$ Hahn-echo and $9~\mathrm{ms}$ dynamical decoupling $T_2$ times, where strain plays a key role to reduce spin-lattice relaxation and the longitudinal electric coupling responsible for decoherence induced by electric field noise. Our analysis shows that transverse electric dipole can be exploited for electric manipulation and qubit coupling while maintaining a weak longitudinal coupling, a feature of $J=\tfrac{3}{2}$ atomic systems with a strain engineered quadrupole degree of freedom. These results establish single-atom hole spins in silicon with quantised total angular momentum, not spin, as a highly coherent platform with tuneable intrinsic spin-orbit coupling advantageous to build artificial quantum systems and couple qubits over long distances.

The origin of classical reality in our quantum world is a long-standing mystery. Here, we examine a nitrogen vacancy center evolving naturally in the presence of its environment to study quantum Darwinism - the proliferation of information about preferred quantum states throughout the world via the environment. This redundantly imprinted information accounts for the perception of objective reality, as it is independently accessible by many without perturbing the system of interest. To observe the emergence of redundant information, we implement a novel dynamical decoupling scheme that enables the measurement/control of several nuclear spins (the environment E) interacting with a nitrogen vacancy (the system S). In addition to showing how to create entangled SE states relevant to quantum metrology, we demonstrate that under the decoherence of S, redundant information is imprinted onto E, giving rise to classical objectivity - a consensus of the nuclear spins about the state of S. This provides the first laboratory verification of the objective classical world emerging from the underlying quantum substrate.

We address the framework of analysing quantum metrology in the information-theoretic picture. Firstly we show how to extract the maximum amount of information in general via suitable state initialization of the probes at the beginning and a quantum measurement at the end. Our analysis can apply to both the single-parameter and the multi-parameter estimation procedures as well as to any other quantum information processing procedures. We then establish a direct connection between the information-theoretic picture of quantum metrology and its conventional variance-covariance picture, by showing that any estimation procedure achieves Heisenberg limit in variance-covariance picture can also reach the information-theoretic Heisenberg limit in the asymptotic sense. As a direct consequence, we argue that the entangled measurement is not necessary for achieving Heisenberg limit in the information-theoretic pictures, which is explicitly illustrated for the Quantum-Classical parallel strategy of quantum metrology with a separable measurement employed and the Heisenberg limit saturated in both pictures.

In this work we experimentally study many-body localization (MBL) in a one-dimensional bichromatic quasiperiodic potential with a single-particle mobility edge (SPME) using ultracold atoms. We measure the time evolution of the density imbalance between even and odd lattice sites from an initial charge density wave, and analyze the corresponding relaxation exponents. We find clear signatures of MBL in this system when the corresponding noninteracting model is deep in the localized phase. We also critically compare and contrast our results with those from a tight-binding Aubry-Andr\'{e} model, which does not exhibit an SPME.

Notwithstanding its great influence in modern physics, the EPR thought-experiment has been explained incorrectly a surprising number of times.

In the standard approach to quantum games, players' moves are local unitary transformations on an entangled state that is subsequently measured. Players' payoffs are then obtained as expected values of the entries in the payoff matrix of the classical game on a set of quantum probabilities obtained from the quantum measurement. In this paper, we approach quantum games from a diametrically opposite perspective. We consider a classical three-player symmetric game along with a known expression for a set of quantum probabilities relevant to a tripartite Einstein-Podolsky-Rosen (EPR) experiment that depends on three players' directional choices in the experiment. We define the players' moves as their directional choices in an EPR setting and then express their payoff relations in the resulting quantum game in terms of their directional choices, the entries of the payoff matrix, and the quantum probability distribution relevant to the tripartite EPR experiment.

We introduce a neural network architecture that models the physical reasoning process and that can be used to extract simple physical concepts from experimental data without being provided with additional prior knowledge. We apply the neural network to a variety of simple physical examples in classical and quantum mechanics, like damped pendulums, two-particle collisions, and qubits. The network finds the physically relevant parameters, exploits conservation laws to make predictions, and can be used to gain conceptual insights. For example, given a time series of the positions of the Sun and Mars as observed from Earth, the network discovers the heliocentric model of the solar system - that is, it encodes the data into the angles of the two planets as seen from the Sun. Our work provides a first step towards answering the question whether the traditional ways by which physicists model nature naturally arise from the experimental data without any mathematical and physical pre-knowledge, or if there are alternative elegant formalisms, which may solve some of the fundamental conceptual problems in modern physics, such as the measurement problem in quantum mechanics.

A recent paper [Z. Yu and S. Prasad, "Quantum limited superresolution of an incoherent source pair in three dimensions," arXiv:1805.09227v2 [quant-ph] (2018)] considered the problem of quantum limited estimation of the separation vector for a pair of incoherent point sources in all three dimensions. Here we extend our analysis to treat the problem of simultaneously estimating the location of the centroid and the separation of the source pair, which is equivalent to localizing both sources simultaneously. We first calculate the quantum Fisher information for simultaneous pair centroid-separation estimation and then discuss the fundamental, estimation-theoretic trade-offs between the two tasks, which we confirm using simulations.