Alkali-metal atomic magnetometers suffer from heading errors in geomagnetic fields as the measured magnetic field depends on the orientation of the sensor with respect to the field. In addition to the nonlinear Zeeman splitting, the difference between Zeeman resonances in the two hyperfine ground states can also generate heading errors depending on initial spin polarization. We examine heading errors in an all-optical scalar magnetometer that uses free precession of polarized $^{87}\text{Rb}$ atoms by varying the direction and magnitude of the magnetic field at different spin polarization regimes. In the high polarization limit where the lower hyperfine ground state $F = 1$ is almost depopulated, we show that heading errors can be corrected with an analytical expression, reducing the errors by two orders of magnitude in Earth's field. We also verify the linearity of the measured Zeeman precession frequency with the magnetic field. With lower spin polarization, we find that the splitting of the Zeeman resonances for the two hyperfine states causes beating in the precession signals and nonlinearity of the measured precession frequency with the magnetic field. We correct for the frequency shifts by using the unique probe geometry where two orthogonal probe beams measure opposite relative phases between the two hyperfine states during the spin precession.

The Everett interpretation of quantum mechanics divides naturally into two parts: first, the interpretation of the structure of the quantum state, in terms of branching, and second, the interpretation of this branching structure in terms of probability. This is the first of two reviews of the Everett interpretation, and focuses on structure, with particular attention to the role of decoherence theory. Written in terms of the quantum histories formalism, decoherence theory just is the theory of branching structure, in Everett's sense.

The stimulated Raman adiabatic passage (STIRAP) shows an efficient technique that accurately transfers population between two discrete quantum states with the same parity, in three-level quantum systems based on adiabatic evolution. This technique has widely theoretical and experimental applications in many fields of physics, chemistry, and beyond. Here, we present a generally robust approach to speed up STIRAP with invariant-based shortcut to adiabaticity. By controlling the dynamical process, we inversely design a family of Hamiltonians that can realize fast and accurate population transfer from the first to the third level, while the systematic error is largely suppressed in general. Furthermore, a detailed trade-off relation between the population of the intermediate state and the amplitudes of Rabi frequencies in the transfer process is illustrated. These results provide an optimal route toward manipulating the evolution of three-level quantum systems in future quantum information processing.

We present the fundamental solutions for the spin-1/2 fields propagating in the spacetimes with power type expansion/contraction and the fundamental solution of the Cauchy problem for the Dirac equation. The derivation of these fundamental solutions is based on formulas for the solutions to the generalized Euler-Poisson-Darboux equation, which are obtained by the integral transform approach.

In this paper, we study measures of quantum non-Markovianity based on the conditional mutual information. We obtain such measures by considering multiple parts of the total environment such that the conditional mutual informations can be defined in this multipartite setup. The benefit of this approach is that the conditional mutual information is closely related to recovery maps and Markov chains; we also point out its relations with the change of distinguishability. Moreover, we show how to extend the non-Markovianity measures to the case in which the initial system-environment state is correlated.

We present two fast algorithms which apply inclusion-exclusion principle to sum over the bosonic diagrams in bare diagrammatic quantum Monte Carlo (dQMC) and inchworm Monte Carlo method, respectively. In the case of inchworm Monte Carlo, the proposed fast algorithm gives an extension to the work ["Inclusion-exclusion principle for many-body diagrammatics", Phys. Rev. B, 98:115152, 2018] from fermionic to bosonic systems. We prove that the proposed fast algorithms reduce the computational complexity from double factorial to exponential. Numerical experiments are carried out to verify the theoretical results and to compare the efficiency of the methods.

It has been discovered that open quantum walks diffusively distribute in space, since they were introduced in 2012. Indeed, some limit distributions have been demonstrated and most of them are described by Gaussian distributions. We operate an open quantum walk on $\mathbb{Z}=\left\{0, \pm 1, \pm 2,\ldots\right\}$ with parameterized operations in this paper, and study its 1st and 2nd moments so that we find its standard deviation. The standard deviation tells us whether the open quantum walker shows diffusive or ballistic behavior, which results in a phase transition of the walker.

Superconducting circuit testing and materials loss characterization requires robust and reliable methods for the extraction of internal and coupling quality factors of microwave resonators. A common method, imposed by limitations on the device design or experimental configuration, is the single-port reflection geometry, i.e. reflection-mode. However, impedance mismatches in cryogenic systems must be accounted for through calibration of the measurement chain while it is at low temperatures. In this paper, we demonstrate a data-based, single-port calibration using commercial microwave standards and a vector network analyzer (VNA) with samples at millikelvin temperature in a dilution refrigerator, making this method useful for measurements of quantum phenomena. Finally, we cross reference our data-based, single-port calibration and reflection measurement with over-coupled 2D- and 3D-resonators against well established two-port techniques corroborating the validity of our method.

We train convolutional neural networks to predict whether or not a given set of measurements is informationally complete to uniquely reconstruct any quantum state with no prior information. In addition, we perform fidelity benchmarking to validate the reconstruction without explicitly carrying out state tomography. These networks are trained to recognize the fidelity and a reliable measure for informational completeness through collective encoding of quantum measurements, data and target states into grayscale images. We confirm the potential of this machine-learning approach by presenting experimental results for both spatial-mode and multiphoton systems of large dimensions. These predictions are further shown to improve with noise recognition when the networks are trained with additional bootstrapped training sets from real experimental data.

Using group-theoretical approach we found a family of four nine-parameter quantum states for the two-spin-1/2 Heisenberg system in an external magnetic field and with multiple components of Dzyaloshinsky-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions. Exact analytical formulas are derived for the entanglement of formation for the quantum states found. The influence of DM and KSEA interactions on the behavior of entanglement and on the shape of disentangled region is studied. A connection between the two-qubit quantum states and the reduced density matrices of many-particle systems is discussed.

In the spirit of device-independent cryptography, we present a two-party quantum authorization primitive with non-locality as its fueling resource. Therein, users are attributed authorization levels granting them access to a private database accordingly. The authorization levels are encoded in the non-local resources distributed to the users, and subsequently confirmed by their ability to win CHSH games using such resources. We formalize the protocol, prove its security, and frame it in the device-independent setting employing the notion of CHSH self-testing via simulation. Finally, we provide a proof-of-concept implementation using the Qiskit open-source framework.

Mutual information is a measure of classical and quantum correlations of great interest in quantum information. It is also relevant in quantum many-body physics, by virtue of satisfying an area law for thermal states and bounding all correlation functions. However, calculating it exactly or approximately is often challenging in practice. Here, we consider alternative definitions based on R\'enyi divergences. Their main advantage over their von Neumann counterpart is that they can be expressed as a variational problem whose cost function can be efficiently evaluated for families of states like matrix product operators while preserving all desirable properties of a measure of correlations. In particular, we show that they obey a thermal area law in great generality, and that they upper bound all correlation functions. We also investigate their behavior on certain tensor network states and on classical thermal distributions.

For a particle moving on a half-line or in an interval the operator $\hat p = - i \partial_x$ is not self-adjoint and thus does not qualify as the physical momentum. Consequently canonical quantization based on $\hat p$ fails. Based upon a new concept for a self-adjoint momentum operator $\hat p_R$, we show that canonical quantization can indeed be implemented on the half-line and on an interval. Both the Hamiltonian $\hat H$ and the momentum operator $\hat p_R$ are endowed with self-adjoint extension parameters that characterize the corresponding domains $D(\hat H)$ and $D(\hat p_R)$ in the Hilbert space. When one replaces Poisson brackets by commutators, one obtains meaningful results only if the corresponding operator domains are properly taken into account. The new concept for the momentum is used to describe the results of momentum measurements of a quantum mechanical particle that is reflected at impenetrable boundaries, either at the end of the half-line or at the two ends of an interval.

We consider correlations, $p_{n,x}$, arising from measuring a maximally entangled state using $n$ measurements with two outcomes each, constructed from $n$ projections that add up to $xI$. We show that the correlations $p_{n,x}$ robustly self-test the underlying states and measurements. To achieve this, we lift the group-theoretic Gowers-Hatami based approach for proving robust self-tests to a more natural algebraic framework. A key step is to obtain an analogue of the Gowers-Hatami theorem allowing to perturb an "approximate" representation of the relevant algebra to an exact one.

For $n=4$, the correlations $p_{n,x}$ self-test the maximally entangled state of every odd dimension as well as 2-outcome projective measurements of arbitrarily high rank. The only other family of constant-sized self-tests for strategies of unbounded dimension is due to Fu (QIP 2020) who presents such self-tests for an infinite family of maximally entangled states with even local dimension. Therefore, we are the first to exhibit a constant-sized self-test for measurements of unbounded dimension as well as all maximally entangled states with odd local dimension.

We explore the spatial enantioseparation of gas chiral molecules for the cyclic three-level systems coupled with three electromagnetic fields. Due to molecular rotations, the specific requirements of the polarization directions of the three electromagnetic fields lead to the space-dependent part of the overall phase of the coupling strengths. Thus, the overall phase of the coupling strengths, which differs with $\pi$ for the enantiomers in the cyclic three-level model of chiral molecules, varies intensely in the length scale of the typical wavelength of the applied electromagnetic fields. Under the induced gauge potentials resulting from the space-dependent part of the overall phase and the space-dependent intensities of coupling strengths, we further show spatial enantioseparation for typical parameters of gas chiral molecules.

Heterodyne detectors as phase-insensitive (PI) devices have found important applications in precision measurements such as space-based gravitational-wave (GW) observation. However, the output signal of a PI heterodyne detector is supposed to suffer from signal-to-noise ratio (SNR) degradation due to image band vacuum and imperfect quantum efficiency. Here we show that the SNR degradation can be overcome when the image band vacuum is quantum correlated with the input signal. We calculate the noise figure of the detector and prove the feasibility of heterodyne detection with enhanced noise performance through quantum correlation. This work should be of great interest to ongoing space-borne GW signal searching experiments.

We study three different measures of quantum correlations -- entanglement spectrum, entanglement entropy, and logarithmic negativity -- for (1+1)-dimensional massive scalar field in flat spacetime. The entanglement spectrum for the discretized scalar field in the ground state indicates a cross-over in the zero-mode regime, which is further substantiated by an analytical treatment of both entanglement entropy and logarithmic negativity. The exact nature of this cross-over depends on the boundary conditions used -- the leading order term switches from a $\log$ to $\log-\log$ behavior for the Periodic and Neumann boundary conditions. In contrast, for Dirichlet, it is the parameters within the leading $\log-\log$ term that are switched. We show that this cross-over manifests as a change in the behavior of the leading order divergent term for entanglement entropy and logarithmic negativity close to the zero-mode limit. We thus show that the two regimes have fundamentally different information content. For the reduced state of a single oscillator, we show that this cross-over occurs in the region $Nam_f\sim \mathscr{O}(1)$.

It was recently argued that one-dimensional systems of several strongly interacting fermions of different mass undergo critical transitions between different spatial orderings when the external confinement adiabatically changes its shape. In this work, we explore their dynamical properties when finite-time drivings are considered. By detailed analysis of many-body spectra, we show that the dynamics is typically guided only by the lowest eigenstates and may be well-understood in the language of the generalized Landau-Zener mechanism. In this way, we can capture precisely the dynamical response of the system to the external driving. As consequence, we show that by appropriate tailoring parameters of the driving one can target desired many-body state in a finite time.

Complex numbers are widely used in both classical and quantum physics, and are indispensable components for describing quantum systems and their dynamical behavior. Recently, the resource theory of imaginarity has been introduced, allowing for a systematic study of complex numbers in quantum mechanics and quantum information theory. In this work we develop theoretical methods for the resource theory of imaginarity, motivated by recent progress within theories of entanglement and coherence. We investigate imaginarity quantification, focusing on the geometric imaginarity and the robustness of imaginarity, and apply these tools to the state conversion problem in imaginarity theory. Moreover, we analyze the complexity of real and general operations in optical experiments, focusing on the number of unfixed wave plates for their implementation. We also discuss the role of imaginarity for local state discrimination, proving that any pair of real orthogonal pure states can be discriminated via local real operations and classical communication. Our study reveals the significance of complex numbers in quantum physics, and proves that imaginarity is a resource in optical experiments.

Synchronization is a dynamical phenomenon found in complex systems ranging from biological systems to human society and is characterized by the constituents parts of a system locking their motion so that they have the same phase and frequency. Recent intense efforts have focused on understanding synchronization in quantum systems without clear semi-classical limits but no comprehensive theory providing a systematic basis for the underlying physical mechanisms has yet been found. Through a complete characterization of the non-decaying persistently oscillating eigenmodes of smooth quantum evolutions corresponding to quantum limit cycles, we provide a general algebraic theory of quantum synchronization which provides detailed criteria for various types of synchronization to occur. These results constitute the previously absent framework within which to pursue a structured study of quantum synchronization. This framework enables us to study both stable synchronization which lasts for infinitely long times limit, and metastable synchronization which lasts for long, but finite, times. Moreover, we give compact algebraic criteria that may be checked in a given system to prove the absence of synchronization. We use our theory to demonstrate the anti-synchronization of two spin-1/2's and discuss synchronization in the Fermi-Hubbard model and its generalisations which are relevant for various fermionic cold atom experiments, including multi-species, multi-orbital and higher spin atoms.