Light beams having a vectorial field structure, or polarization, that varies over the transverse profile and a central optical singularity are called vector vortex (VV) beams and may exhibit specific properties such as focusing into “light needles” or rotation invariance. VV beams have already found applications in areas ranging from microscopy to metrology, optical trapping, nano-optics, and quantum communication. Individual photons in such beams exhibit a form of single-particle quantum entanglement between different degrees of freedom. On the other hand, the quantum states of two photons can be also entangled with each other. Here, we combine these two concepts and demonstrate the generation of quantum entanglement between two photons that are both in VV states: a form of entanglement between two complex vectorial fields. This result may lead to quantum-enhanced applications of VV beams as well as to quantum information protocols fully exploiting the vectorial features of light.

We smoothly tune the dimensionality of pancake-shaped ${}^6\mathrm{Li}$ Fermi gas clouds from quasi-two-dimensional to two-dimensional (2D) to measure radio-frequency spectra and cloud profiles in both regimes. In the quasi-2D case, where $E_F/h{\nu }_z\simeq 1$, with $E_F$ the Fermi energy and $h{\nu }_z$ the harmonic oscillator energy in the tightly confined direction, we confirm that the radio-frequency spectra strongly disagree with 2D mean-field theory. Then we tune to the 2D regime, $E_F<<h{\nu }_z$, where the measured radio-frequency spectra are in very good agreement with 2D mean-field theory. Nevertheless, the measured cloud profiles strongly disagree, confirming predictions that a beyond mean-field approach is required throughout the 2D to quasi-2D crossover.

In this work we generalize the quantum trajectory (QT) theory from Markovian to non-Markovian environments. We model the non-Markovian environment by using a Lorentzian spectral density function with bandwidth $\left(\mathrm{\Lambda }\right)$, and find a perfect “scaling” property with the measurement frequency $\left({\tau }^{-1}\right)$ in terms of the scaling variable $x=\mathrm{\Lambda }\tau$. Our result bridges the gap between the existing QT theory and the Zeno effect, by rendering them as two extremes corresponding to $x\to \infty$ and $x\to 0$, respectively. This $x$-dependent criterion improves the idea of using $\tau$ alone and quantitatively identifies the validity condition of the conventional QT theory.

We consider the most general correlations that can be obtained by a group of parties whose causal relations are well defined, although possibly probabilistic and dependent on past parties' operations. We show that, for any fixed number of parties and inputs and outputs for each party, the set of such correlations forms a convex polytope, whose vertices correspond to deterministic strategies and whose (nontrivial) facets define so-called causal inequalities. We completely characterize the simplest tripartite polytope in terms of its facet inequalities, propose generalizations of some inequalities to scenarios with more parties, and show that our tripartite inequalities can be violated within the process matrix formalism, where quantum mechanics is locally valid but no global causal structure is assumed.

We investigate the entanglement dynamics of two uniformly accelerated atoms with the same acceleration perpendicular to their separation. The two-atom system is treated as an open system coupled with fluctuating electromagnetic fields in the Minkowski vacuum, and in the Born–Markov approximation the master equation that describes the completely positive time evolution of the two-atom system is derived. In particular, we investigate the phenomena of entanglement degradation, generation, revival and enhancement. As opposed to the scalar-field case, the entanglement dynamics is crucially dependent on the polarization directions of the atoms. For the two-atom system with certain acceleration and separation, the polarization directions of the atoms may determine whether entanglement generation, revival or enhancement happens, while for entanglement degradation, they affect the decay rate of entanglement. A comparison between the entanglement evolution of accelerated atoms and that of static ones immersed in a thermal bath at the Unruh temperature shows that they are the same only when the acceleration is extremely small.

The Jordan-Wigner transformation maps a one-dimensional (1D) spin-$1/2$ system onto a fermionic model without spin degree of freedom. A double chain of quantum bits with $XX$ and $ZZ$ couplings of neighboring qubits along and between the chains, respectively, can be mapped on a spin-full 1D Fermi-Hubbard model. The qubit system can thus be used to emulate the quantum properties of this model. We analyze physical implementations of such analog quantum simulators, including one based on transmon qubits, where the $ZZ$ interaction arises due to an inductive coupling and the $XX$ interaction due to a capacitive interaction. We propose protocols to gain confidence in the results of the simulation through measurements of local operators.

We report photoassociation (PA) of ultracold Na and Cs atoms in a dual-species magneto-optical trap. Trap loss spectroscopy of the ultracold polar NaCs molecules formed by PA, which carries information about relative PA transition strengths, has been experimentally obtained by using highly sensitive modulation spectroscopy technique. The fine and hyperfine effects at near-dissociation levels of NaCs molecular $c{}^3\mathrm{\Sigma }^{+}$ state are observed and modeled. The interaction Hamiltonian is described in terms of the Hund's case ($a$) coupling scheme. The molecular hyperfine structure of near-dissociation levels is simulated within a simplified model of four interacting vibrational levels belonging to different initially unperturbed electronic states. The results of the simulation infer that the interaction parameters of the observed near-dissociation levels are close to the asymptotic parameters of the pair of atoms. The coupling of the electronic states is essential for forming the hyperfine structure.

We discuss the superfluid properties of a uniform, weakly interacting Bose-Einstein condensed gas with spin-orbit coupling, realized recently in experiments. We find a finite normal fluid density ${\rho }_n$ at zero temperature which turns out to be a function of the Raman coupling. In particular, the entire fluid becomes normal at the transition point from the zero momentum to the plane wave phase, even though the condensate fraction remains finite. We emphasize the crucial role played by the breaking of Galilean invariance and by the gapped branch of the elementary excitations whose contribution to various sum rules is discussed explicitly. Our predictions for the superfluid density are successfully compared with the available experimental results based on the measurement of the sound velocities.

Loss-induced transmission in waveguides and reversed pump dependence in lasers are two prominent examples of counterintuitive effects in non-Hermitian systems with patterned gain and loss. By analyzing the eigenvalue dynamics of complex symmetric matrices when a system parameter is varied, we introduce a general set of theoretical conditions for these two effects. We show that these effects arise in any irreducible system where the gain or loss is added to a subset of the elements of the system, without the need for parity-time symmetry or for the system to be near an exceptional point. These results are confirmed using full-wave numerical simulations. The conditions presented here vastly expand the design space for observing these effects. We also show that a similarly broad class of systems exhibit a loss-induced narrowing of the density of states.

Friedel's law states that the modulus of the Fourier transform of real functions is centrosymmetric, while the phase is antisymmetric. As a consequence of this, elastic scattering of plane-wave photons or electrons within the first-order Born-approximation, as well as Fraunhofer diffraction on any aperture, is bound to result in centrosymmetric diffraction patterns. Friedel's law, however, does not apply for vortex beams, and centrosymmetry in general is not present in their diffraction patterns. In this work we extend Friedel's law for vortex beams by showing that the diffraction patterns of vortex beams with opposite topological charge, scattered on the same two-dimensional potential, always are centrosymmetric to one another, regardless of the symmetry of the scattering object. We verify our statement by means of numerical simulations and experimental data. Our research provides deeper understanding in vortex-beam diffraction and can be used to design new experiments to measure the topological charge of vortex beams with diffraction gratings or to study general vortex-beam diffraction.

Two-photon annihilation of an electron-positron pair in the field of a plane low-intensity circularly polarized pulsed electromagnetic wave was studied. The conditions for resonance of the process which are related to an intermediate particle that falls within the mass shell are studied. In the resonant approximation the probability of the process was obtained. It is demonstrated that the resonant probability of two-photon annihilation of an electron-positron pair may be several orders of magnitude higher than the probability of this process in the absence of the external field. The obtained results may be experimentally verified by the laser facilities of the international megaprojects, for example, SLAC (National Accelerator Laboratory), FAIR (Facility for Antiproton and Ion Research), and XFEL (European X-Ray Free-Electron Laser).

The characterization and quantification of quantum correlations, which play an instrumental role in exploring and exploiting the quantum world, have been extensively and intensively studied in the past few decades. Of special prominence and significance are the concepts of entanglement and discord, which are usually regarded as very distinctive quantum correlations, with the latter going beyond the former. In this work we establish a direct and natural link between entanglement and discord via state extensions and reveal that entanglement is actually the intrinsic discord, by which we mean that entanglement is the irreducible residue of discord viewed from ambient spaces. Our approach, taking into account the contextuality of a quantum state and being of a global nature, stands in sharp contrast to the local operations and classical communication paradigm of entanglement, which focuses on the state itself via a local approach. Furthermore, we introduce a figure of merit which, on the one hand, captures the essence of entanglement, i.e., nonlocality and quantumness of correlations, and, on the other hand, leads to a quantitative decomposition of total correlations into classical correlations, dissonance, and entanglement. This demystifies the meaning of entanglement from the perspective of quantum measurements and provides a unified framework for the interplay of various correlations in terms of quantum measurements and mutual information.

Quantum computing technology has reached a second renaissance in the past five years. Increased interest from both the private and public sector combined with extraordinary theoretical and experimental progress has solidified this technology as a major advancement in the 21st century. As anticipated my many, some of the first realizations of quantum computing technology has occured over the cloud, with users logging onto dedicated hardware over the classical internet. Recently, IBM has released the Quantum Experience, which allows users to access a five-qubit quantum processor. In this paper we take advantage of this online availability of actual quantum hardware and present four quantum information experiments. We utilize the IBM chip to realize protocols in quantum error correction, quantum arithmetic, quantum graph theory, and fault-tolerant quantum computation by accessing the device remotely through the cloud. While the results are subject to significant noise, the correct results are returned from the chip. This demonstrates the power of experimental groups opening up their technology to a wider audience and will hopefully allow for the next stage of development in quantum information technology.

Elastic collisions between initially unpolarized electrons and hydrogenlike atoms are discussed aiming to analyze the entanglement properties of the correlated final spin system. Explicit spin-dependent interactions are neglected and electron exchange only is taken into account. We show the final spin system to be completely characterized by a single spin correlation parameter depending on scattering angle and energy. Its numerical value identifies the final spins of the collision partners to be either in the separable, entangled, or Bell correlated regions. The symmetry of the scattering process allows for the construction of explicit examples applying methods of classical communication and local operations for illustrating the concepts of nonlocality versus separability. It is shown that strong correlations can be produced violating Bell's inequalities significantly. Furthermore, the degree of entanglement can be continuously varied simply by changing either the scattering angle and/or energy. This allows for the generation of tunable spin pairs with any desired degree of entanglement. It is suggested to use such nonlocally entangled spin pairs as a resource for further experiments, for example in quantum information processes.

We compare the standard 50%-efficient single beam splitter method for Bell-state measurement to a proposed 75%-efficient auxiliary-photon-enhanced scheme [W. P. Grice, Phys. Rev. A 84, 042331 (2011)] in light of realistic conditions. The two schemes are compared with consideration for high input state photon loss, auxiliary state photon loss, detector inefficiency and coupling loss, detector dark counts, and non-number-resolving detectors. We also analyze the two schemes when multiplexed arrays of non-number-resolving detectors are used. Furthermore, we explore the possibility of utilizing spontaneous parametric down-conversion as the auxiliary photon pair source required by the enhanced scheme. In these different cases, we determine the bounds on the detector parameters at which the enhanced scheme becomes superior to the standard scheme and describe the impact of the different imperfections on measurement success rate and discrimination fidelity. This is done using a combination of numeric and analytic techniques. For many of the cases discussed, the size of the Hilbert space and the number of measurement outcomes can be very large, which makes direct numerical solutions computationally costly. To alleviate this problem, all of our numerical computations are performed using pure states. This requires tracking the loss modes until measurement and treating dark counts as variations on measurement outcomes rather than modifications to the state itself. In addition, we provide approximate analytic expressions that illustrate the effect of different imperfections on the Bell-state analyzer quality.

Remote entanglement of distant, noninteracting quantum entities is a key primitive for quantum information processing. We present a protocol to remotely entangle two stationary qubits by first entangling them with propagating ancilla qubits and then performing a joint two-qubit measurement on the ancillas. Subsequently, single-qubit measurements are performed on each of the ancillas. We describe two continuous variable implementations of the protocol using propagating microwave modes. The first implementation uses propagating $\mathrm{Schr}\ddot{\mathrm{o}}$ dinger cat states as the flying ancilla qubits, a joint-photon-number-modulo-2 measurement of the propagating modes for the two-qubit measurement, and homodyne detections as the final single-qubit measurements. The presence of inefficiencies in realistic quantum systems limit the success rate of generating high fidelity Bell states. This motivates us to propose a second continuous variable implementation, where we use quantum error correction to suppress the decoherence due to photon loss to first order. To that end, we encode the ancilla qubits in superpositions of Schrödinger cat states of a given photon-number parity, use a joint-photon-number-modulo-4 measurement as the two-qubit measurement, and homodyne detections as the final single-qubit measurements. We demonstrate the resilience of our quantum-error-correcting remote entanglement scheme to imperfections. Further, we describe a modification of our error-correcting scheme by incorporating additional individual photon-number-modulo-2 measurements of the ancilla modes to improve the success rate of generating high-fidelity Bell states. Our protocols can be straightforwardly implemented in state-of-the-art superconducting circuit-QED systems.

When classically searching a database, having additional correct answers makes the search easier. For a discrete-time quantum walk searching a graph for a marked vertex, however, additional marked vertices can make the search harder by causing the system to approximately begin in a stationary state, so the system fails to evolve. In this paper, we completely characterize the stationary states, or 1-eigenvectors, of the quantum walk search operator for general graphs and configurations of marked vertices by decomposing their amplitudes into uniform and flip states. This infinitely expands the number of known stationary states and gives an optimization procedure to find the stationary state closest to the initial uniform state of the walk. We further prove theorems on the existence of stationary states, with them conditionally existing if the marked vertices form a bipartite connected component and always existing if nonbipartite. These results utilize the standard oracle in Grover's algorithm, but we show that a different type of oracle prevents stationary states from interfering with the search algorithm.

The decoy-state quantum key distribution (QKD) protocol has been widely used in commercial QKD systems. Several QKD field networks show its practicability and commercial prospects. Importantly, practical decoy-state QKD systems should be characterized with device imperfections. In this paper, for the case without intensity fluctuations, we present the parameter estimation based on the Chernoff bound for a practical decoy-state QKD protocol and compare performances of that based on Hoeffding's inequality and the Chernoff bound, respectively. Taking intensity fluctuations into consideration, we present the finite-key analysis with composable security against general attacks based on Azuma's inequality. Our numerical results show that the finite-key analysis based on the Chernoff bound is tighter than Hoeffding's inequality when the total number of transmitting signals $N<1\times {10}^{12}$. Moreover, the intensity fluctuations' influence is more obvious when the data size of total transmitting signals is small. Our results emphasize the importance of the stability of the intensity modulator as well as the accurate estimation of emitted pulse's intensity.

We study mechanisms that allow one to synchronize the quantum phase of two qubits relative to a fixed basis. Starting from one qubit in a fixed reference state and the other in an unknown state, we find that, contrary to the impossibility of perfect quantum cloning, the quantum phase can be synchronized perfectly through a joined unitary operation. When both qubits are initially in a pure unknown state, perfect quantum-phase synchronization through unitary operations becomes impossible. In this situation we determine the maximum average quantum-phase synchronization fidelity and the distribution of relative phases and fidelities, and we identify optimal quantum circuits that achieve this maximum fidelity. A subset of these optimal quantum circuits enable perfect quantum-phase synchronization for a class of unknown initial states restricted to the equatorial plane of the Bloch sphere.