A Markovian process of a system is defined classically as a process in which the future state of the system is fully determined by only its present state, not by its previous history. There have been several measures of non-Markovianity to quantify the degrees of non-Markovian effect in a process of an open quantum system based on information backflow from the environment to the system. However, the condition for the witness of the system information backflow does not coincide with the classical definition of a Markovian process. Recently, a new measure with a condition that coincides with the classical definition in the relevant limit has been proposed. Here, we focus on the new definition (measure) for quantum non-Markovian processes, and characterize the Markovian condition as a quantum process that has no information backflow through the reduced environment state (IBTRES) and no system-environment correlation effect (SECE). The action of IBTRES produces non-Markovian effects by flowing the information of quantum operations performed by an experimenter at earlier times back to the system through the environment, while the SECE can produce non-Markovian effect without carrying any earlier quantum operation information. We give the necessary and sufficient conditions for no IBTRES and no SECE, respectively, and show that a process is Markovian if and only if it has no IBTRES and no SECE. The quantitative measures and algorithms for calculating non-Markovianity, IBTRES, and solely SECE are explicitly presented.

In the framework of generalized probabilistic theories (GPT), we illustrate a class of statistical processes in the case of two noninteracting identical particles in two modes that satisfies a well-motivated notion of physicality conditions, namely the double stochasticity and the no-interaction condition proposed by Karczewski et al. [Phys. Rev. Lett. 120, 080401 (2018)], which cannot be realized through a quantum mechanical process. This class of statistical process is ruled out by an additional requirement, called the evolution condition, imposed on two-particle evolution. We also show that any statistical process of two noninteracting identical particles in two modes that satisfies all three physicality conditions can be realized within quantum mechanics using the beam-splitter operation.

We introduce photonic architectures for universal quantum computation. The first step is to produce a resource state which is a superposition of the first four Fock states with a probability greater than or equal to ${10}^{-2}$, an increase by a factor of ${10}^4$ over standard sequential photon-subtraction techniques. The resource state is produced with near-perfect fidelity from a quantum gadget that uses displaced squeezed vacuum states, interferometers, and photon-number-resolving detectors. The parameters of this gadget are trained using machine learning algorithms for variational circuits. We discuss in detail various aspects of the non-Gaussian state preparation resulting from the numerical experiments. We then propose a notion of resource farms where these gadgets are stacked in parallel, to increase the success probability further. We find a trade-off between the success probability of the farm, the error tolerance, and the number of gadgets. Using the resource states in conventional gate teleportation techniques, we can then implement weak tunable cubic phase gates. The numerical tools that have been developed could potentially be useful for other applications in photonics as well.

With the advance of quantum information technology, the question of how to most efficiently test quantum circuits is becoming of increasing relevance. Here we introduce the statistics of lengths of measurement sequences that allows one to certify entanglement across a given bipartition of a multiqubit system over the possible sequence of measurements of random unknown states and identify the best measurement strategies in the sense of the (on average) shortest measurement sequence of (multiqubit) Pauli measurements. The approach is based on the algorithm of truncated moment sequences, which allows one to deal naturally with incomplete information, i.e., information that does not fully specify the quantum state. We find that the set of measurements corresponding to diagonal matrix elements of the moment matrix of the state are particularly efficient. For symmetric states their number increases only like the third power of the number $N$ of qubits. Their efficiency increases rapidly with $N$, leaving already for $N=4$ less than a fraction ${10}^{-6}$ of randomly chosen entangled states undetected.

The shifts of the $1s3p{}^1{P}_1\to 1s^2{}^1{S}_0$ He-$\beta$ transition of ${\mathrm{Cl}}^{15+}$ were measured in hot ($\ge 600$ eV), dense (1–2 g/${\mathrm{cm}}^3$) plasmas generated by a (66–151)-J short-pulse laser beam at the Orion laser facility. The subpicosecond laser beam irradiated optically thin, KCl microdot targets buried in layers of plastic. The measured red shifts ranged from $4.8\pm 1.1$ eV for unshocked to $5.9\pm 1.2$ eV for shocked targets. These values are significantly smaller than recent predictions from a self-consistent-field ion-sphere model.

We investigate electron-impact single ionization of He-like ions of charge state $q=0,\cdots ,6$ in the initial ground ($1{}^{1}S$) and metastable ($2{}^{3}S$) states. Good agreement between theory and experiment is established for the total cross sections, and then the scaling behavior with $q$ is considered as a function of the ratio $u=E_i/E_I\le 10$ of the incident electron energy $E_i$ and the ionization threshold $E_I$. While the expected $E_I^2$ scaling of the cross sections is confirmed, we also find that at each scaled energy $u$ the spin asymmetry (for the $2{}^{3}S$ state) converges rapidly to a nonzero constant with increasing $q$. This indicates that, despite $E_I$ increasing with $q^2$, exchange effects remain undiminished on the broad scaled-energy range considered. We suggest that this physical behavior is more universal than just for the He-like ions.

We measure the photoelectron momentum distributions of Ar atoms in cross-linearly-polarized two-color (800 nm+400 nm) laser field with an angle of ${45}^{\circ }$. The photoelectron momentum distributions are controlled by tuning the phase of the synthesized two-color fields. With semiclassical numerical simulation, we have analyzed the subcycle dynamics of the tunneling electron wave packets and have studied the Coulomb effect on the evolution of the tunneling electron wave packets. Our investigation indicates that the Coulomb effects are strongly dependent on the trace of the electric field after the tunneling. The Coulomb focusing effect and the Coulomb defocusing effects can be controlled on the subcycle timescale at this interaction geometry. This cross-linearly-polarized field could be widely used in strong-field physics, such as high-order harmonic generation.

We investigate the sequential double-ionization dynamics for the dissociative channel ${\mathrm{C}}^{+}+{\mathrm{O}}^{+}$ of CO molecules in strong circularly polarized laser fields using four-particle coincidence measurements. By combining the fragmentation-pathway-resolved ionic angular distributions with the molecular frame photoelectron angular distributions distinguished for each ionization step, the significant effects of multiorbital ionization and laser-driven excitation are revealed. For the main distribution of ionic fragments in the polarization plane, the participation of the highest-occupied molecular orbitals (HOMO, HOMO-1, and HOMO-2) and the important contribution of postionization excitation are identified for various fragmentation pathways. Comparisons among different intensities further indicate the dependence of the multiorbital ionization on laser intensities. For the substantial emissions of fragments out of the polarization plane, however, the ionization from HOMO-1 (and subsequent excitation) always plays a crucial role. This work demonstrates the feasibility of disentangling the complex dynamics in molecular dissociative double ionization with the angular streaking method.

Complex circuits of cold atoms can be exploited to devise new protocols for the diagnostics of cold-atom systems. Specifically, we study the quench dynamics of a condensate confined in a ring-shaped potential coupled with a rectilinear guide of finite size. We find that the dynamics of the atoms inside the guide is distinctive of the states with different winding numbers in the ring condensate. We also observe that the depletion of the density, localized around the tunneling region of the ring condensate, can decay in a pair of excitations experiencing a Sagnac effect. In our approach, the current states of the condensate in the ring can be read out by inspection of the rectilinear guide only, leaving the ring condensate minimally affected by the measurement. We believe that our results set the basis for definition of new quantum rotation sensors. At the same time, our scheme can be employed to explore fundamental questions involving the dynamics of bosonic condensates.

A dynamical quantum phase transition can be characterized by a nonanalytic change in the quench dynamics when a parameter in the governing Hamiltonian is varied. Such a transition typically only shows up in long-time dynamics for extensive systems with short-range couplings. We analyze a model Hamiltonian of spin-1 particles with effectively infinite-range couplings and demonstrate that for this system the nonanalytic transition occurs for local observables in short-time durations even when the system is of a large size. We experimentally realize this model Hamiltonian and observe the dynamical quantum phase transition in an antiferromagnetic spinor Bose-Einstein condensate of around ${10}^5$ sodium atoms. Our observations agree well with the theoretical prediction. We also analyze the scaling exponent near the dynamical phase transition and discuss its relation with the excited-state spectrum of the system.

The mechanical response of transparent materials to optical forces is a topic that concerns a wide range of fields, from the manipulation of biological material by optical tweezers to the design of nano-optomechanical systems. However, the fundamental aspects of such forces have always been surrounded by controversies, and several different formulations have been proposed. In this paper, we propose a general stress tensor formalism to put all optical forces in a consistent presentation that allows us to study how different predictions emerge, and use the specific case of light propagating as a superposition of guided modes in lossless dielectric waveguides as a physical example. We use this formalism to calculate optical forces for straight and curved waveguide sections and all possible excitation configurations for a given set of coupled eigenmodes, and then compare the results for each of the known proposed optical-force laws in a framework that permits distinguishing where there will be differences between the force laws proposed. The general formalism also allows us to show that proper use of the divergence theorem is crucial to account for all force terms, many of which vanish if the procedure most commonly used is applied for situations other than eigenmodes in straight waveguides in vacuum. Finally, it is known that discrepancies in the predicted forces arise from the incompleteness of each stress tensor with respect to the total-energy-momentum tensor of the system. A better understanding of how different stress tensors predict very different forces for certain waveguide geometries should open a pathway to identifying how to properly assemble the full tensor, as well as for experimental tests to confirm the predictions.

Using a variational approach, we obtain the self-focusing critical power for a single and for any number of interacting Laguerre-Gauss beams propagating in a Kerr nonlinear optical medium. As is known, the critical power for freely propagating higher-order modes is always greater than that of the fundamental Gaussian mode. Here we generalize that result for an arbitrary incoherent superposition of Laguerre-Gauss beams, adding interactions between them. This leads to a vast and rich spectrum of self-focusing phenomena, which is absent in the single-beam case. Specifically, we find that interactions between different modes may increase or decrease the required critical power relative to the sum of individual powers. In particular, high-orbital angular momentum modes can be focused with less power in the presence of low-orbital angular momentum beams than when propagating alone. The decrease in required critical power can be made arbitrarily large by choosing the appropriate combinations of modes. Additionally, in the presence of interactions, an equilibrium configuration of stationary spot size for all modes in a superposition may not even exist, a fundamental difference from the single-beam case in which a critical power for self-focusing always exists.

Understanding the spin relaxation in superconducting quantum circuit and solid-state spin hybrid systems is of great importance especially for quantum storage purposes. We have studied the longitudinal relaxation for electron spins of substitutional nitrogen (P1) centers in a hybrid quantum device containing a diamond and a superconducting coplanar waveguide resonator. From a series of pump-probe experiments we conclude that the dominated spin relaxation mechanism is a cross-relaxation process induced by a four-spin interaction (four-spin cross relaxation) among different hyperfine split spin transitions. Some features of the four-spin process are discussed based on a set of rate equations. This work provides interesting perspectives in understanding the coherence properties of the hyperfine split spin ensembles in a hybrid quantum system.

Quantum fidelity is a measure to quantify the closeness between two quantum states. In an operational sense, it is defined as the minimal overlap between the probability distributions of measurement outcomes and the minimum is taken over all possible positive-operator valued measures (POVMs). Quantum fidelity has been investigated in various scientific fields, but the identification of associated optimal measurements has often been overlooked despite its great importance both for fundamental interest and practical purposes. We find here the optimal POVMs for quantum fidelity between multimode Gaussian states in a closed analytical form. Our general finding is applied for selected single-mode Gaussian states of particular interest and we identify three types of optimal measurements: an excitation-number-resolving detection, a projection onto the eigenbasis of operator $\widehat{x}\widehat{p}+\widehat{p}\widehat{x}$, and a quadrature variable detection, each of which corresponds to distinct types of single-mode Gaussian states. We also show the equivalence between optimal measurements for quantum fidelity and those for quantum parameter estimation when two arbitrary states are infinitesimally close. It is applied for simplifying the derivations of quantum Fisher information and the associated optimal measurements, exemplified by displacement, phase, squeezing, and loss parameter estimation using Gaussian states.

The braiding of two non-Abelian Majorana modes is important for realizing topological quantum computation. It can be achieved through tuning the coupling between the two Majorana modes to be exchanged and two ancillary Majorana modes. However, this coupling also makes the braiding subject to environment-induced decoherence. Here, we study the effects of decoherence on the diabatic errors in the braiding process for a set of time-dependent Hamiltonians with finite smoothness. To this end, we employ the master equation to calculate the diabatic excitation population for three kinds of decoherence processes. (1) Only pure dehasing: the scaling of the excitation population changed from $T^{-2k-2}$ to $T^{-1}$ ($k$ is the number of the Hamiltonian's time derivatives vanishing at the initial and final times) as the braiding duration $T$ exceeds a certain value. (2) Only relaxation: the scaling transforms from $T^{-2k-2}$ to $T^{-2}$ for $k=0$ and to $T^{-a}$ ($a>3$) for $k>0$. (3) Pure dephasing and relaxation: the original scaling switches to $T^{-1}$ first and then evolves to $T^{-2}$ in the adiabatic limit. Interestingly, the third scaling-varying style holds even when the expectation of pure dephasing rate is much smaller than that of the relaxation rate, which is attributed to the vanishing relaxation at the turning points of the braiding.

An experiment evaluating continuous-variable quantum key distribution (CV-QKD) in an urban environment free-space channel has been accomplished using a single homodyne detector. This is based on Gaussian modulation with coherent states in the polarization degree of freedom. We achieved a QKD distance at 460 m at a repetition rate of 10 kHz. The secure key rate is 0.152 kbps at the typical reconciliation efficiency of 0.95. The experimental setup of this scheme is simplified, and the barrier for implementation has been remarkably reduced compared to that for traditional symmetric modulation protocols, for example, the GG02 protocol proposed in F. Grosshans and P. Grangier [Phys. Rev. Lett. 88, 057902 (2002)]. The influence of the security key rate by asymmetric modulation is small for a relatively low channel loss condition in a free-space environment. This scheme is expected to have significance for future practical applications.