It is shown that a convex combination of two non-Markovian evolutions may lead to a Markovian semigroup. This shows that the convex combination of quantum evolutions displaying nontrivial memory effects may result in a perfectly memoryless evolution.

We provide a characterization of memory effects in non-Markovian system-bath interactions from a quantum information perspective. More specifically, we establish sufficient conditions for which generalized measures of multipartite quantum, classical, and total correlations can be used to quantify the degree of non-Markovianity of a local quantum decohering process. We illustrate our results by considering the dynamical behavior of the trace-distance correlations in multiqubit systems under local dephasing and generalized amplitude damping.

The future of quantum repeater networking will require interoperability between various error-correcting codes. A few specific code conversions and even a generalized method are known, however, no detailed analysis of these techniques in the context of quantum networking has been performed. In this paper we analyze a generalized procedure to create Bell pairs encoded heterogeneously between two separate codes used often in error-corrected quantum repeater network designs. We begin with a physical Bell pair and then encode each qubit in a different error-correcting code, using entanglement purification to increase the fidelity. We investigate three separate protocols for preparing the purified encoded Bell pair. We calculate the error probability of those schemes between the Steane [[7,1,3]] code, a distance-3 surface code, and single physical qubits by Monte Carlo simulation under a standard Pauli error model and estimate the resource efficiency of the procedures. A local gate error rate of ${10}^{-3}$ allows us to create high-fidelity logical Bell pairs between any of our chosen codes. We find that a postselected model, where any detected parity flips in code stabilizers result in a restart of the protocol, performs the best.

A robust control over quantum dynamics is of paramount importance for quantum technologies. Many of the existing control techniques are based on smooth Hamiltonian modulations involving repeated calculations of basic unitaries resulting in time complexities scaling rapidly with the length of the control sequence. Here we show that bang-bang controls need one-time calculation of basic unitaries and hence scale much more efficiently. By employing a global optimization routine such as the genetic algorithm, it is possible to synthesize not only highly intricate unitaries, but also certain nonunitary operations. We demonstrate the unitary control through the implementation of the optimal fixed-point quantum search algorithm in a three-qubit nuclear magnetic resonance (NMR) system. Moreover, by combining the bang-bang pulses with the crusher gradients, we also demonstrate nonunitary transformations of thermal equilibrium states into effective pure states in three- as well as five-qubit NMR systems.

A permutation-invariant code on $m$ qubits is a subspace of the symmetric subspace of the $m$ qubits. We derive permutation-invariant codes that can encode an increasing amount of quantum information while suppressing leading-order spontaneous decay errors. To prove the result, we use elementary number theory with prior theory on permutation-invariant codes and quantum error correction.

One of the great challenges of electronic structure theory is the quest for the exact functional of density functional theory. Its existence is proven, but it is a complicated multivariable functional that is almost impossible to conceptualize. In this paper the asymmetric two-site Hubbard model is studied, which has a two-dimensional universe of density matrices. The exact functional becomes a simple function of two variables whose three-dimensional energy landscape can be visualized and explored. A walk on this unique landscape, tilted to an angle defined by the one-electron Hamiltonian, gives a valley whose minimum is the exact total energy. This is contrasted with the landscape of some approximate functionals, explaining their failure for electron transfer in the strongly correlated limit. We show concrete examples of pure-state density matrices that are not $v$ representable due to the underlying nonconvex nature of the energy landscape. The exact functional is calculated for all numbers of electrons, including fractional, allowing the derivative discontinuity to be visualized and understood. The fundamental gap for all possible systems is obtained solely from the derivatives of the exact functional.

A dispersionally corrected Gaussian profile describing Doppler-broadened spectral line shapes is presented. Proposed corrections include the frequency dependence of the Doppler shifting caused by dispersion as well as by light frequency variation over the whole spectral line shape. It is shown that the frequency dependence of the Doppler shifting can have a non-negligible influence on the line-shape model and can affect the line shape even at the relative level of ${10}^{-5}$. Moreover, this effect also influences the determination of the line position at the level of kilohertz. Finally, the impact of the presented results on the Doppler width thermometry and precise molecular spectroscopy for fundamental studies is emphasized.

The recent progress in designing optical lattice clocks with fractional uncertainties below ${10}^{-17}$ requires unprecedented precision in estimating the role of higher-order effects of atom-lattice interactions. In this paper, we present results of systematic theoretical evaluations of the multipole, nonlinear, and anharmonic effects on the optical-lattice-based clocks of alkaline-earth-like atoms. Modifications of the model-potential approach are introduced to minimize discrepancies of theoretical evaluations from the most reliable experimental data. Dipole polarizabilities, hyperpolarizabilities, and multipolar polarizabilities for neutral Ca, Sr, Yb, Zn, Cd, and Hg atoms are calculated in the modified approach.

We investigate the impact of a rotating-wall potential on perpendicular laser cooling in a Penning ion trap. By including energy exchange with the rotating wall, we extend previous Doppler laser-cooling theory and show that low perpendicular temperatures are more readily achieved with a rotating wall than without. Detailed numerical studies determine optimal operating parameters for producing low-temperature, stable two-dimensional crystals, important for quantum information processing experiments employing Penning traps.

We examine analytically and numerically the spectral properties of three quasi-one-dimensional lattices, namely, kagome, Lieb, and stub lattices, which are characterized for having flatbands in their spectrum. It is observed that the degenerate eigenmodes modes of these flatbands form a Starklike ladder where each mode is shifted by one lattice site. Their combination can give rise to compact modes that do not diffract due to a geometrical phase cancellation. For all three cases we computed the stability of the fundamental band mode against perturbation of their amplitude and phase, the effect of possible anisotropy of the couplings, and the presence of small random perturbations of the coupling. For the Lieb and stub ribbon, the compact mode turns out to be quite robust and the flatband survives, while for the kagome ribbon, the compact mode is destroyed and the flatband is lost. When adding nonlinear effects, the compact mode turns out to be also a nonlinear eigenvector, with a power curve that is proportional to the eigenvalue and exists for any eigenvalue, in marked contrast to the usual case of discrete solitons, which can exist only outside the linear bands. These properties look promising for a future design of a robust system for long-distance propagation of information.

The tuning of odd and even high-order harmonics of ultrashort pulses along the strong resonance of laser-produced indium plasma using an optical parametric amplifier of white-light continuum radiation (1250–1400 nm) allowed observation of different harmonics enhanced in the vicinity of the $4d^{10}5s^2{}^1{S}_0\to 4d^{9}5s^{2}5p{}^1{P}_1$ transition of In ii ions. We demonstrate various peculiarities and discuss the theoretical model of the phenomenon of tunable harmonics enhancement in the region of 62 nm using indium plasma. With the theoretical analysis we can reproduce the experimental observations and characterize the dynamics of the resonant harmonic emissions.

Applying a multiphoton-subtraction technique to the two-color macroscopic squeezed vacuum state of light generated via high-gain parametric down-conversion we conditionally prepare a different state of light: bright multimode low-noise twin beams. A lower noise in the sum of the photon numbers opens a possibility to encode information into this variable while keeping the nonclassical character of the state. The obtained results demonstrate up to eightfold suppression of noise in each beam while preserving and even moderately improving the nonclassical photon-number correlations between the beams. The prepared low-noise macroscopic state, containing up to 2000 photons per mode, is not among the Gaussian states achievable through nonlinear optical processes. Apart from that, we suggest a method for measuring quantum efficiency, which is based on the Fano factor measurement. The proposed technique substantially improves the usefulness of twin beams for quantum communication and metrology.

We propose a feasible scheme to implement a universal set of quantum gates based on geometric phases and superadiabatic quantum control. Consolidating the advantages of both strategies, the proposed quantum gates are robust and fast. The diamond nitrogen-vacancy center system is adopted as a typical example to illustrate the scheme. We show that these gates can be realized in a simple two-level configuration by appropriately controlling the amplitude, phase, and frequency of just one microwave field. The gate's robust and fast features are confirmed by comparing the fidelity of the proposed superadiabatic geometric phase (controlled-phase) gate with those of two other kinds of phase (controlled-phase) gates.

The eigenvalues of a non-Hermitian Hamilton operator are complex and provide not only the energies but also the lifetimes of the states of the system. They show a nonanalytical behavior at singular (exceptional) points (EPs). The eigenfunctions are biorthogonal, in contrast to the orthogonal eigenfunctions of a Hermitian operator. A quantitative measure for the ratio between biorthogonality and orthogonality is the phase rigidity of the wave functions. At and near an EP, the phase rigidity takes its minimum value. The lifetimes of two nearby eigenstates of a quantum system bifurcate under the influence of an EP. When the parameters are tuned to the point of maximum width bifurcation, the phase rigidity suddenly increases up to its maximum value. This means that the eigenfunctions become almost orthogonal at this point. This unexpected result is very robust as shown by numerical results for different classes of systems. Physically, it causes an irreversible stabilization of the system by creating local structures that can be described well by a Hermitian Hamilton operator. Interesting nontrivial features of open quantum systems appear in the parameter range in which a clustering of EPs causes a dynamical phase transition.

We present a self-consistent mean-field model based on a two-component Pauli-like equation that incorporates quantum and relativistic effects (up to second order in $1/c$) for both external and internal electromagnetic fields. By taking the semirelativistic limit of the Dirac-Maxwell equations in the presence of an external electromagnetic field we obtain an analytical expression of a coherent light-induced mean-field Hamiltonian. The latter exhibits several mechanisms that involve the internal mean fields created by all the electrons and the external electromagnetic field (laser). The role played by the light-induced current density and the light-induced second-order charge density acting as sources in Maxwell's equations are clarified. In particular, we identify clearly four different mechanisms involving the spins that may play an important role in coherent ultrafast spin dynamics.

One of the central features of quantum theory is that there are pairs of quantum observables that cannot be measured simultaneously. This incompatibility of quantum observables is a necessary ingredient in several quantum phenomena, such as measurement uncertainty relations, violation of Bell inequalities, and steering. Two quantum observables that admit a simultaneous measurement are, in this respect, classical. A finer classification of classicality can be made by formulating four symmetric relations on the set of observables that are stronger than compatibility; they are broadcastability, one-side broadcastability, mutual nondisturbance, and nondisturbance. It is proven that the five relations form a hierarchy and their differences in terms of the required devices needed in a simultaneous measurement are explained. All four relations that are stronger than compatibility are completely characterized in the case of qubit observables.

We study families of positive and completely positive maps acting on a bipartite system ${\mathbb{C}}^M\otimes {\mathbb{C}}^N$ (with $M\le N$). The maps have a property that, when applied to any state (of a given entanglement class), result in a separable state or, more generally, a state of another certain entanglement class (e.g., Schmidt number $\le k$). This allows us to derive useful families of sufficient separability criteria. Explicit examples of such criteria have been constructed for arbitrary $M,N$, with a special emphasis on $M=2$. Our results can be viewed as generalizations of the known facts that in the sufficiently close vicinity of the completely depolarized state (the normalized identity matrix), all states are separable (belong to “weakly” entangled classes). Alternatively, some of our results can be viewed as an entanglement classification for a certain family of states, corresponding to mixtures of the completely polarized state with pure states, partial transposes, and/or local transformations thereof.

Inspired by the experimental measurement of the Rényi entanglement entropy in a lattice of ultracold atoms by Islam et al. [Nature (London) 528, 77 (2015)], we propose a method to entangle two spatially separated qubits using the quantum many-body state as a resource. Through local operations accessible in an experiment, entanglement is transferred to a qubit register from atoms at the ends of a one-dimensional chain. We compute the operational entanglement, which bounds the entanglement physically transferable from the many-body resource to the register, and discuss a protocol for its experimental measurement. Finally, we explore measures for the amount of entanglement available in the register after transfer, suitable for use in quantum information applications.

Density-functional theory (DFT) is notorious for the absence of gradient corrections to the two-dimensional (2D) Thomas-Fermi kinetic-energy functional; it is widely accepted that the 2D analog of the 3D von Weizsäcker correction vanishes, together with all higher-order corrections. Contrary to this long-held belief, we show that the leading correction to the kinetic energy does not vanish, is unambiguous, and contributes perturbatively to the total energy. This insight emerges naturally in a simple extension of standard DFT, which has the effective potential energy as a functional variable on equal footing with the single-particle density.

The process of electron-loss to the continuum (ELC) has been studied for the collision systems ${\mathrm{U}}^{28+}+{\mathrm{H}}_2$ at a collision energy of 50 MeV/u, ${\mathrm{U}}^{28+}+{\mathrm{N}}_2$ at 30 MeV/u, and ${\mathrm{U}}^{28+}+\mathrm{Xe}$ at 50 MeV/u. The energy distributions of cusp electrons emitted at an angle of $0^{\circ }$ with respect to the projectile beam were measured using a magnetic forward-angle electron spectrometer. For these collision systems far from equilibrium charge state, a significantly asymmetric cusp shape is observed. The experimental results are compared to calculations based on first-order perturbation theory, which predict an almost symmetric cusp shape. Some possible reasons for this discrepancy are discussed.