The scheme of entanglement-assisted quantum error-correcting (EAQEC) codes assumes that the ebits of the receiver are error free. In practical situations, errors on these ebits are unavoidable, which diminishes the error-correcting ability of these codes. We consider two different versions of this problem. We first show that any (nondegenerate) standard stabilizer code can be transformed into an EAQEC code that can correct errors on the qubits of both sender and receiver. These EAQEC codes are equivalent to standard stabilizer codes, and hence the decoding techniques of standard stabilizer codes can be applied. Several EAQEC codes of this type are found to be optimal. In a second scheme, the receiver uses a standard stabilizer code to protect the ebits, which we call a “combination code.” The performances of different quantum codes are compared in terms of the channel fidelity over the depolarizing channel. We give a formula for the channel fidelity over the depolarizing channel (or any Pauli error channel), and show that it can be efficiently approximated by a Monte Carlo calculation. Finally, we discuss the tradeoff between performing extra entanglement distillation and applying an EAQEC code with imperfect ebits.

In this paper, we present a general upper bound on the success probability for unambiguous discrimination among arbitrary $m$ mixed quantum states with given a priori probability. We further analyze how this upper bound can be achievable by presenting a sufficient condition related to it, and we compare this upper bound with three other upper bounds. Moreover, for the issue of the unambiguous identification of $m$ unknown multicopy qudit pure states, we also get a bound.

We propose a measure of the nonclassicality of quantum gates which is particularly suitable for probabilistic devices. This measure enables to compare deterministic devices which prepare entangled states with a low amount of entanglement with probabilistic devices which generate highly entangled states but which fail sometimes. We provide examples demonstrating the advantages of this measure over the so-far employed entangling power. The experimentally determined entangling efficiency of a tunable linear-optical controlled-phase gate is presented to highlight the practical aspects of this measure.

We experimentally demonstrate, using qubits encoded in photon polarization, that two parties who share a single reference direction and use locally orthogonal measurements will always violate a Bell inequality, up to experimental deficiencies. This contrasts with the standard view of Bell inequalities, in which the parties need to completely align their measurements. Furthermore, we experimentally demonstrate that as the reference direction degrades the probability of the observers randomly choosing measurements that violate a Bell inequality decreases gradually and smoothly to $39.7\%\pm 0.1\%$ in the limiting case that the observers do not share a reference direction. This result promises simplified distribution of entanglement between separated parties, with applications in fundamental investigations of quantum physics and tasks such as quantum communication.

Measurements of neutral atom fractions for Li${}^{+}$ scattered by Cu(111) and Cu(001) surfaces as a function of the exit ion energy and exit angle are reported. Large neutralization rates (between 20$\%$ and 60$\%$) are found in all cases. A first-principles quantum-mechanical based theoretical formalism is applied to describe the time-dependent scattering process, where neutralization to the Li ground state is considered as the unique relevant charge transfer channel during the collision. The increase of the neutralization fraction as the exit energy decreases is well described by the model. The proximity of the projectile energy level to the solid Fermi level and the large extension of the ion-surface coupling interactions, affecting a large number of surface atoms, play a decisive role in explaining the experimental yields.

We study the cancellation of differential ac Stark shifts in the $5s$ and $5p$ states of the rubidium atom using the linearly and circularly polarized lights by calculating their dynamic polarizabilities. Matrix elements were calculated using a relativistic coupled-cluster method at the single and double excitations and at the important valence triple excitation approximation including all possible nonlinear correlation terms. Some of the important matrix elements were further optimized using the experimental results available for the lifetimes and static polarizabilities of atomic states. “Magic wavelengths” are determined from the differential Stark shifts and results for the linearly polarized light are compared with the previously available results. The possible scope of facilitating state-insensitive optical trapping schemes using the magic wavelengths for circularly polarized light is discussed. Using the optimized matrix elements, the lifetimes of the $4d$ and $6s$ states of this atom are ameliorated.

We demonstrate that the frequency-selected enhancement of high-order-harmonic generation (HHG) can be achieved by a few-cycle laser pulse interacting with a coherent superposition state, which is prepared by the ground state and two degenerate Rydberg states. The degenerate states have the same orbital radius and hence have a large overlap in the electronic density distribution. By controlling the relative phase between the two degenerate states, the constructive or destructive interference of them can markedly change the initial density distribution of the Rydberg electron, thereby we can manipulate the characteristics and the conversion efficiency of HHG. Specifically, a significant enhancement in the continuous harmonics near HHG cutoff can be obtained, hence an intense isolated pulse with a duration less than 100 attoseconds is straightforwardly generated. On the other hand, since there exists a specific dependence of the harmonic efficiency on the relative phase of the two degenerate states, one can expect that the relative phase may be probed by examining the corresponding harmonic intensity. In practice, we may apply a weak static electric field in the whole dynamic process to obtain an asymmetry electron density distribution at a large radius; hence similar HHG results can be obtained.

The center of mass of a bright soliton in a Bose-Einstein condensate may reveal Anderson localization in the presence of a weak disorder potential. We analyze the effects of interactions between two bright solitons on the Anderson localization phenomenon. Perturbation calculus shows that even very weak interactions modify localization properties of the system eigenstates. For stronger interactions (i.e., when the solitons are close to each other), the localization is totally broken. It implies that in order to experimentally observe the Anderson localization effects, a single bright soliton has to be prepared and excitation of soliton trains must be avoided.

We present a simple and efficient scheme to reduce atom-number fluctuations in optical lattices. The interaction-energy difference for atoms in different vibrational states is used to remove excess atomic occupation. The remaining vacant sites are then filled with atoms by merging adjacent wells, for which we implement a protocol that circumvents the constraints of unitarity. The preparation of large regions with precisely one atom per lattice site is discussed for both bosons and fermions. The resulting low-entropy Mott-insulating states may serve as high-fidelity register states for quantum computing and as a starting point for investigations of many-body physics.

We consider a simple experimental setup, based on a harmonic confinement, where a Bose-Einstein condensate and a thermal cloud of weakly interacting alkali-metal atoms are trapped in two different vessels connected by a narrow channel. Using the classical field approximation, we theoretically investigate the analog of the celebrated superfluid-helium fountain effect. We show that this thermomechanical effect might indeed be observed in this system. By analyzing the dynamics of the system, we are able to identify the superfluid and normal components of the flow as well as to distinguish the condensate fraction from the superfluid component. We show that the superfluid component can easily flow from the colder vessel to the hotter one while the normal component is practically blocked in the latter. In the long-time limit, the superfluid component exhibits periodic oscillations reminiscent of the ac Josephson effect obtained in superfluid weak-link experiments.

Svetlichny's inequality (SI) is a Bell-like inequality, the violation of which can be used to confirm the existence of genuine multipartite correlations. However, poor detector efficiency can possibly cause a so-called detection loophole in actual Svetlichny experiments. We derive an alternative SI to deal with this loophole. If the experimental data can violate this SI, it must result in loophole-free violation of the original SI. We show that the minimum detection efficiency needed for a loophole-free violation of the tripartite SI is about $0.97$. For the general case of $n$ particles, we give the analytic expression of the needed detection efficiency, and find that its value monotonically and rapidly approaches 1 as the number of particles increases.

We calculate all the elements of the Mueller matrix for light scattering from a two-dimensional randomly rough lossy metal surface. The calculations are carried out for arbitrary angles of incidence by the use of nonperturbative numerical solutions of the reduced Rayleigh equations. We foresee that the ability to model polarization effects in light scattering from surfaces will enable better interpretation of experimental data and allow for the design of surfaces which possess useful polarization effects.

We present a theory of coherent propagation and energy or power transfer in a low-dimension array of coupled nonlinear waveguides. It is demonstrated that in the array with nonequal cores (e.g., with the central core) stable steady-state coherent multicore propagation is possible only in the nonlinear regime, with a power-controlled phase matching. The developed theory of energy or power transfer in nonlinear discrete systems is rather generic and has a range of potential applications including both high-power fiber lasers and ultrahigh-capacity optical communication systems.

The dynamics of driven binary oscillators in the $\mathcal{PT}$-symmetric harmonic potential is investigated and the corresponding analytical solutions of the time-dependent wave function are obtained. Our numerical results exhibit that there is the population oscillation, which is different from the case of normal dissipation or gain systems. After studying the motion of driven harmonic oscillators which are coupled via the $E⨂e$ Jahn-Teller effect in the Hermitian potential, we find that the dynamics behavior of these two systems is similar under certain conditions. As we know, the oscillation behavior is induced by the exchange interaction in the oscillator system with Jahn-Teller coupling. Our study shows that the binary quantum systems with $\mathcal{PT}$-symmetric Hamiltonians may be used to approximately describe the dynamics of coupling quantum systems and the quantum transport process in few-particle or other systems.

We study an optimum measurement for quantum state discrimination, which maximizes the probability of correct results when the probability of inconclusive results is fixed at a given value. The measurement describes minimum-error discrimination if this value is zero, while under certain conditions it corresponds to optimized maximum-confidence discrimination, or to optimum unambiguous discrimination, respectively, when the fixed value reaches a definite minimum. Using operator conditions that determine the optimum measurement, we derive analytical solutions for the discrimination of two mixed qubit states, including the case of two pure states occurring with arbitrary prior probabilities, and for the discrimination of $N$ symmetric states, both pure and mixed. We also consider a case where the given density operators resolve the identity operator, and we specify the optimality conditions for partially symmetric states. Moreover, we show that from the complete solution for arbitrary values of the fixed rate of inconclusive results one can always obtain the optimum measurement in another strategy where the error rate is fixed, and vice versa.

Teleportation witnesses are Hermitian operators which can identify useful entanglement for quantum teleportation. Here we provide a systematic method to construct teleportation witnesses from entanglement witnesses corresponding to general qudit systems. The witnesses so constructed are shown to be optimal for qubit and qutrit systems and therefore detect the largest set of states useful for teleportation within a given class. We demonstrate the action of the witness pertaining to different classes of states in qubits and qutrits. Decomposition of the witness in terms of spin operators facilitates experimental identification of useful resources for teleportation.

We consider the problem of discrimination between a set of quantum states with the maximum probability of correct detection for a fixed rate of inconclusive results. We show that this type of measurement can be decomposed into two steps. The first step is the discrimination of whether the measurement result is inconclusive. The second step, which is performed in the case in which a conclusive result was obtained, is minimum error discrimination of output states of the first step. Using this result, we derive a closed-form analytical expression for an optimal measurement for both a geometrically uniform pure-state set and a set of binary doubly symmetric mixed states for any probability of an inconclusive result.

We investigate full symmetrization of two-mode entangled Gaussian states by local Gaussian operations and classical communication. We propose and analyze three deterministic strategies that convert an arbitrary two-mode entangled Gaussian state to a fully symmetric entangled Gaussian state that is not only invariant with respect to the exchange of the modes but also exhibits equally strong correlations of amplitude and phase quadratures of the two modes.

We present an experimental procedure to determine the usefulness of a measurement scheme for quantum error correction (QEC). A QEC scheme typically requires the ability to prepare entangled states, carry out multiqubit measurements, and perform certain recovery operations conditioned on measurement outcomes. As a consequence, the experimental benchmark of a QEC scheme is a tall order because it requires the conjuncture of many elementary components. Our scheme opens the path to experimental benchmarks of individual components of QEC. Our numerical simulations show that certain parity measurements realized in circuit quantum electrodynamics are on the verge of being useful for QEC.

We investigate retardation effects in two-photon ionization from the ground state of low-$Z$ hydrogenic atoms for photon energies ranging from 20 eV to 25 keV, using the general formulas of nonrelativistic second-order perturbation theory, including retardation. Our numerical calculations, including all multipoles, show that, as in the $K$-shell photoeffect, the electron angular distributions are sensitive to retardation. The deviations from the dipole approximation are mainly determined by the terms linear in photon momentum. We also present results for the total generalized cross section along the hydrogen isoelectronic series (for $Z=1–5$) at scaled laser frequencies.