It is revealed that ensembles consisting of multipartite quantum states can exhibit different kinds of nonlocalities. An operational measure is introduced to quantify nonlocalities in ensembles consisting of bipartite quantum states. Various upper and lower bounds for the measure are estimated and the exact values for ensembles consisting of mutually orthogonal maximally entangled bipartite states are evaluated.

The Pauli potential $V_P$ in density functional theory is known to be the difference between the functional derivative of the single-particle kinetic energy $T_s[n]$ with respect to the electron density $n$ and its von Weizsäcker counterpart. For the leading Coulombic term in the $1/Z$ expansion for spherical atomic ions, $V_P[n]$ is written in terms of the kinetic energy density plus $n(r)$ and its low-order derivatives. For comparison, the example of an arbitrary number of closed shells with purely harmonic confinement is also treated.

We propose an efficient scheme for the generation of two-mode squeezed states for two separated atomic ensembles trapped in distant cavities. The scheme is based on selective couplings between the collective atomic modes and two linearly transformed common field modes mediated by an optical fiber or a third cavity. The quanta of the transformed atomic modes are exhausted due to the linear coupling with the transformed field modes, bringing the original atomic modes into the two-mode squeezed states. The experimental implementation of the scheme would be an important step toward quantum communication and networking with continuous variables.

We study the error threshold of topological color codes on Union Jack lattices that allow for the full implementation of the whole Clifford group of quantum gates. After mapping the error-correction process onto a statistical mechanical random three-body Ising model on a Union Jack lattice, we compute its phase diagram in the temperature–disorder plane using Monte Carlo simulations. Surprisingly, topological color codes on Union Jack lattices have a similar error stability to color codes on triangular lattices, as well as to the Kitaev toric code. The enhanced computational capabilities of the topological color codes on Union Jack lattices with respect to triangular lattices and the toric code combined with the inherent robustness of this implementation show good prospects for future stable quantum computer implementations.

There are well-known protocols for performing controlled NOT (CNOT) quantum logic with qubits coupled by particular high-symmetry (Ising or Heisenberg) interactions. However, many architectures being considered for quantum computation involve qubits or qubits and resonators coupled by more complicated and less symmetric interactions. Here we consider a widely applicable model of weakly but otherwise arbitrarily coupled two-level systems, and use quantum gate design techniques to derive a simple and intuitive CNOT construction. Useful variations and extensions of the solution are given for common special cases.

We report an experimental preparation of the so-called Knill-Laflamme-Milburn states (KLM states) that have been known to have interesting properties related to quantum information processing. Our experiment has demonstrated successful preparation of entangled two-photon four-mode KLM states using spontaneous parametric down-conversion as a source of entangled photon pairs, linear optical components, and avalanche photodiodes for single-photon detection. We have verified the successful generation of KLM states by complete quantum state tomography.

Differential cross sections for elastic electron scattering in krypton have been measured at the energies of $5,7.5$, and $10$ eV over the scattering angle range from ${30}^{°}$ to ${180}^{°}$. The measurements for backward scattering employed the magnetic angle-changing technique. These differential cross sections have been integrated to yield the elastic integral and momentum transfer cross sections at the above energies. These new results are compared with the most recent measurements and calculations of the respective cross sections in krypton. The dependence of the differential cross sections on atomic polarizability of the heavier rare gas atoms argon, krypton, and xenon has also been investigated over the electron energy range $5–30$ eV and for forward, backward, and intermediate scattering angles.

A recent paper reported elliptically polarized high-order harmonics from aligned ${\mathrm{N}}_2$ using a linearly polarized driving field [X. Zhou et al., Phys. Rev. Lett. 102, 073902 (2009)]. This observation cannot be explained in the standard treatment of the Lewenstein model and has been ascribed to many-electron effects or the influence of the Coulomb force on the continuum electron. We show that nonvanishing ellipticity naturally appears within the Lewenstein model when using a multicenter stationary-phase method for treating the dynamics of the continuum electron. The reason for this is the appearance of additional contributions, which can be interpreted as quantum orbits in which the active electron is ionized at one atomic center within the molecule and recombines at another. The associated exchange harmonics are responsible for the nonvanishing ellipticity and result from a correlation between the ionization site and the recombination site in high-order harmonic generation.

A quantum control scheme for multilevel systems utilizing effective decomposition is proposed. In this method, a subsystem chosen for control target is effectively isolated by irradiating intense continuous-wave laser fields onto the complimentary space. By choosing the control target space consisting of small number of eigenstates, effective dressed states for the isolated space are analytically given, which makes it possible to express the performance index defined in the target space as an explicit function of laser parameters. Then, designing the control field can be treated as a static parameter optimization. The present scheme makes it possible not only to optimize the laser parameters but also to investigate the parameter search space, which clarifies the physics of the control process.

We study the stability of multipole-mode solitons in one-dimensional thermal nonlinear media. We show how the sample geometry impacts the stability of multipole-mode solitons and reveals that the tripole and quadrupole can be made stable in their whole domain of existence, provided that the sample width exceeds a critical value. In spite of such geometry-dependent soliton stability, we find that the maximal number of peaks in stable multipole-mode solitons in thermal media is the same as that in nonlinear materials with finite-range nonlocality.

We propose an algorithm to simulate interacting fermions on a two-dimensional lattice. The approach is an extension of the entanglement renormalization technique [Phys. Rev. Lett. 99, 220405 (2007)] and the related multiscale entanglement renormalization ansatz. Benchmark calculations for free and interacting fermions on lattices ranging from $6\times 6$ to $162\times 162$ sites with periodic boundary conditions confirm the validity of this proposal.

Relative and center-of-mass coordinates are used to generalize mutually unbiased bases (MUB) and define mutually unbiased collective bases (MUCB). Maximally entangled states are given as product states in the collective variables. These states are analyzed in terms of the Wigner representative function of the states and shown to display a discontinuous attribute of the entanglement. Finite Hilbert space dimensionality collective coordinates are introduced and provide a framework for the analysis.

This article deals with the quantum optimal discrimination among mixed quantum states enjoying geometrical uniform symmetry with respect to a reference density operator ${\rho }_0$. It is well known that the minimal error probability is given by the positive operator-valued measure obtained as a solution of a convex optimization problem, namely a set of operators satisfying geometrical symmetry, with respect to a reference operator ${\Pi }_0$ and maximizing $\mathrm{Tr}({\rho }_0{\Pi }_0)$. In this article, by resolving the dual problem, we show that the same result is obtained by minimizing the trace of a semidefinite positive operator $X$ commuting with the symmetry operator and such that $X⩾{\rho }_0$. The new formulation gives a deeper insight into the optimization problem and allows to obtain closed-form analytical solutions, as shown by a simple but not trivial explanatory example. In addition to the theoretical interest, the result leads to semidefinite programming solutions of reduced complexity, allowing to extend the numerical performance evaluation to quantum communication systems modeled in Hilbert spaces of large dimension.

We study the relationship between entanglement and parametric resonance in a system of two coupled time-dependent oscillators. As a measure of bipartite entanglement, we calculate the linear entropy for the reduced density operator, from which we study the entanglement dynamics. In particular, we find that the bipartite entanglement increases in time up to a maximal mixing scenario, when the set of auxiliary dynamical parameters are under parametric resonance. Moreover, we obtain a closed relationship between the correlations in the ground state, the localization of the Wigner function in phase space, and the localization of the wave function of the total system.

Transformations involving only local operations assisted with classical communication are investigated for multipartite entangled pure states having tensor rank 2. All necessary and sufficient conditions for the possibility of deterministically converting truly multipartite, rank-2 states into each other are given. Furthermore, a chain of local operations that successfully achieves the transformation has been identified for all allowed transformations. The identified chains have two nice features: (1) each party needs to carry out at most one local operation and (2) all of these local operations are also deterministic transformations by themselves. Finally, it is found that there are disjoint classes of states, all of which can be identified by a single real parameter, which remain invariant under deterministic transformations.

Quantum key distribution (QKD) is a secure key generation method between two distant parties by wisely exploiting properties of quantum mechanics. In QKD, experimental measurement outcomes on quantum states are transformed by the two parties to a secret key. This transformation is composed of many logical steps (as guided by security proofs), which together will ultimately determine the length of the final secret key and its security. We detail the procedure for performing such classical postprocessing taking into account practical concerns (including the finite-size effect and authentication and encryption for classical communications). This procedure is directly applicable to realistic QKD experiments and thus serves as a recipe that specifies what postprocessing operations are needed and what the security level is for certain lengths of the keys. Our result is applicable to the BB84 protocol with a single or entangled photon source.

We study ionization and fragmentation of CO in electron loss and capture collisions of ${\mathrm{B}}^{2+}$, ${\mathrm{O}}^{2+}$, and ${\mathrm{Si}}^{2+}$ ions at an energy of $71.4$ keV$/$u ($v=1.69$ a.u.). Coincidence measurements of fragment ions from CO and charge-selected ions were performed by means of a momentum three-dimensional imaging technique. Production cross sections of CO${}^{r+}$ and branching ratios into various fragmentation channels were obtained for $r=1–4$. We also measured kinetic energy release (KER) in individual fragmentation channels. The KER spectra for $r⩽2$ are found to be different for electron loss and capture collisions, while the difference becomes small for $r⩾3$. As a measure of the degree of molecular fragmentation, the magnitude of the binding energy of the relevant electronic states seems the important parameter both in loss and capture collisions.

Results of spin-resolved angle-differential Stokes parameters from electron-photon coincidence studies of electron-impact excitation of the $6s6p\hspace{0.5em}{}^3{P}_1$ state of mercury, resulting in $254$ nm radiation, are presented. Due to the intermediate-coupling nature of the excited state, the wave function of this state has a small singlet part. With increasing scattering energy, the influence of exchange scattering decreases, so that direct scattering via the singlet part can become relevant. Recent angle-integrated Stokes-parameter measurements indicated that exchange is still important for the $254$ nm line ($6s6p\hspace{0.5em}{}^3{P}_1\to 6s^2\hspace{0.5em}{}^1{S}_0$) up to at least $50$ eV incident energy [Jüttemann et al., Phys. Rev. A 79, 042712 (2009)]. At energies above $15$ eV, however, cascade effects complicate a detailed comparison of these angle-integrated results with theoretical calculations. The angle-differential Stokes parameters presented here are unaffected by cascade effects due to the coincidence technique and thus allow for an analysis of the discrepancies observed by Jüttemann et al. and also by Srivastava et al. [Phys. Rev. A 80, 022718 (2009)]. Comparison of the experimental data with theoretical predictions reveals that the description of the initial target state and the excited state in intermediate coupling have a significant influence on the overall agreement.

Squeezed states of light constitute an important nonclassical resource in the field of high-precision measurements, for example, gravitational wave detection, as well as in the field of quantum information, for example, for teleportation, quantum cryptography, and distribution of entanglement in quantum computation networks. Strong squeezing in combination with high purity, high bandwidth, and high spatial mode quality is desirable in order to achieve significantly improved performances contrasting any classical protocols. Here we report on the observation of 11.5 dB of squeezing, together with relatively high state purity corresponding to a vacuum contribution of less than 5%, and a squeezing bandwidth of about 170 MHz. The analysis of our squeezed states reveals a significant production of higher-order pairs of quantum-correlated photons and the existence of strong photon-number oscillations.

The uncertainty principle places a fundamental limit on the accuracy with which we can measure conjugate quantities. However, the fluctuations of these variables can be assessed in terms of different estimators. We propose an angular performance that allows for tighter uncertainty relations for angle and angular momentum. The differences with previous bounds can be significant for particular states and indeed may be amenable to experimental measurement with the present technology.