We develop a simple method for constructing polynomial invariants of degree 4 for even-$n$ qubits and give explicit expressions for these polynomial invariants. We demonstrate the invariance of the polynomials under stochastic local operations and classical communication and exemplify the use of the invariance in classifying entangled states. The absolute values of these polynomial invariants are entanglement monotones, thereby allowing entanglement measures to be built. Finally, we discuss the properties of these entanglement measures.

Discordant states appear in a large number of quantum phenomena and seem to be a good indicator of divergence from classicality. While there is evidence that they are essential for a quantum algorithm to have an advantage over a classical one, their precise role is unclear. We examine the role of discord in quantum algorithms using the paradigmatic framework of restricted distributed quantum gates and show that manipulating discordant states using local operations has an associated cost in terms of entanglement and communication resources. Changing discord reduces the total correlations and reversible operations on discordant states usually require nonlocal resources. Discord alone is, however, not enough to determine the need for entanglement. A more general type of similar quantities, which we call $K$ discord, is introduced as a further constraint on the kinds of operations that can be performed without entanglement resources.

Quantum key distribution (QKD) utilizes the laws of quantum mechanics to achieve information-theoretically secure key generation. This field is now approaching the stage of commercialization, but many practical QKD systems still suffer from security loopholes due to imperfect devices. In fact, practical attacks have successfully been demonstrated. Fortunately, most of them only exploit detection-side loopholes, which are now closed by the recent idea of measurement-device-independent QKD. On the other hand, little attention is paid to the source, which may still leave QKD systems insecure. In this work, we propose and demonstrate an attack that exploits a source-side loophole existing in qubit-based QKD systems using a weak coherent state source and decoy states. Specifically, by implementing a linear-optics unambiguous state discrimination measurement, we show that the security of a system without phase randomization—which is a step assumed in conventional security analyses but sometimes neglected in practice—can be compromised. We conclude that implementing phase randomization is essential to the security of decoy-state QKD systems under current security analyses.

The quantum dynamics of two weakly coupled nonlinear oscillators is analytically and numerically investigated in the context of nonlinear dissipation. The latter facilitates the creation and preservation of nonclassical steady states. Starting from a microscopic description of two oscillators individually interacting with their dissipative environments, it is found that in addition to energy relaxation, dephasing arises due to the mutual coupling. Using the negativity as an entanglement measure, it is shown that the coupling entangles the oscillators in the long-time limit. For finite temperatures, entanglement sudden death and rebirth are observed.

Using a recoil-ion momentum spectrometer (RIMS), transverse momenta ($q_{\perp }$) of recoil atomic and molecular ions emerging from collisions between 2.5-MeV/u Xe${}^{34+}$ projectiles and neutral Ne, Ar, CO, N${}_2$, and O${}_2$ gases were measured as a function of the degree of target ionization. For the molecular targets the resulting distributions of $q_{\perp }$ corresponding to different dissociation channels were separated. Measurements with all the targets were performed under virtually identical conditions so that the results could be directly compared in detail. It was found that the shapes of the $q_{\perp }$ distributions are characterized by single asymmetric peaks and that, at least in the vicinity of their maximum values, they are well described by Weibull functions. Except for the Ar target, the velocities corresponding to the maxima of the $q_{\perp }$ distributions were found to follow (within the uncertainties of the results) a universal function of the target charge-to-mass number ratio for values up to 0.33. For larger charge-to-mass number ratios the results for the molecular targets appear to remain universal, but are slightly lower than the results for the Ne target. A more elaborate scaling was required to obtain a universal function that describes the low-charge-state results for Ne and Ar targets in a similar way. For different dissociation channels of the same parent molecular ion with charge states exceeding 6+, significant differences were found between the measured $q_{\perp }$ distributions. These differences were ascribed to increases in the ionization potential and to more prominent contributions from target-to-projectile electron transfer for the more asymmetric dissociation channels. For symmetric and nearly symmetric molecular dissociation channels the fragments with combined charge number $Q$ exceeding 9 for N${}_2$ and 10 for O${}_2$ were found to be distributed with a reduced probability at angles close to 90° relative to the beam direction. The magnitude of this effect was found to depend on the number of electrons removed in addition to one half of the number of available electrons ($Q$–$Z$). On the other hand, for highly asymmetric dissociation channels the angular distributions seem to indicate that the fragments of highly charged molecular ions may be distributed with an enhanced probability at angles close to 90° relative to the beam direction. A slight dependence of the $q_{\perp }$ distribution on molecular orientation was found to be present for the symmetric and nearly symmetric dissociation channels having $Q–Z⩾0$. The magnitude of this effect also seems to be determined by the value of $Q$–$Z$.

Based on ab initio time-dependent calculations for helium, we study the joint angular distribution (JAD) of the two electrons ionized by absorbing one or two photons. On the JAD plane for the equal energy sharing case, one can identify a common symmetric ejection mode with respect to the laser polarization for three different processes, i.e., one-photon double ionization, two-photon nonsequential ionization, and sequential double ionization. In this symmetric ejection case, the two ejected electrons strongly favor a particular interelectron angle. We show that this angle can mimic the electron correlation strength in these double-ionization processes. The interelectron angle in the three types of double ionization is found to be obviously different.

We study the quantum dynamics of a Michelson interferometer with Fabry-Perot cavity arms and one movable end mirror, and driven by a single photon—an optomechanical device previously studied by Marshall et al. as a device that searches for gravity decoherence. We obtain an exact analytical solution for the system's quantum mechanical equations of motion, including details about the exchange of the single photon between the cavity mode and the external continuum. The resulting time evolution of the interferometer's fringe visibility displays interesting new features when the incoming photon's frequency uncertainty is narrower or comparable to the cavity's line width—only in the limiting case of much broader-band photon does the result return to that of Marshall et al., but in this case the photon is not very likely to enter the cavity and interact with the mirror, making the experiment less efficient and more susceptible to imperfections. In addition, we show that in the strong-coupling regime, by engineering the incoming photon's wave function, it is possible to prepare the movable mirror into an arbitrary quantum state of a multidimensional Hilbert space.

We characterize the local properties of an optomechanical system comprising the movable mirror of a resonator and its intracavity field, mutually coupled via radiation pressure. Our approach shows that both the state of the mirror and the field can be interpreted as squeezed thermal states whose dynamical properties can be tuned by properly choosing the working parameters. This allows us to design conditional procedures for the amplification of the correlation properties of the optomechanical state. Our study is a step forward in the understanding of the physics that rules a system of current enormous experimental interest.

We investigate both analytically and numerically violations of a Leggett-Garg inequality (LGI) for a composite quantum system in contact with two separate reservoirs at different temperatures. Remarkably we find that LGI violations can be enhanced when a heat current is established at low temperatures in a steady-state regime. Based on a Kraus operator decomposition of the nonunitary evolution for a system formed by two interacting spins or quantum bits, we provide analytical support for power-law relations between dissipation strength and mean temperature in the borderlines separating parameter regions where nonequilibrium conditions affect differently the maximal LGI violation. Furthermore, a correspondence between spatial and temporal correlation inequalities is shown to persist even in such nonequilibrium thermal settings.

Anyons have exotic statistical properties, fractional statistics, differing from bosons and fermions. They can be created as excitations of some Hamiltonian models. Here, we present an experimental demonstration of anyonic fractional statistics by simulating a version of the Kitaev spin-lattice model proposed by Han et al. [Phys. Rev. Lett. 98, 150404 (2007)] using an NMR quantum-information processor. We use a seven-qubit system to prepare a six-qubit pseudopure state to implement the ground-state preparation and realize anyonic manipulations, including creation, braiding and anyon fusion. The anyonic braiding process is equivalent to two successive particle exchanges. We obtain a phase difference of $(0.52\pm 0.01)\pi \times 2$ between the states with and without anyon braiding, which is different from the $\pi \times 2$ and $2\pi \times 2$ phase changes for fermions and bosons after two successive particle exchanges, and agrees with the prediction of the anyonic fractional statistics.

We calculate the radio frequency (RF) spectrum of fermionic atoms near a narrow Feshbach resonance, explaining observations made in ultracold samples of ${}^6\mathrm{Li}$ [E. L. Hazlett et al., Phys. Rev. Lett. 108, 045304 (2012)]. We use a two channel resonance model to show that the RF spectrum contains two peaks. In the wide-resonance limit, nearly all spectral weight lies in one of these peaks, and typically the second peak is very broad. We find strong temperature dependence, which can be traced to the energy dependence of the two-particle scattering. In addition to microscopic calculations, we use sum rule arguments to find generic features of the spectrum which are model independent.

We investigate the efficient free-space excitation of high-$Q$ resonance modes in deformed microcavities via dynamical tunneling-assisted coupling. A quantum scattering theory is employed to study the free-space transmission properties, and it is found that the transmission includes the contribution from (1) the off-resonance background and (2) the on-resonance modulation, corresponding to the absence and presence of high-Q modes, respectively. The theory predicts asymmetric Fano-like resonances around high-$Q$ modes in background transmission spectra, which are in good agreement with our recent experimental results. Dynamical tunneling across Kolmogorov-Arnold-Moser tori, which plays an essential role in the Fano-like resonance, is further studied. This efficient free-space coupling holds potential advantages to simplify experimental conditions and excite high-$Q$ modes in higher-index-material microcavities.

We study the optical second-harmonic radiation (SHG) generated by scattering from a homogeneous centrosymmetric thin composite material illuminated by higher-order Gaussian laser beams. The induced second-order source polarization is taken as of quadrupolar type $(\mathbf{E}·\nabla )\mathbf{E}$, which depends on the inhomogeneity of the incident electric field $\mathbf{E}$. This nonlinear source has the same form as that responsible of the SH signal observed in a composite made of Si nanocrystals embedded uniformly in a SiO${}_2$ matrix and that calculated for a thin disordered array of nanospheres. We calculate the SH radiation angular patterns generated by several incident combinations of spatial modes and states of polarizations. In particular, excitation with radially and azimuthally polarized doughnut modes and helical beams carrying orbital angular momentum with linear or circular polarization are considered. We found that this quadrupolar SHG depends sensitively on the transverse structure and polarization of the driving field. The response to $\nabla \mathbf{E}$ introduces a factor $\mathbf{E}(\mathbf{E}·\mathbf{K})$ in the Fourier component of the SH scattering amplitude, absent in electric-dipole-allowed SHG, that can give additional nodal lines or rings in the SH angular patterns, changes of the state of polarization, or additional azimuthal phases in the harmonic radiation. For circularly polarized beams with helical phase wave front, we found a selection rule according to which the nonlinear scattering of an optical vortex with charge $l_{\omega }$ and spin $\sigma =\pm 1$ induces a SH vortex field with a spin-dependent charge doubling $l_{2\omega }=2l_{\omega }+\sigma$. These features may be useful to identify SHG processes of quadrupolar nature and suggest a way to produce scattered SH radiation with a desired angular pattern and state of polarization.

In their interesting paper Jiang, Luo, and Fu [Phys. Rev. A 87, 022310 (2013)] present a nice historical review of what is usually referred to as the Choi-Jamiołkowski isomorphism and discuss some of its subtle properties. Our aim is to point out that there is a stronger correspondence between quantum maps and bipartite states: an isometric isomorphism between linear maps and functionals. This correspondence stems from the famous Grothendieck memoirs, and it has been a known fact at least since the 1970s. In particular, some properties studied by Jiang et al. are simple reminiscences of this more general approach. Moreover, for the sake of a complete historical review, we would like to note that the positive partial transpose criterion studied in the 1980s by Choi was, in fact, rediscovered in quantum information by Peres [Phys. Rev. Lett. 77, 1413 (1996)] and M. Horodecki et al. [Phys. Lett. A 223, 1 (1996)].

A set of 14 high-accuracy x-ray transition energies in the 2.4–3.1 keV range is presented, which can be used as x-ray standards. They were measured in two- to four-electron sulfur, chlorine, and argon ions produced in an electron-cyclotron resonance ion source, using a single spherically bent crystal spectrometer. The results include the first measurement of six transitions and improve the accuracy of six other experimental values. These measurements considerably extend the set of high-accuracy x-ray energies reported for highly charged ions. Their relative uncertainties range from 1 to 10 ppm. Theory only reaches such a precision in one- and two-electron ions. Our results thus have two distinct applications. On the one hand, they test predictions in two-electron ions [Artemyev, Shabaev, Yerokhin, Plunien, and Soff, Phys. Rev. A 71, 062104 (2005)], at the precision level of some two-photon QED contributions. We observe an agreement with theory for most of the transitions. On the other hand, the three- and four-electron ion transitions provide new benchmark energies for the calculation of missing theoretical contributions, such as Auger shifts or electronic correlations. Spectra were analyzed with an x-ray tracing simulation that contains all the relevant physics of the spectrometer.

Despite inherently complex multiphoton dynamics, our observations show that Ba double ionization with an infrared laser (8800–8920 cm${}^{-1}$) resembles a single-photon process; namely, its probability is proportional to the laser intensity. In this regime, single-electron ionization is due to a four-photon resonant transition through the highly perturbed state $6p^2{}^1{D}_2$, whereas double ionization is realized by the two-electron mechanism. Furthermore, we argue that these conclusions are valid for other alkaline-earth-metal atoms and other parameters of laser radiation.

We have numerically explored the possibility of controlling the branching ratio of the two distinguishable photodissociation products of HD${}^{+}$ (neutral D and neutral H) in an ultrashort laser field. In our multipulse scheme, a bound vibrational wave packet is generated in the ground electronic state of HD${}^{+}$ by vertical ionization from the ground state of HD. The control pulse acts on this wave packet at different time delays after the wave-packet generation is completed. It was found that, for a broad range of delay times between the pump pulse and the control pulse, any possible asymmetry in the branching ratio disappears due to the nonadiabatic coupling effects present in HD${}^{+}$. A third pulse, termed the driving pulse, with a relatively longer duration and a much weaker field strength, is introduced to counterbalance the nonadiabatic effects relevant for this heteronuclear system and to guide the dissociative reaction to a specific product channel. In fact, we have shown that the application of the driving pulse reproduces the branching-ratio pattern obtained on variation in the interpulse delay time between the pump pulse and the control pulse in the absence of the nonadiabatic coupling effects. The role of both the delay time between the pump pulse and the control pulse as well as the carrier envelope phase effects of the optical field of the control laser on the branching ratios in the two reaction channels were studied. The robustness of the driving pulse mediated asymmetry control, and any possible introduction of asymmetry by the driving pulse itself were also investigated.

We study the detached-electron flux distributions from the photodetachment of a negative ion near a repulsive center. Using a semiclassical approach, we calculate the electron flux on spherical detectors with various radii. The classically allowed angular range of the interference patterns on the spherical screen increases as the detached-electron energy is increased. In the classically allowed range, we find that there are always two trajectories going from the negative ion to the observation point on the screen, inducing quantum interference patterns. We have also extended the formulas into the tunneling region. The interference patterns also reflect the quantum angular distribution of electrons leaving the ion. A scaling property for the detached-electron flux is investigated. The accuracy of our semiclassical formulas is established by comparison with a quantum treatment using the exact Coulomb Green's function.