Gibbs states are familiar from statistical mechanics, yet their use is not limited to that domain. For instance, they also feature in the maximum entropy reconstruction of quantum states from incomplete measurement data. Outside the macroscopic realm, however, estimating a Gibbs state is a nontrivial inference task, due to two complicating factors: the proper set of relevant observables might not be evident a priori; and whenever data are gathered from a small sample only, the best estimate for the Lagrange parameters is invariably affected by the experimenter’s prior bias. I show how the two issues can be tackled with the help of Bayesian model selection and Bayesian interpolation, respectively, and illustrate the use of these Bayesian techniques with a number of simple examples.

Using the well-known necessary and sufficient conditions for minimum error discrimination (MED), we extract an equivalent form for the MED conditions. In fact, by replacing the inequalities corresponding to the MED conditions with an equivalent but more suitable and convenient identity, the problem of mixed state discrimination with optimal success probability is solved. Moreover, we show that the mentioned optimality conditions can be viewed as a Helstrom family of ensembles under some circumstances. Using the given identity, MED between $N$ similarity transformed equiprobable quantum states is investigated. In the case that the unitary operators are generating a set of irreducible representation, the optimal set of measurements and corresponding maximum success probability of discrimination can be determined precisely. In particular, it is shown that for equiprobable pure states, the optimal measurement strategy is the square-root measurement (SRM), whereas for the mixed states, SRM is not optimal. In the case that the unitary operators are reducible, there is no closed-form formula in the general case, but the procedure can be applied in each case in accordance to that case. Finally, we give the maximum success probability of optimal discrimination for some important examples of mixed quantum states, such as generalized Bloch sphere $m$-qubit states, spin-$j$ states, particular nonsymmetric qudit states, etc.

Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitary operations play a relevant role. In the present work we show that the application of suitable local unitary operations defines a family of bipartite entanglement monotones, collectively referred to as “mirror entanglement.” They are constructed by first considering the (squared) Hilbert-Schmidt distance of the state from the set of states obtained by applying to it a given local unitary operator. To the action of each different local unitary operator there corresponds a different distance. We then minimize these distances over the sets of local unitary operations with different spectra, obtaining an entire family of different entanglement monotones. We show that these mirror-entanglement monotones are organized in a hierarchical structure, and we establish the conditions that need to be imposed on the spectrum of a local unitary operator for the associated mirror entanglement to be faithful, i.e., to vanish in and only in separable pure states. We analyze in detail the properties of one particularly relevant member of the family, the “stellar mirror entanglement” associated with the traceless local unitary operations with nondegenerate spectra and equispaced eigenvalues in the complex plane. This particular measure generalizes the original analysis of S. M. Giampaolo and F. Illuminati [Phys. Rev. A 76, 042301 (2007)], valid for qubits and qutrits. We prove that the stellar entanglement is a faithful bipartite entanglement monotone in any dimension and that it is bounded from below by a function proportional to the linear entropy and from above by the linear entropy itself, coinciding with it in two- and three-dimensional spaces.

This work uses shaped femtosecond laser pulses to control the two-photon absorption (TPA) of coumarin 153 in a dispersive toluene medium. The dispersive medium reshapes the pulse along the optical path, and management of this effect is used to achieve spatial localization of TPA. Other control objectives were successfully implemented, including dual localization and high resolution local optimization of TPA. The solutions to these objectives were explored by means of evolutionary single- and multi-objective algorithms within a laboratory feedback loop.

The quantum evolution of the Wigner function for Gaussian wave packets generated by a non-Hermitian Hamiltonian is investigated. In the semiclassical limit $\hslash \to 0$ this yields the non-Hermitian analog of the Ehrenfest theorem for the dynamics of observable expectation values. The lack of Hermiticity reveals the importance of the complex structure on the classical phase space: The resulting equations of motion are coupled to an equation of motion for the phase-space metric—a phenomenon having no analog in Hermitian theories.

In distributed quantum computation, small devices composed of a single or a few qubits are networked together to achieve a scalable machine. Typically, there is an optically active matter qubit at each node, so that photons are exploited to achieve remote entanglement. However, in many systems the optically active states are unstable or poorly defined. We report a scheme to perform a high-fidelity entanglement operation even given severe instability. The protocol exploits the existence of optically excited states for phase acquisition without actually exciting those states; it functions with or without cavities and does not require number-resolving detectors.

Following atomic photoionization, the abrupt change in potential can lead to secondary ionization of an outer-shell electron in a phenomenon known as shake-off, a process which gives rise to the asymmetric $K\alpha$ profile and satellite lines. Investigation of chemical effects and relativistic quantum mechanics requires a theoretical determination of these satellite intensities; however, existing theoretical predictions are inconsistent with experimental results by up to an order of magnitude. Previously theoretical modeling required up to 12 fitting parameters to account for transition widths, energy corrections, spectator intensities, and spectator broadening. Using a multiconfiguration atomic model to account for electron-electron correlation, we provide here the first ab initio calculations of shake-off probabilities which are in agreement with experimental results (except for copper), an important step toward a complete theoretical profile.

Analytical results beyond the mean-field-limit approximation for several observables of the two-dimensional limit of the vibron model are presented. Finite-size scaling exponent values are also analytically derived. The computed corrections and scaling exponents are compared to numerical calculations for this algebraic model, based on a bosonic u(3) spectrum-generating algebra, obtaining good agreement.

We study the noisy GHZ-W mixture (where GHZ denotes Greenberger-Horne-Zeilinger). We demonstrate some necessary but not sufficient criteria for different classes of separability of these states. It turns out that the partial transposition criterion of Peres [Phys. Rev. Lett. 77, 1413 (1996)] and the criteria of Gühne and Seevinck [New J. Phys. 12, 053002 (2010)] dealing with matrix elements are the strongest ones for different separability classes of this two-parameter state. As a result, we determine a set of entangled states of positive partial transpose.

A Holevo measure is used to discuss how much information about a given positive operator valued measure (POVM) on system $a$ is present in another system $b$, and how this influences the presence or absence of information about a different POVM on $a$ in a third system $c$. The main goal is to extend information theorems for mutually unbiased bases or general bases to arbitrary POVMs, and especially to generalize “all-or-nothing” theorems about information located in tripartite systems to the case of partial information, in the form of quantitative inequalities. Some of the inequalities can be viewed as entropic uncertainty relations that apply in the presence of quantum side information, as in recent work by Berta et al. [Nature Physics 6, 659 (2010)]. All of the results also apply to quantum channels: For example, if $\mathcal{E}$ accurately transmits certain POVMs, the complementary channel $\mathcal{F}$ will necessarily be noisy for certain other POVMs. While the inequalities are valid for mixed states of tripartite systems, restricting to pure states leads to the basis invariance of the difference between the information about $a$ contained in $b$ and $c$.

The continuous-variable controlled-$Z$ gate is a canonical two-mode gate for universal continuous-variable quantum computation. It is considered as one of the most fundamental continuous-variable quantum gates. Here we present a scheme for realizing continuous-variable controlled-$Z$ gate between two optical beams using an atomic ensemble. The gate is performed by simply sending the two beams propagating in two orthogonal directions twice through a spin-squeezed atomic medium. Its fidelity can run up to one if the input atomic state is infinitely squeezed. Considering the noise effects due to atomic decoherence and light losses, we show that the observed fidelities of the scheme are still quite high within presently available techniques.

We identify the molecular ion NH${}^{+}$ as a potential candidate for probing variations in the fine-structure constant $\alpha$ and electron-to-proton mass ratio $\mu$. NH${}^{+}$ has an anomalously low-lying excited ${}^4{\Sigma }^{-}$ state, being only a few hundred cm${}^{-1}$ above the ground ${}^2\Pi$ state. Being a light molecule, this proximity is such that rotational levels of the respective states are highly intermixed for low angular momenta. We find that several low-frequency transitions within the collective rotational spectrum experience enhanced sensitivity to $\alpha$ and $\mu$ variation. This is attributable to the close proximity of the ${}^2\Pi$ and ${}^4{\Sigma }^{-}$ states, as well as the ensuing strong spin-orbit coupling between them. Suggestions that NH${}^{+}$ may exist in interstellar space and recent predictions that trapped-ion precision spectroscopy will be adaptable to molecular ions make NH${}^{+}$ a promising system for future astrophysical and laboratory studies of $\alpha$ and $\mu$ variation.

The reported algorithm determines the exact exchange potential $v_{\mathrm{x}}$ in an iterative way using energy shifts (ESs) and orbital shifts (OSs) obtained with finite-difference formulas from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to $v_{\mathrm{x}}$ and the latter for increments of ES and OS due to subsequent changes of $v_{\mathrm{x}}$. Thus, the need for solution of the differential equations for OSs, used by Kümmel and Perdew [Phys. Rev. Lett. 90, 043004 (2003)], is bypassed. The iterated exchange potential, expressed in terms of ESs and OSs, is improved by modifying ESs at odd iteration steps and OSs at even steps. The modification formulas are related to the optimized-effective-potential equation (satisfied at convergence) written as the condition of vanishing density shift (DS). They are obtained, respectively, by enforcing its satisfaction through corrections to approximate OSs and by determining the optimal ESs that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the density functional theory exchange-only approximation, proves highly efficient. The calculations using the pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact $v_{\mathrm{x}}$ so that, for Ne, Ar, and Zn, the corresponding DS norm becomes less than ${10}^{-6}$ after 13, 13, and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of ${10}^{-4}$ hartree accuracy are obtained for these atoms after, respectively, 9, 12, and 12 density iteration steps, each involving just two steps of $v_{\mathrm{x}}$ iteration, while the accuracy limit of ${10}^{-6}$ to ${10}^{-7}$ hartree is reached after 20 density iterations.

The double ionization of isolated water molecules fixed in space is investigated within a theoretical approach based on the second-order Born approximation. Electron angular distributions have been studied for specific kinematical conditions. The three usual mechanisms, the shake-off and the two two-step mechanisms, have been identified. A significant contribution of the two-step mechanism is clearly visible for some particular kinematics.

Molecular high-order harmonic generation (MHOHG) by a combined intense circularly polarized laser pulse and static electric field has been studied from the appropriate time-dependent Schrödinger equation (TDSE) for the ${{\mathrm{H}}_2}^{+}$ molecular ion. It is found that for a particular static field strength derived from a classical model, efficient MHOHG spectra are obtained with maximum energy $I_p$ $+$ 9.05$U_p$, where $I_p$ is the ionization potential and $U_p=E_0^2/4m_e{\omega }_0^2$ is the ponderomotive energy at amplitude $E_0$ and frequency ${\omega }_0$ of the circularly polarized laser pulse. The static field controls recollision of the electron with parent ions and is confirmed by numerical solutions of the ${{\mathrm{H}}_2}^{+}$ TDSE at equilibrium. To produce circularly polarized MHOHG spectra, a combination of an elliptically polarized pulse and a static electric field is found to be most efficient. A time-frequency analysis obtained via Gabor transforms is employed to identify electron recollision times responsible for the generation of these high-order harmonics. It is found that only single recollision trajectories contribute to the circularly polarized harmonics, thus generating new sources for high-frequency circularly polarized attosecond pulses.

Phase diagrams and collective excitations are investigated for a trapped imbalanced Fermi gas in two dimensions with $s$-wave pairing at finite temperatures. The treatment of collective modes is performed within the hydrodynamic approach using the Euler and continuity equations. The equations of state for different phases are simulated by a polytropic law with parameters obtained using a fit to the microscopic equilibrium distributions of the pressure and density. These are determined within the whole range of the BCS-BEC crossover using a path-integral description and taking into account fluctuations about the saddle point. We focus on the case of imbalanced gases, when the number of “spin-up” and “spin-down” fermions that form the pair is not equal. The superfluid-to-normal transition in the trapped Fermi gas is governed by the Berezinskii-Kosterlitz-Thouless mechanism. The eigenfrequencies of collective modes behave differently from those in the zero-temperature case. They can be used to study a realistic equation of state of a trapped Fermi gas at finite temperatures.

We perform an investigation into the properties of Pr${}^{3+}$:Y${}_2$SiO${}_5$ whispering-gallery-mode resonators as a first step toward achieving the strong coupling regime of cavity QED with rare-earth-metal-ion-doped crystals. Direct measurement of cavity QED parameters are made using photon echoes, giving good agreement with theoretical predictions. By comparing the ions at the surface of the resonator to those in the center, it is determined that the physical process of making the resonator does not negatively affect the properties of the ions. Coupling between the ions and resonator is analyzed through the observation of optical bistability and normal-mode splitting.

In a recent paper, Bancal et al. [Phys. Rev. Lett. 106, 250404 (2011)] put forward the concept of device-independent witnesses of genuine multipartite entanglement. These witnesses are capable of verifying genuine multipartite entanglement produced in a laboratory without resorting to any knowledge of the dimension of the state space or of the specific form of the measurement operators. As a by-product they found a multiparty three-setting Bell inequality which makes it possible to detect genuine $n$-partite entanglement in a noisy $n$-qubit Greenberger-Horne-Zeilinger (GHZ) state for visibilities as low as $2/3$ in a device-independent way. In this paper, we generalize this inequality to an arbitrary number of settings, demonstrating a threshold visibility of $2/\pi ~0.6366$ for number of settings going to infinity. We also present a pseudotelepathy Bell inequality achieving the same threshold value. We argue that our device-independent witnesses are optimal in the sense that for $n$ odd the above value cannot be beaten with $n$-party-correlation Bell inequalities.

The aim of this work is to calculate explicitly the result of the experiment of superposition of a mirror in the Michelson photon cavities interferometric device proposed by Marshall, Simon, Penrose, and Bouwmeester, as expected within a recently proposed model of nonunitary self-gravity-inducing localization. As for other proposals of modifications of quantum mechanics in a nonunitary sense, aimed to account for both unitary evolution and irreversible collapse, like in the famous Ghirardi-Rimini-Weber and Pearle’s models, it turns out that, for the experimental parameters proposed, no effect is detectable at all. It is pointed out that the enhancing properties of matter granularity does not substantially change this conclusion. Parameters have also been exploratively varied in a certain range beyond the proposed values. It is shown that within “sensible” parameters, which are not yet attainable within current technology, the model exhibits a peculiar signature with respect to other collapse models as far as parameters space is explored. Besides, the calculation offers a way to see nonunitary gravity at work in a quasirealistic setting.

The ground-state hyperfine resonance line of alkali-metal atoms is frequency shifted in the presence of noble or molecular gases. The buffer gases used in vapor-cell atomic clocks thus induce a temperature-dependent shift of the clock transition frequency. We report on measurements of the pressure and temperature dependence of the Cs clock transition frequency in the presence of Ne, Ar, and ${\mathrm{N}}_2$ buffer gases. The pressure in the sealed glass vapor cells is measured by means of the shift of the Cs $D_1$ line. We have also investigated the temperature dependence of the optical shift. From these measurements, we infer the pressure and temperature coefficients of the hyperfine frequency shift. It is then possible to predetermine gas mixture ratios that cancel the temperature sensitivity at a given temperature. This prediction is confirmed experimentally for Ar-N${}_2$ mixtures. These results can be useful for improving the long-term frequency stability of Cs vapor-cell clocks.