We present a detailed study on the properties of single photons generated by spontaneous parametric down conversion (SPDC) when both the spectral and spatial degrees of freedom are controlled by means of filters. Our results show that it is possible to obtain pure heralded single photons with high heralding efficiency despite the use of filters. Moreover, we report an asymmetry on the single-photon properties exhibited in type-II SPDC sources that depends on choosing the signal or the idler photon as the heralding one.

Recently, S. Bravyi and R. König [Phys. Rev. Lett. 110, 170503 (2013)] have shown that there is a trade-off between fault-tolerantly implementable logical gates and geometric locality of stabilizer codes. They consider locality-preserving operations which are implemented by a constant-depth geometrically local circuit and are thus fault tolerant by construction. In particular, they show that, for local stabilizer codes in $D$ spatial dimensions, locality-preserving gates are restricted to a set of unitary gates known as the $D\mathrm{th}$ level of the Clifford hierarchy. In this paper, we explore this idea further by providing several extensions and applications of their characterization to qubit stabilizer and subsystem codes. First, we present a no-go theorem for self-correcting quantum memory. Namely, we prove that a three-dimensional stabilizer Hamiltonian with a locality-preserving implementation of a non-Clifford gate cannot have a macroscopic energy barrier. This result implies that non-Clifford gates do not admit such implementations in Haah's cubic code and Michnicki's welded code. Second, we prove that the code distance of a $D$-dimensional local stabilizer code with a nontrivial locality-preserving $m\mathrm{th}$-level Clifford logical gate is upper bounded by $O\left(L^{D+1-m}\right)$. For codes with non-Clifford gates ($m>2$), this improves the previous best bound by S. Bravyi and B. Terhal [New. J. Phys. 11, 043029 (2009)]. Topological color codes, introduced by H. Bombin and M. A. Martin-Delgado [Phys. Rev. Lett. 97, 180501 (2006); Phys. Rev. Lett. 98, 160502 (2007); Phys. Rev. B 75, 075103 (2007)], saturate the bound for $m=D$. Third, we prove that the qubit erasure threshold for codes with a nontrivial transversal $m\mathrm{th}$-level Clifford logical gate is upper bounded by $1/m$. This implies that no family of fault-tolerant codes with transversal gates in increasing level of the Clifford hierarchy may exist. This result applies to arbitrary stabilizer and subsystem codes and is not restricted to geometrically local codes. Fourth, we extend the result of Bravyi and König to subsystem codes. Unlike stabilizer codes, the so-called union lemma does not apply to subsystem codes. This problem is avoided by assuming the presence of an error threshold in a subsystem code, and a conclusion analogous to that of Bravyi and König is recovered.

Recently, Motes, Gilchrist, Dowling, and Rohde [Phys. Rev. Lett. 113, 120501 (2014).] presented a scheme for photonic boson sampling using a fiber-loop architecture. Here we show that the same architecture can be modified to implement full, universal linear-optics quantum computing, in various incarnations. The scheme employs two embedded fiber loops, a single push-button photon source, three dynamically controlled beamsplitters, and a single time-resolved photodetector. The architecture has only a single point of interference, and thus may be significantly easier to align than other schemes. The experimental complexity of the scheme is constant, irrespective of the size of the computation, limited only by fiber lengths and their respective loss rates.

Boson sampling has attracted much interest as a simplified approach to implementing a subset of optical quantum computing. Boson sampling requires indistinguishable photons, but far fewer of them than universal optical quantum computing architectures. In reality, photons are never indistinguishable, and exhibit a rich spectral structure. Here we consider the operation of boson sampling with photons of arbitrary spectral structure and relate the sampling statistics of the device to matrix permanents. This sheds light on the computational complexity of different regimes of the photons' spectral characteristics, and provides very general results for the operation of linear optics interferometers in the presence of partially distinguishable photons. Our results apply to both the cases of spectrally resolving and nonspectrally resolving detectors.

Models of universal quantum computation in which the required interactions between register (computational) qubits are mediated by some ancillary system are highly relevant to experimental realizations of a quantum computer. We introduce such a universal model that employs a $d$-dimensional ancillary qudit. The ancilla-register interactions take the form of controlled displacements operators, with a displacement operator defined on the periodic and discrete lattice phase space of a qudit. We show that these interactions can implement controlled phase gates on the register by utilizing geometric phases that are created when closed loops are traversed in this phase space. The extra degrees of freedom of the ancilla can be harnessed to reduce the number of operations required for certain gate sequences. In particular, we see that the computational advantages of the quantum bus (qubus) architecture, which employs a field-mode ancilla, are also applicable to this model. We then explore an alternative ancilla-mediated model which employs a spin ensemble as the ancillary system and again the interactions with the register qubits are via controlled displacement operators, with a displacement operator defined on the Bloch sphere phase space of the spin coherent states of the ensemble. We discuss the computational advantages of this model and its relationship with the qubus architecture.

Absolute cross sections for electron-impact dissociation of ${{\text{O}}_3}^{+}$ ions yielding an ${\mathrm{O}}^{+}$ fragment are measured. The animated electron-ion crossed-beam method is applied in the energy range from 1 eV to 2.5 keV. The maximum total cross section for ${\mathrm{O}}^{+}$ fragment production is found to be $(3.6\pm 0.3)\times {10}^{-16}$ ${\mathrm{cm}}^2$ at 75 eV and such a large value of the cross section extends down to low energies. The threshold energy is found to be below 2 eV. Contributions of dissociative excitation and dissociative ionization to ${\mathrm{O}}^{+}$ fragment production are determined separately. The total kinetic energy release distributions are determined at select electron energies. Present data are discussed and compared with recent results [S. H. M. Deng et al., Phys. Rev. A 82, 062715 (2010)].

We compute fully differential cross sections for double ionization of helium by electrons, within the high-impact-energy and low-momentum transfer regimes, using the generalized Sturmian functions approach. Our results are converged relative to the total angular momentum and variable domain size. The method shows very good agreement with convergent close coupling calculations performed by Kheifets et al. [J. Phys. B 32, 5047 (1999)] for all ejection angles for the two electron emission energies considered in the experiments reported in that contribution. Both theoretical methods provide fully differential cross sections that require the same upscaling factors to compare with experimental data and are based on a first-order Born model for the projectile-target interaction. Since that reference was published, there were several theoretical efforts to account for the absolute scale of the experimental results, but agreement in the cross-section magnitude was not achieved even between theories. With the present contribution we conclude that the first-order Born model is now adequately solved, shifting the magnitude controversy towards either the experimental data and/or the addition of higher degrees of projectile-target interaction to the calculation.

Accurate knowledge of interaction potentials among the alkali-metal atoms and alkaline-earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali-metal atoms with the ${\mathrm{Ca}}^{+}$, ${\mathrm{Ba}}^{+}$, ${\mathrm{Sr}}^{+}$, and ${\mathrm{Ra}}^{+}$ alkaline-earth ions systematically, which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation $R$. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above-mentioned systems, which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random-phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representations of the dispersion coefficients versus $R$ are given among all the alkaline ions with Rb.

Studies of $2s\to np$ autoionization resonances in the neon isoelectronic sequence using relativistic multichannel quantum-defect theory are reported. The relativistic random-phase approximation is used to calculate the quantum-defect parameters. The autoionization resonances are characterized using Fano resonance parameters. The results are compared with available experimental and theoretical data, and the behavior of the resonances as a function of $Z$ is discussed.

We use the virial expansion to investigate the behavior of the two-component, attractive Fermi gas in the high-temperature limit, where the system smoothly evolves from weakly attractive fermions to weakly repulsive bosonic dimers as the short-range attraction is increased. We present a formalism for computing the virial coefficients that employs a diagrammatic approach to the grand potential and allows one to easily include an effective range $R^{*}$ in the interaction. In the limit where the thermal wavelength $\lambda \ll R^{*}$, the calculation of the virial coefficients is perturbative even at unitarity and the system resembles a weakly interacting Bose-Fermi mixture for all scattering lengths $a$. By interpolating from the perturbative limits $\lambda /\left|a\right|\gg 1$ and $R^{*}/\lambda \gg 1$, we estimate the value of the fourth virial coefficient at unitarity for $R^{*}=0$ and we find that it is close to the value obtained in recent experiments. We also derive the equations of state for the pressure, density, and entropy, as well as the spectral function at high temperatures.

Quantum interference of correlated particles is a fundamental quantum phenomenon which carries signatures of the statistics properties of the particles, such as bunching or antibunching. In the presence of particular symmetries, interference effects take place with high visibility, one of the simplest cases being the suppression of coincident detection in the Hong-Ou-Mandel effect. Tichy et al., [Phys. Rev. Lett. 104, 220405 (2010)] recently demonstrated a simple sufficient criterion for the suppression of output events in the more general case of Fourier multiport beam splitters. Here we study the case in which $2^q$ particles (either bosonic or fermionic) are injected simultaneously in different ports of a Sylvester interferometer with $2^p\ge 2^q$ modes. In particular, we prove a necessary and sufficient criterion for a significant fraction of output states to be suppressed, for specific input configurations. This may find application in assessing the indistinguishability of multiple single-photon sources and in the validation of boson sampling machines.

Ultrastrong light-matter interaction in an optomechanical system can result in nonlinear optical effects such as photon blockade. The system-bath couplings in such systems play an essential role in observing these effects. Here we study the quantum coherence of an optomechanical system with a dressed-state master equation approach. Our master equation includes photon-number-dependent terms that induce dephasing in this system. Cavity dephasing, second-order photon correlation, and two-cavity entanglement are studied with the dressed-state master equation.

The generalized rotating-wave approximation (GRWA) is presented for the two-qubit quantum Rabi model. The analytical expressions in the zeroth-order approximation recover the previous adiabatic ones. The counter-rotating-wave terms can be eliminated by performing the first-order corrections. An effective solvable Hamiltonian with the same form as the ordinary RWA one is then obtained, giving very accurate eigenvalues and eigenstates. Energy levels in the present GRWA are in accordance with the numerical exact diagonalization ones in a wide range of coupling strengths. The population dynamics in the GRWA are in quantitative agreement with the numerical results and exhibit the absence of collapses clearly, revealing the effects of the counter-rotating wave.

We present a simple scheme for the fast and efficient generation of quantum superpositions of two coherent fields with different classical amplitudes in a cavity. It relies on the simultaneous interaction of two two-level systems with the field. Their final detection with a high probability in the proper state projects the field onto the desired mesoscopic field state superposition. We show that the scheme is notably more efficient than those using a single atom. We discuss the method in the context of microwave cavity quantum electrodynamics, but it is also highly relevant for the thriving field of circuit QED. It may lead to interesting experimental studies of decoherence at the quantum-classical boundary.

We propose a method of classifying $n$-qubit states into stochastic local operations and classical communication inequivalent families in terms of the rank of the square matrix $C{\left(i{\sigma }_y\right)}^{\otimes k}{C}^T$, where $C$ is the rectangular coefficient matrix of the state and ${\sigma }_y$ is the Pauli operator. The rank of the square matrix $C{\left(i{\sigma }_y\right)}^{\otimes k}{C}^T$ is capable of distinguishing between $n$-qubit Greenberger-Horne-Zeilinger and $W$ states. The determinant of the matrix gives rise to a family of polynomial invariants for $n$ qubits which include as special cases well-known polynomial invariants in the literature. In addition, explicit expressions can be given for these polynomial invariants and this allows us to investigate the properties of entanglement measures built upon the absolute values of polynomial invariants for product states.

We exploit and clarify the use of random matrix theory for the calculation of the entanglement entropy of free Fermi gases. We apply this method to obtain analytic predictions for Rényi entanglement entropies of a one-dimensional gas trapped by a harmonic potential in all the relevant scaling regimes. We confirm our findings with accurate numerical calculations obtained by means of an ingenious discretization of the reduced correlation matrix.

We investigate the correlation properties of separable two-qubit states with maximally mixed marginals. These states are divided to two sets with the same geometric quantum correlation. However, a closer scrutiny of these states reveals a profound difference between their quantum correlations as measured by more probing measures. Although these two sets of states are prepared by the same type of quantum operations acting on classically correlated states with equal classical correlations, the amount of final quantum correlation is different. We investigate this difference and trace it back to the hidden classical correlation which exists in their preparation process. We also compare these states with regard to their usefulness for entanglement distribution and their robustness against noise.

We present a theoretical and experimental investigation of the $3d\to 2p$ resonance to the intercombination line ratio in low- to mid-$Z$ neonlike ions of astrophysical interest, i.e., of the $2p_{1/2}2p_{3/2}^{4}3d_{3/2}{}^1{P}_1^o\to 2p^6{}^1{S}_0$ and $2p_{1/2}^{2}2p_{3/2}^{3}3d_{5/2}{}^3{D}_1^o\to 2p^6{}^1{S}_0$ transitions commonly labeled $3C$ and $3D$, respectively. In particular, we have employed the configuration-interaction method with three different numbers of basis states and the many-body perturbation theory method to calculate oscillator strengths and energies for neonlike ions from $Z=18$ to 36. Combining our calculations with a systematic study of previous works in the literature, we show that these methods can predict accurate and converged energies for these transitions. We also find convergence for the oscillator strengths, but the ratio of oscillator strengths, which can be compared to experimental values of the relative intensity ratios of these lines, appears to converge to values higher than measured. We speculate that this is due to the role of electron-electron correlations. While the amount of electron correlations associated with the intercombination line $3D$ appears to be well described, it seems that the contributions from highly excited states are not sufficiently accounted for in the case of the resonance line $3C$. In order to augment the body of available experimental data for neonlike ions, we present a measurement of the $3C$ and $3D$ lines in neonlike ${\mathrm{Ar}}^{8+}$. We report a wavelength of $41.480\pm 0.001$ Å for line $3C$ and $42.005\pm 0.001$ Å for line $3D$. The intensity ratio of the two lines was determined to be $I\left(3C\right)/I\left(3D\right)=11.32\pm 1.40$.

While dissipation is widely considered to be harmful for quantum coherence, it can, when properly engineered, lead to the stabilization of nontrivial pure quantum states. We propose a scheme for continuous generation and stabilization of Schrödinger cat states in a cavity using dissipation engineering. We first generate nonclassical photon states with definite parity by means of a two-photon drive and dissipation, and then stabilize these transient states against single-photon decay. The single-photon stabilization is autonomous, and is implemented through a second engineered bath, which exploits the photon-number-dependent frequency splitting due to Kerr interactions in the strongly dispersive regime of circuit QED. Starting with the Hamiltonian of the baths plus cavity, we derive an effective model of only the cavity photon states along with analytic expressions for relevant physical quantities, such as the stabilization rate. The deterministic generation of such cat states is one of the key ingredients in performing universal quantum computation.