We study the sensitivity of phase estimation in a lossy Mach-Zehnder interferometer (MZI) using two general, and practical, resources generated by a laser and a nonlinear optical medium with passive optimal elements, which are readily available in the laboratory: One is a two-mode separable coherent and squeezed vacuum state at a beam splitter and the other is a two-mode squeezed vacuum state. In view of the ultimate precision given by quantum Fisher information, we show that the two-mode squeezed vacuum state can achieve a lower bound of estimation error than the coherent and squeezed vacuum state under a photon-loss channel. We further consider practical measurement schemes, homodyne detection and photon number resolving detection (PNRD), to characterize the accuracy of phase estimation in reality and find that the coherent and squeezed vacuum state largely achieves a lower bound than the two-mode squeezed vacuum in the lossy MZI while maintaining quantum enhancement over the shot-noise limit. By comparing homodyne detection and PNRD, we demonstrate that quadrature measurement with homodyne detection is more robust against photon loss than parity measurement with PNRD. We also show that double homodyne detection can provide a better tool for phase estimation than single homodyne detection against photon loss.

An operational approach to the study of computation based on correlations considers black boxes with one-bit inputs and outputs, controlled by a limited classical computer capable only of performing sums modulo-two. In this setting, it was shown that noncontextual correlations do not provide any extra computational power, while contextual correlations were found to be necessary for the deterministic evaluation of nonlinear Boolean functions. Here we investigate the requirements for reliable computation in this setting; that is, the evaluation of any Boolean function with success probability bounded away from $1/2$. We show that bipartite CHSH quantum correlations suffice for reliable computation. We also prove that an arbitrarily small violation of a multipartite Greenberger–Horne–Zeilinger noncontextuality inequality also suffices for reliable computation.

We consider the problem of estimating an unknown but constant carrier phase modulation $\theta$ using a general, possibly entangled, $n$-mode optical probe through $n$ independent and identical uses of a lossy bosonic channel with additive thermal noise. We find an upper bound to the quantum Fisher information (QFI) of estimating $\theta$ as a function of $n$, the mean and variance of the total number of photons $N_{\mathrm{S}}$ in the $n$-mode probe, the transmissivity $\eta$, and mean thermal photon number per mode ${\overline{n}}_{\mathrm{B}}$ of the bosonic channel. Since the inverse of QFI provides a lower bound to the mean-square error (MSE) of an unbiased estimator $\tilde{\theta }$ of $\theta$, our upper bound to the QFI provides a lower bound to the MSE. It already has found use in proving fundamental limits of covert sensing and could find other applications requiring bounding the fundamental limits of sensing an unknown parameter embedded in a correlated field.

It is well known that the lanthanide and actinide elements are formed by the filling of $4f$ and $5f$ subshells which occurs after the filling of $5d$ and $6d$ subshells, respectively, has begun. With increasing ionization one expects the energy levels to eventually regroup to their hydrogenic ordering, i.e., in terms of principal quantum number. In the lanthanides, the $4f$ electron binding energy overtakes that of $5p$ near the 6th or 7th ion stage and $5s$ near the 14th or 15th ion stage, leading to dramatic rearrangements of ground-state configurations. In this paper we report on the results of a study to explore the effects of increasing ionization on the ground-state configurations of actinide ions as a result of $5f$ and $6p$ or $6s$ level crossings. It is seen that the effects generally occur later and are more strongly influenced by spin-orbit splitting than in the lanthanides. The near degeneracies of $5f$ and $6l$ energies in these stages lead to configuration interaction (CI) amongst configurations with variable numbers of $5f$ and $6p$ electrons. The effects of CI on the level complexity are explored for ions along the Rn I sequence and are found to lead to the formation of “compound states” as predicted for the lanthanides. The extreme ultraviolet and soft x-ray spectra of medium and highly charged lanthanides are dominated by emission from unresolved transition arrays (UTAs) of the type $\mathrm{\Delta }n=0$, $4p^{6}4d^{N+1}-4p^{5}4d^{N+2}+4p^{6}4d^{N}4f$, which, in general, overlap in adjacent ion stages of a particular element. Here, the corresponding $\mathrm{\Delta }n=0$, $5p^{6}5d^{N+1}-5p^{5}5d^{N+2}+5p^{6}5d^{N}5f$ UTAs have been studied theoretically with the aid of Hartree-Fock with configuration interaction calculations. As well as predicting the wavelengths and spectral details of the anticipated features, the calculations show that the effects of configuration interaction are quite different for the two different families of $\mathrm{\Delta }n=0$ transitions and, once more, spin-orbit interactions play a major role.

We use paramagnetic Faraday rotation to study spin noise spectrum from unpolarized Rb vapor in a tightly focused probe beam in the presence of ${\mathrm{N}}_2$ buffer gas. We derive an analytical form for the diffusion component of the spin noise time-correlation function in a Gaussian probe beam. We also obtain analytical forms for the frequency spectrum of the spin noise in the limit of a tightly focused or a collimated Gaussian beam in the presence of diffusion. In particular, we find that in a tightly focused probe beam the spectral line shape can be independent of the buffer gas pressure. Experimentally, we find good agreement between the calculated and the measured spin noise spectra for ${\mathrm{N}}_2$ gas pressures ranging from 56 to 820 Torr.

The Talbot-Lau interferometer is a proven tool to perform measurements in the near-field regime. It has been extensively used for investigating the wave nature of electrons, atoms, and complex organic molecules. However, when designing devices with high geometrical acceptances, which would be desirable when dealing with low-intensity sources of particles, the alignment requirements become much more stringent. Furthermore, if the particles are charged, the influence of external fields becomes quickly non-negligible when increasing the length of the device. This paper focuses on both the geometric and physical constraints of an ion Talbot-Lau interferometer, with emphasis on the scaling of such constraints with the size of the device. Mathematical formulas which set limits on the critical parameters are derived and applied to a test setup for protons.

The Kondo effect describes the spin-exchange interaction between localized impurities and itinerant fermions. The ultracold alkaline-earth atomic gas provides a natural platform for quantum simulation of the Kondo model, utilizing its long-lived clock state and the nuclear-spin exchange interaction between clock state and ground state. One of the key issue now is whether the Kondo temperature can be high enough to be reached in current experiments, for which we have proposed to use transverse confinement to confine atoms into a one-dimensional tube and to use the confinement-induced resonance to enhance Kondo coupling. In this work, we further consider the $(1+0)$-dimensional scattering problem when the clock state is further confined by an axial harmonic confinement. We show that this axial confinement for the clock-state atoms not only plays a role for localizing them, but can also act as an additional control knob to reach the confinement-induced resonance. We show that, in the presence of both the transverse and the axial confinements, the confinement-induced resonance can be reached in the practical conditions and the Kondo effect can be attainable in this system.

Simple joint measurements of pairs of observables reveal that states considered universally as classical-like, such as SU(2) spin coherent states, Glauber coherent states, and thermal states, are actually nonclassical. We show that this holds because we can find a joint measurement the statistics of which is not separable. Eventually this may be extended to all states different from the maximally mixed state.

We present a study of optical quantum states generated by subtraction of photons from the thermal state. Some aspects of their photon number and quadrature distributions are discussed and checked experimentally. We demonstrate an original method of up to ten photon subtracted state preparation with use of just one single-photon detector. All the states were measured with use of a balanced homodyne technique and the corresponding density matrices were reconstructed. The fidelity between desired and reconstructed states exceeds $99\%$. Combined with homodyne detection it can also be used for precise measurement of high-order autocorrelation functions.

Recently, an approach to tomography with extended anisotropic radiation sources has been introduced, which helps to overcome the challenges resulting from the low brilliance typical for x-ray laboratory sources. The method is based on the three-dimensional Radon transform (3DRT) which uses planar integrals instead of line integrals. By extending the source spot in one direction, more photons can contribute to image formation while the impact on the resolution is minor with the 3DRT approach. In this work we present a more comprehensive description of the method, derive quantitative error estimates for the extraction of these planar integrals measured with a finite source size, and validate the 3DRT scheme by analytical theory. We also demonstrate a simple and efficient reconstruction algorithm for 3D Radon data. Finally, we further substantiate the method with experimental results obtained at a microfocus x-ray source with an extremely anisotropic source spot.

We present a thorough classification of the isotropic quantum walks on lattices of dimension $d=1,2,3$ with a coin system of dimension $s=2$. For $d=3$ there exist two isotropic walks, namely, the Weyl quantum walks presented in the work of D'Ariano and Perinotti [G. M. D'Ariano and P. Perinotti, Phys. Rev. A 90, 062106 (2014)], resulting in the derivation of the Weyl equation from informational principles. The present analysis, via a crucial use of isotropy, is significantly shorter and avoids a superfluous technical assumption, making the result completely general.

Conditional von Neumann entropy is an intriguing concept in quantum information theory. In the present work, we examine the effect of global unitary operations on the conditional entropy of the system. We start with a set containing states with a non-negative conditional entropy and find that some states preserve the non-negativity under unitary operations on the composite system. We call this class of states the absolute conditional von Neumann entropy non-negative (ACVENN) class. We characterize such states for $2\otimes 2$–dimensional systems. From a different perspective the characterization accentuates the detection of states whose conditional entropy becomes negative after the global unitary action. Interestingly, we show that this ACVENN class of states forms a set which is convex and compact. This feature enables the existence of Hermitian witness operators. With these we can distinguish the unknown states which will have a negative conditional entropy after the global unitary operation. We also show that this has immediate application to superdense coding and state merging, as the negativity of the conditional entropy plays a key role in both these information processing tasks. Some illustrations followed by analysis are also provided to probe the connection of such states with absolutely separable states and absolutely local states.

Hybrid quantum circuits combining advantages of each individual system have provided a promising platform for quantum information processing. Here we propose an experimental scheme to directly couple a transmon qubit to an individual spin in the nitrogen-vacancy (NV) center, with a coupling strength three orders of magnitude larger than that for a single spin coupled to a coplanar waveguide microwave cavity. This direct coupling between the transmon and the NV center could be utilized to make a transmon bus, leading to a coherently virtual exchange among different single spins. Furthermore, we demonstrate that, by coupling a transmon to a low-density NV ensemble, a swap operation between the transmon and NV ensemble is feasible and a quantum nondemolition measurement on the state of the NV ensemble can be realized on the cavity-transmon-NV-ensemble hybrid system. Moreover, in this system, a virtual coupling can be achieved between the cavity and NV ensemble, which is much larger in magnitude than the direct coupling between the cavity and the NV ensemble. The photon state in the cavity can thus be stored into NV spins more efficiently through this virtual coupling.

We propose and experimentally demonstrate an efficient framework for the quantum simulation of quantum channels in nuclear magnetic resonance (NMR). Our approach relies on the suitable decomposition of nonunitary operators in a linear combination of $d$ unitary ones, which can be then experimentally implemented with the assistance of a number of ancillary qubits that grows logarithmically in $d$. As a proof-of-principle demonstration, we realize the quantum simulation of three quantum channels for a single-qubit: phase damping, amplitude damping, and depolarizing channels. For these paradigmatic cases, we measure key features, such as the fidelity of the initial state and the associated von Neumann entropy for a qubit evolving through these channels. Our experiments are carried out using nuclear spins in a liquid sample and NMR control techniques.

In this work we introduce modifications to the wave-packet method proposed by Kaneko to calculate the energy-loss moments of a projectile traversing a target which is represented in terms of Gaussian functions for the momentum distributions of electrons in the atomic shells. These modifications are introduced using the Levine and Louie technique to take into account the energy gaps corresponding to the different atomic levels of the target. We use the extended wave-packet model to evaluate the stopping power, the energy straggling, the inverse mean free path, and the ionization cross sections for protons in several targets, obtaining good agreements for all these quantities on an extensive energy range that covers low-, intermediate-, and high-energy regions. The extended wave-packet model proposed here provides a method to calculate in a very straightforward way all the significant terms of the inelastic interaction of light ions with any element of the periodic table.

High-order harmonic generation with bicircular fields—the combination of counter-rotating circularly polarized pulses at different frequencies—results in a series of short-wavelength XUV harmonics with alternating circular polarizations, and experiments show that there is an asymmetry in the emission between the two helicities: a slight one in helium and a larger one in neon and argon, where the emission is carried out by $p$-shell electrons. Here we analyze this asymmetry by switching to a rotating frame in which the field is linearly polarized; this induces an effective magnetic field which lowers the ionization potential of the $\mathit{p}{}_{+}$ orbital that corotates with the lower-frequency driver, enhancing its harmonic emission and the overall helicity of the generated harmonics, while also introducing nontrivial effects from the transformation to a noninertial frame in complex time. In addition, this analysis directly relates the small asymmetry produced by $s$-shell emission to the imaginary part of the recollision velocity in the standard strong-field-approximation formalism.

We describe a dispersive Faraday optical probe of atomic spin which performs a weak measurement of spin projection of a quantum gas continuously for more than one second. To date, focusing bright far-off-resonance probes onto quantum gases has proved invasive due to strong scalar and vector light shifts exerting dipole and Stern-Gerlach forces. We show that tuning the probe near the magic-zero wavelength at 790 nm between the fine-structure doublet of ${}^{87}\mathrm{Rb}$ cancels the scalar light shift, and careful control of polarization eliminates the vector light shift. Faraday rotations due to each fine-structure line reinforce at this wavelength, enhancing the signal-to-noise ratio for a fixed rate of probe-induced decoherence. Using this minimally invasive spin probe, we perform microscale atomic magnetometry at high temporal resolution. Spectrogram analysis of the Larmor precession signal of a single spinor Bose-Einstein condensate measures a time-varying magnetic field strength with 1 $\mu \mathrm{G}$ accuracy every 5 ms; or, equivalently, makes more than 200 successive measurements each at $10\mathrm{pT}/\sqrt{\mathrm{Hz}}$ sensitivity.

We present an all-electron, ab initio calculation of time-resolved photoelectron momentum distributions (PMDs) induced by resonant two-color, two- or three-photon ionization of helium and neon atoms, as recently measured by Villeneuve et al. [Science 356, 1150 (2017)] using a femtosecond infrared (IR) laser pulse and an attosecond pulse train (APT) produced with high harmonic generation as an extreme ultraviolet (XUV) photon source. In contrast to a monochromatic XUV pulse commonly used at the free-electron laser facilities, an APT is broadband and ultrashort ($<1$ fs), so that it could induce nonresonant one-photon transitions above ionization threshold as well as a resonantly excited state. They may interfere with each other upon subsequent absorption or emission of an IR photon, so that the resultant PMD loses clear orbital symmetry. Our time-dependent density functional calculation demonstrates that the selection of a particular excited state in the time-resolved PMD is nevertheless possible if energy and timing of an APT are adjusted properly.