We consider the asymptotic regularization of the maximal fidelity for the generalized Pauli channels, which is a problem similar to the classical channel capacity. In particular, we find the exact formulas for the extremal channel fidelities and the maximal output $\infty$-norm. For wide classes of channels, we show that these quantities are weakly multiplicative. Finally, we find the regularized maximal fidelity for the channels satisfying the time-local master equations.

Highly correlated pure ab initio relativistic configuration-interaction theory is in the present paper applied to the calculation of the tensor-pseudotensor $\mathcal{P},\mathcal{T}$-violating nucleon-electron interaction constant in the electronic ground states of atomic mercury and radium. The final best obtained results are $R_T\left(\mathrm{Hg}\right)=-4.43$ $\left[{10}^{-20}\langle {\sigma }_N\rangle e\mathrm{cm}\right]$ and $R_T\left(\mathrm{Ra}\right)=-15.0$ $\left[{10}^{-20}\langle {\sigma }_N\rangle e\mathrm{cm}\right]$. The accuracy of the employed electronic-structure models are confirmed by determining the static electric-dipole polarizability ${\alpha }_d\left(\mathrm{Hg}\right)=35.7$ a.u. which is in accord with the experimental value to about $5\%$. $R_T$(Ra) will be useful for constraining (or obtaining) the $\mathcal{CP}$-violating parameter $C_T$ when combined with future measurements of the electric-dipole moment of the radium atom.

Strong-field photoelectron momentum distributions (PEMDs) generated in the ionization of molecules by circularly polarized laser pulses contain valuable information on the structure of the ionizing molecular orbital. In this paper, we investigate using the adiabatic theory how this information is imprinted in and can be extracted from such PEMDs. The PEMDs have a donutlike shape. The variation of a PEMD along the donut reproduces the orientation dependence of the ionization rate of the ionizing orbital, and hence reflects its nodal structure and shape. The transverse structure of the PEMD in cross sections of the donut corresponding to orientations of the molecule at which the ionizing orbital has a node in the direction opposite to that of the instantaneous laser field reflects the interplay of two competing ionization channels, which provides additional information on the orbital structure. We illustrate these features by the analysis of PEMDs for three states of different symmetries of the hydrogen molecular ion ${\mathrm{H}}_2{}^{+}$.

We present a theoretical study of self-amplification of extreme ultraviolet light in a helium gas target. Resonant excitation to the $3a{}^{1}P^o$ doubly excited state below the $N=2$ threshold by $100\mathrm{fs}$ free-electron laser pulses is followed by fluorescence at $40.7\mathrm{eV}$ photon energy. The process is modeled by a three-level atomic system coupled to the continuum and described by the Maxwell-Bloch equations. The evolution of state populations and radiation fields is studied over a wide range of pump intensities and target pressures, clearly showing the regions of spontaneous emission, amplification, and saturation of light emitted in the forward direction. The treatment includes both coherent and SASE pump pulses. In both cases the amplified pulses are temporally coherent and exhibit a duration similar to that of the pump pulses.

According to the Schiff theorem, the atomic electrons completely screen the atomic nucleus from an external static electric field. However, this is not the case if the field is time dependent. Electronic orbitals in atoms either shield the nucleus from an oscillating electric field when the frequency of the field is off the atomic resonances or enhance this field when its frequency approaches an atomic transition energy. In molecules, not only electronic but also rotational and vibrational states are responsible for the screening of oscillating electric fields. As will be shown in this paper, the screening of a low-frequency field inside molecules is much weaker than it appears in atoms owing to the molecular rovibrational states. We systematically study the screening of oscillating electric fields inside diatomic molecules in different frequency regimes, i.e., when the field's frequency is either of the order of rovibrational or electronic transition frequencies. In the resonance case, we demonstrate that the microwave-frequency electric field may be enhanced up to six orders in magnitude due to rovibrational states. We also derive the general formulas for the screening and resonance enhancement of oscillating electric field in polyatomic molecules. Possible applications of these results include nuclear electric dipole moment measurements and stimulation of nuclear reactions by laser light.

Recently, trapped dipolar gases were observed to form high-density droplets in a regime where mean-field theory predicts collapse. These droplets present a form of equilibrium where quantum fluctuations are critical for stability. So far, the effect of quantum fluctuations has only been considered at zero temperature through the local chemical potential arising from the Lee-Huang-Yang correction. Here, we extend the theory of dipolar droplets to nonzero temperatures using Hartree-Fock-Bogoliubov theory (HFBT) and show that the equilibrium is strongly affected by temperature fluctuations. HFBT, together with local density approximation for excitations, reproduces the zero-temperature results and predicts that the condensate density can change dramatically even at low temperatures where the total depletion is small. In particular, we find that typical experimental temperatures ($T\sim 100$ nK) can significantly modify the transition between low-density and droplet phases.

We present analytical results revealing the impact of higher-order dispersion on four-wave mixing in quantum applications. We derive fundamental relations between input and output modes in dispersive four-wave mixing processes and apply the theory to photon-pair generation. We analyze specific examples of four-wave-mixing configurations and find that, in some cases, spectral correlations are severely affected by dispersion while other cases are strongly unaffected. For the considered examples, we derive analytic conditions for dispersion cancellation, resulting in highly factorable two-photon states.

We analyze the dynamics of a set of two-level atoms coupled to the electromagnetic environment within a waveguide. This problem is often tackled by assuming a weak coupling between the atoms and the environment as well as the associated Markov approximation. We show that the accuracy of such an approximation may be more limited than in the single-atom case and may also be strongly determined by the presence of collective effects produced by atom-atom interactions. To this aim, we solve the full problem with exact diagonalization and also the time-dependent density matrix renormalization group method, and we compare the result to that obtained within a weak-coupling master equation and with the Dicke approximation. Finally, we study the dynamics of the entanglement within the system when considering several interatomic distances and atomic frequencies.

The distribution of quantum correlations among remote users is a key procedure underlying many quantum information technologies. Einstein-Podolsky-Rosen steering, which is one kind of such a correlation stronger than entanglement, has been identified as a resource for secure quantum networks. We show that this resource can be established between two and even more distant parties by transmission of a system being separable from all the parties. For two-user scenarios, we design a protocol allowing one to distribute one-way Gaussian steering which can be used subsequently for one-sided device-independent (1sDI) quantum key distribution. Further, we extend the protocol to three-user scenarios to distribute richer steerability properties including one-to-multimode steering and collective steering which can be used for 1sDI quantum secret sharing. All the proposed protocols can be implemented with squeezed states, beam splitters, and displacements, and thus they can be readily realized experimentally. Our findings reveal that not only entanglement but even steering can be distributed via communication of a separable system. Viewed from a different perspective, the present protocols also demonstrate that one can switch multipartite states between different steerability classes by operations on parts of the states.

We recently reported a ${}^{40}{\mathrm{Ca}}^{+}$ optical clock comparison with an uncertainty at $5.5\times {10}^{-17}$, mainly limited by the excess micromotion shift. Here we report the progress made to reduce this shift and its uncertainty below $1\times {10}^{-18}$ by precise measurement of the “magic” rf drive frequency ${\mathrm{\Omega }}_0$ at which the micromotion-induced scalar Stark shift and second-order Doppler shift cancel each other. ${\mathrm{\Omega }}_0$ is measured as $2\pi \times 24.801\left(2\right)\mathrm{MHz}$, and the differential static scalar polarizability $\mathrm{\Delta }{\alpha }_0$ of the ${}^{40}{\mathrm{Ca}}^{+}$ ion clock transition is measured as $-7.2677\left(21\right)\times {10}^{-40}\mathrm{J}{\mathrm{m}}^2{\mathrm{V}}^{-2}$. The blackbody radiation shift is then calculated to be 0.37913(12) Hz at 300 K considering the dynamic correction. The contribution of the blackbody shift coefficient to the uncertainty of the optical clock at room temperature has been reduced to the $3\times {10}^{-19}$ level. With further improvements made to reduce the servo error, the total clock uncertainty is reduced to $2.2\times {10}^{-17}$, limited by the blackbody radiation field evaluation.

Quantum coherence interference between electronic states in molecules is an important factor for controlling electronic and nuclear dynamics in photoinduced physics and chemistry. We measure and model molecular angle-dependent photoionization yields to explore coherent interference dynamics between quasiequal energy electronic-vibrational states of the nitric oxide molecule, NO, by ultrafast phase-controlled two-color femtosecond laser pulses. We demonstrate by experiment and theory that the photoelectron angular distribution of NO, where two excited electronic states are coherently combined by ultrafast pulses, is a function of the relative phase of the pulses, and the photoelectron kinetic energy. The modification of photoelectron emission angular patterns encodes the information of the coherence via electronic state interference. The result allows access to phase-dependent state correlations and ultrafast vibrationic dynamics in molecules.

Quantum phase transitions are usually classified into discrete universality classes that typically only depend on symmetries and spatial dimensionalities. In this article, we demonstrate an opportunity to continuously vary the critical exponents or universalities by tuning experimental parameters in a given physical system. Particularly, we show that critical exponents in long-range spin systems simulated in ion traps can be tuned with laser detuning. We suggest that such experiments also effectively simulate some aspects of critical phenomena in conventional spin systems but in artificial noninteger spatial dimensions.

We present analytic solutions of the Klein-Gordon equation for an electron of momentum $p$ in $N$ crossed laser beams ${\mathbf{A}}_j\left({\phi }_j\right)$ with phases ${\phi }_j={\omega }_{j}t-{\mathbf{k}}_j·\mathbf{r}+{\delta }_j.$ The solutions are of the form ${\mathrm{\Psi }}_p=e^{ipx}{\mathit{ϝ}}_p\left(\mathbf{r},t\right).$ The determination of the distortion factor ${\mathit{ϝ}}_p$ is pursued within a method of “auxiliary variables,” which uses the ${\phi }_j$ as variables, ${\mathit{ϝ}}_p\left(\mathbf{r},t\right)\equiv {\mathit{ϝ}}_p\left({\phi }_1,...,{\phi }_N\right)$. The equation for ${\mathit{ϝ}}_p\left({\phi }_1,...,{\phi }_N\right)$ is a linear second-order partial differential equation and it does not appear to be soluble analytically exactly. However, the second-order derivative terms are multiplied by coeffients that are small with respect to those of the first-order derivatives, if (A) the angles between all beams are small or (B) for all beams we have ${\omega }_j/m{c}^2\ll 1.$ In the second case, their neglect would be quite justified for frequencies up into the x-ray range. With this approximation the equation would reduce to a first-order derivatives “reduced equation.” Mathematically, however, this cannot be done without further analysis. This is because we are in a situation typical of singular perturbations theory, in which the exact, perturbed solution might not be connected continuously to the unperturbed one. Nevertheless, on the basis of exactly soluble models (see the Appendix), we argue that the approximation is justified in our case and proceed to solve it. It turns out that the reduced equation can be solved exactly for certain crossed-beam geometries of interest. We consider first the case of laser pulses of arbitrary shape. The most general geometry we solve is that in which all beams have coplanar propagation directions and the fields are linearly polarized perpendicular to the propagation plane, except possibly for two that can be oblique and elliptically polarized. For two beams $(N=2)$ this covers the most general case possible. As an application, we calculate the closed-form solution for Gaussian-pulse crossed beams. Next, we treat the case of monochromatic beams as a limit of the laser-pulse case and derive closed-form solutions for some geometries, including standing waves. We then discuss the effect of the passage of crossed beams over an electronic wave packet and show that its momentum distribution is not modified and no pair production is possible (in the reduced equation approximation). We also show that the final wave packet displays the classical ponderomotive Lorentz shift, if low relativistic momenta are involved. The Appendix deals with soluble models of the exact equation for ${\mathit{ϝ}}_p$ which have the salient features of the original. For these models, the reduced equation solution is indeed a valid approximation to the exact one, if conditions similar to (A) or (B) above are met.

Recently, there has been growing interest in using quantum error correction in practical devices. A central issue in quantum error correction is the initialization of quantum data into a quantum error-correction code. Most studies have concentrated on generating quantum codes based on their encoding quantum circuits. However, this often leads to a large number of steps required in the initialization, and hence this process can be prone to errors. The purpose of this work is to demonstrate that permutation-invariant quantum error-correction codes can be created with high fidelity by exploiting their underlying symmetry. The code is initialized on multiple qubits that mutually interact or are themselves coupled to a quantum harmonic oscillator. We show that the so-called selective resonant interaction is derivable on such physical systems. By utilizing the selective resonant interaction, these highly symmetric codes may be rapidly generated with excellent fidelity. We also discuss the potential of initializing permutation-invariant quantum error-correction codes based on the state-of-art experimental techniques.

High-dimensional quantum information processing has become a mature field of research with several different approaches being adopted for the encoding of $D$-dimensional quantum systems. Such progress has fueled the search of reliable quantum tomographic methods aiming for the characterization of these systems, most of these methods being specifically designed for a given scenario. Here, we report on a tomographic method based on multiply symmetric states and on experimental investigations to study its performance in higher dimensions. Unlike other methods, it is guaranteed to exist in any dimension and provides a significant reduction in the number of measurement outcomes when compared to standard quantum tomography. Furthermore, in the case of odd dimensions, the method requires the least possible number of measurement outcomes. In our experiment we adopt the technique where high-dimensional quantum states are encoded using the linear transverse momentum of single photons and are controlled by spatial light modulators. Our results show that fidelities of $0.984\pm 0.009$ with ensemble sizes of only $1.5\times {10}^5$ photons in dimension $D=15$ can be obtained in typical laboratory conditions, thus showing its practicability in higher dimensions.

We present the positive-partial-transpose (PPT) square conjecture introduced by M. Christandl Banff International Research Station Workshop: Operator Structures in Quantum Information Theory (Banff International Research Station, Alberta, 2012). We prove the conjecture in the case $n=3$ as a consequence of the fact that two-qutrit PPT states have Schmidt number of at most 2. The PPT square conjecture in the case of $n\ge 4$ is still open. We present an example to support the conjecture for $n=4$.

We introduce a technique for recovering noise-free observables in noisy quantum systems by combining the results of many slightly different experiments. Our approach is applicable to a variety of quantum systems, but we illustrate it with applications to quantum information and quantum sensing. The approach corresponds to repeating the same quantum evolution many times with known variations on the underlying systems' error properties, e.g., the spontaneous emission and dephasing times $T_1$ and $T_2$. As opposed to standard quantum error correction methods, which have an overhead in the number of qubits (many physical qubits must be added for each logical qubit), our method has only an overhead in the number of evaluations, allowing the overhead to, in principle, be hidden via parallelization. We show that the effective spontaneous emission $T_1$ and dephasing $T_2$ times can be increased using this method in both simulation and experiments on an actual quantum computer. We also show how to correct more complicated entangled states and how Ramsey fringes relevant to quantum sensing can be significantly extended in time.

The multiconfiguration Dirac-Hartree-Fock method is employed to calculate the continuum electron wave functions, which are then used to estimate their contribution to the atomic electric dipole moment (EDM) of ${}^{129}\mathrm{Xe}$. The EDM arises from $(P,T)$-odd electron-nucleon tensor-pseudotensor and pseudoscalar-scalar interactions, the nuclear Schiff moment, the interaction of the electron electric dipole moment with nuclear magnetic moments, and atomic electric dipole matrix elements. In addition to being estimated in the continuum states, all of these interactions are also estimated in the ground state, as well as in the Rydberg states of ${}^{129}\mathrm{Xe}$. Calculations of one-electron atomic orbitals include the interelectronic interactions, through valence and core-valence electron correlation effects. The contribution to the EDM from continuum states is found to be of the same order of magnitude as the contribution from discrete states.

Harnessing the dynamics of a microscopic system lies at the core of quantum information processing. For quantum systems with a small number of spins, optimal control has been shown to be an efficient method to realize high-fidelity quantum control. As the number of the spins increases, it becomes challenging to steer the dynamics of the quantum system due to the exponentially increasing dimension of Hilbert space. Herein, we propose a method to realize optimal control of a spin bath consisting of hundreds of spins. A central spin is used to monitor the dynamics of the spin bath under a control Hamiltonian. The information obtained from the central spin is fed back to the control Hamilton to realize optimal control over the spin bath. We take a nitrogen vacancy (NV) center in diamond as an example, and our numerical simulation shows that the dephasing time of the NV center can be improved by more than 2 orders of magnitude. Furthermore, our method is compatible with dc magnetometry, whose sensitivity can be improved by an order of magnitude compared to conventional Ramsey interference. Our method is also feasible for various other spin-based systems, such as quantum dots, phosphorus-doped silicon, and defects in silicon carbide.