We address the question of finding the most unbalanced convex decompositions into boundary elements (so-called boundariness) for sets of quantum states, observables, and channels. We show that in general convex sets the boundariness essentially coincides with the question of the most distinguishable element, thus providing an operational meaning for this concept. Unexpectedly, we discovered that for any interior point of the set of channels the most unbalanced decomposition necessarily contains a unitary channel. In other words, for any given channel the most distinguishable one is some unitary channel. Further, we prove that boundariness is submultiplicative under the composition of systems and explicitly evaluate its maximal value that is attained only for the most mixed elements of the considered sets.

The determination of many special types of quantum states has been studied thoroughly, such as the generalized $|\text{GHZ}\rangle$ states, stochastic local operations and classical communication equivalent $|W\rangle$ states, and Dicke states. In this paper, we study another special entanglement state, that is, stabilizer states, which play an important role in quantum error correcting codes, multipartite purification, and so on. We show that all $n$-qubit stabilizer states are uniquely determined (among arbitrary states, pure or mixed) by their reduced density matrices for systems which are the supports of $n$ independent generators of the corresponding stabilizer formalisms.

Compton scattering of twisted photons is investigated within a nonrelativistic framework using first-order perturbation theory. We formulate the problem in the density-matrix theory, which enables one to gain new insights into scattering processes of twisted particles by exploiting the symmetries of the system. In particular, we analyze how the angular distribution and polarization of the scattered photons are affected by the parameters of the initial beam such as the opening angle and the projection of orbital angular momentum. We present analytical and numerical results for the angular distribution and the polarization of Compton scattered photons for initially twisted light and compare them with the standard case of plane-wave light.

We investigate the ground-state and finite-temperature properties of the Bose-Hubbard model using the standard basis operator method applied to the equation of motion for Green's functions. We show that by introducing the self-consistent approach, the theory goes significantly beyond the mean-field approximation, allowing more-precise description of quantum and thermal fluctuations. For optical lattice systems with ultracold bosons, we find relevant quantitative agreement with numerical and experimental data. In particular, the presented method reveals the importance of thermal fluctuations in time-of-flight experiments. For the most reliable fitting of the visibility analytical curve to the experimental data, the value of temperature is determined and proximity to the quantum regime is discussed. The problem of identification of the superfluid–Mott-insulator phase boundary from time-of-flight experiments is also considered.

We establish a nonequilibrium scaling regime in the short-time evolution of one-dimensional interacting open quantum systems subject to a generic heating mechanism. This dynamical regime is characterized by uncompensated phonon production and a superdiffusive, universal scaling of quasiparticle lifetimes with momentum $\sim q^{-5/3}$, distinct from the finite- and zero-temperature cases. It is separated from a high-momentum regime by a time-dependent scale fading out as $q_0\left(t\right)\sim t^{-4/5}$. In the latter region we observe thermalization to an effective time-dependent equilibrium with linearly increasing temperature. By mapping out the dynamical phase diagram and computing the dynamical structure factor within an open-system Keldysh functional integral approach, we show how these predictions can be explored in cold-atom experiments by means of Bragg spectroscopy.

We systematically investigate the ground-state and elementary excitations of a Bose-Einstein condensate within a synthetic vector potential, which is induced by the many-body effects and atom-light coupling. For a sufficiently strong spin-dependent interaction, we find the condensate undergoes a Stoner-type ferromagnetic transition through the self-consistent coupling with the vector potential. For a weak interaction, the critical velocity of a supercurrent is anisotropic due to the density fluctuations affecting the gauge field. We further analytically demonstrate the topological ground state with a coreless vortex ring in a three-dimensional (3D) harmonic trap and a coreless vortex-antivortex pair in a two-dimensional (2D) trap. The circulating persistent current is measurable in the time-of-flight experiment or in the dipolar oscillation through the violation of the Kohn theorem.

Arrays of evanescently coupled waveguides can be used to retrieve simultaneously the first-order correlation functions in multiple-field interferometry. Here it is shown that this remarkable property of waveguide arrays is enabled only by the existence of nonlocal interaction, i.e., non-nearest-neighbor coupling between the waveguides.

We examine a class of operations for topological quantum computation based on fusing and measuring topological charges for systems with $\mathrm{SU}{\left(2\right)}_4$ or $k=4$ Jones-Kauffman anyons. We show that such operations augment the braiding operations, which, by themselves, are not computationally universal. This augmentation results in a computationally universal gate set through the generation of an exact, topologically protected irrational phase gate and an approximate, topologically protected controlled-$Z$ gate.

By coupling pairs of superconducting qubits through a small Josephson junction with a time-dependent flux bias, we show that arbitrary interactions involving any combination of Pauli matrices can be generated with a small number of drive tones applied through the flux bias of the coupling junction. We then demonstrate that similar (though not fully universal) results can be achieved in capacitively coupled qubits by exploiting the higher energy states of the devices through multiphoton drive signals applied to the qubits' flux degrees of freedom. By using this mechanism to couple a qubit to a detuned resonator, the qubit's rotating-frame state can be nondestructively measured along any direction on the Bloch sphere. Finally, we describe how the frequency-converting nature of the couplings can be used to engineer a mechanism analogous to dynamic nuclear polarization in NMR systems, capable of cooling an array of qubits well below the ambient temperature, and outline how higher-order interactions, such as local three-body terms, can be engineered through the same couplings. Our results demonstrate that a programmable quantum simulator for large classes of interacting spin models could be engineered with the same physical hardware.

The quantum Zeno effect (QZE) is the phenomenon in which the unitary evolution of a quantum state is suppressed, e.g., due to frequent measurements. Here, we investigate the use of the QZE in a class of communication complexity problems (CCPs). Quantum entanglement is known to solve certain CCPs beyond classical constraints. However, recent developments have yielded CCPs for which superclassical results can be obtained using only communication of a single $d$-level quantum state (qudit) as a resource. In the class of CCPs considered here, we show quantum reduction of complexity in three ways: using (i) entanglement and the QZE, (ii) a single qudit and the QZE, and (iii) a single qudit. We have performed a proof of concept experimental demonstrations of three party CCP protocol based on single-qubit communication with and without QZE.

We report the absolute frequency values of all (ten) hyperfine transitions of $5P_{3/2}-4D_{5/2}$ and $5P_{3/2}-4D_{3/2}$ for ${}^{87}\mathrm{Rb}$ and ${}^{85}\mathrm{Rb}$ atoms via the use of an optical frequency comb by measuring the frequency of a laser diode stabilized onto the line centers of the double-resonance optical pumping spectra. Here we report on the absolute frequencies for the two transitions $[{}^{85}\mathrm{Rb},5P_{3/2}(F^{\prime }=4)-4D_{5/2}(F^{\prime \prime }=3,4)]$. Furthermore, the frequency uncertainties are reduced significantly for the other transitions. Moreover, the magnetic dipole and the electric quadrupole hyperfine structure constants of $4D_{5/2}$ for ${}^{87}\mathrm{Rb}$ and ${}^{85}\mathrm{Rb}$ are determined by using the measured values of the absolute frequency.

We use quantum Monte Carlo and exact diagonalization calculations to study the Mott-insulator–to–superconductor quantum phase transition in a two-dimensional fermionic Hubbard model with attractive interactions in the presence of a superlattice potential. The model introduced offers unique possibilities to study such transitions in optical lattice experiments. We show that, in regimes with moderate to strong interactions, the transition belongs to the three-dimensional $XY$ universality class. We also explore the character of the lowest-energy charge excitations in the insulating and superconducting phases and show that they can be fermionic or bosonic depending on the parameters chosen.

Interaction of atoms with quantum states of light is a long-standing problem that apart from fundamental physics has potential applications for optical quantum-state storage, quantum communication, and quantum information. A fully quantum mechanical treatment of this problem is usually very complicated mathematically. Here we show, however, that quantum mechanical evolution equations describing single-photon emission (absorption) by atomic ensembles can be written in a form equivalent to the semiclassical Maxwell-Bloch equations. This connection allows us to find exact analytical solutions of the fully quantum mechanical problem. We also found that semiclassical Maxwell-Bloch equations should be written in a form different from those commonly used. Namely, the classical limit of the quantum problem gives a propagation equation with the Laplacian operator on the right-hand side rather than with the second-order time derivative.

In conical refraction, when a focused Gaussian beam passes along one of the optic axes of a biaxial crystal, it is transformed into a pair of concentric bright rings at the focal plane. We demonstrate both theoretically and experimentally that this transformation is hardly affected by partially blocking the Gaussian input beam with an obstacle. We analyze the influence of the size of the obstruction both on the transverse intensity pattern of the beam and on its state of polarization, which is shown to be very robust.

Mutually unbiased bases (MUBs) are interesting for various reasons. The most attractive example of (a complete set of) MUBs is the one constructed by Ivanović as well as Wootters and Fields, which is referred to as the canonical MUB. Nevertheless, little is known about anything that is unique to this MUB. We show that the canonical MUB in any prime power dimension is uniquely determined by an extremal orbit of the (restricted) Clifford group except in dimension 3, in which case the orbit defines a special symmetric informationally complete measurement (SIC), known as the Hesse SIC. Here the extremal orbit is the orbit with the smallest number of pure states. Quite surprisingly, this characterization does not rely on any concept that is related to bases or unbiasedness. As a corollary, the canonical MUB is the unique minimal 2-design covariant with respect to the Clifford group except in dimension 3. In addition, these MUBs provide an infinite family of highly symmetric frames and positive-operator-valued measures (POVMs), which are of independent interest.

We improve upon a recently introduced efficient quantum state reconstruction procedure targeted to states well approximated by the multiscale entanglement renormalization ansatz (MERA), e.g., ground states of critical models. We show how to numerically select a subset of experimentally accessible measurements which maximize information extraction about renormalized particles, thus dramatically reducing the required number of physical measurements. We numerically estimate the number of measurements required to characterize the ground state of the critical one-dimensional Ising (resp. XX) model and find that MERA tomography on 16-qubit (resp. 24-qubit) systems requires the same experimental effort as brute-force tomography on 8 qubits. We derive a bound computable from experimental data which certifies the distance between the experimental and reconstructed states.

Single-photon interference due to passage through a periodic grating is considered in a novel proposal for processing $D$-dimensional quantum systems (quDits) encoded in the spatial degrees of freedom of light. We show that free-space propagation naturally implements basic single-quDit gates by means of the Talbot effect: an intricate time-space carpet of light in the near-field diffraction regime. By adding a diagonal phase gate, we show that a complete set of single-quDit gates can be implemented. We then introduce a spatially dependent beam splitter that allows for projective measurements in the computational basis and can be used for the implementation of controlled operations between two quDits. Universal quantum information processing can then be implemented with linear optics and ancilla photons via postselection and feed-forward following the original proposal of Knill-Laflamme and Milburn. Although we consider photons, our scheme should be directly applicable to a number of other physical systems. Interpretation of the Talbot effect as a quantum logic operation provides a beautiful and interesting way to visualize quantum computation through wave propagation and interference.

We present a critical assessment of the applicability of the Debye-Hückel (DH) approximation to the redshift of the Lyman-$\alpha$ emission line of the H-like ions under a dense plasma environment. By carefully considering the $2p\to 1s$ transition spatially and temporally, our investigation suggests that the DH approximation may be applied to a limited number of H-like ions, such as the ones with $Z$ between 5 and 18 or with $Z$ greater than 50. Our numerical calculation, in fact, leads to quantitative agreement with the observed redshift of the well-isolated Lyman-$\alpha$ line at plasma density of the order of $1\times {10}^{22}$ ${\mathrm{cm}}^{-3}$ or higher with an electron temperature of several hundred eV of H-like ${\mathrm{Al}}^{12+}$. Our study also yields simulated data consistent with those from more elaborate quantum mechanical approaches.

We show theoretically that periodic density patterns are stabilized in two counterpropagating Bose-Einstein condensates of atoms in different hyperfine states under Rabi coupling. In the presence of coupling, the relative velocity between the two components is localized around density depressions in quasi-one-dimensional systems. When the relative velocity is sufficiently small, the periodic pattern reduces to a periodic array of topological solitons as kinks of the relative phase. According to our variational and numerical analyses, the soliton solution is well characterized by the soliton width and density depression. We demonstrate the dependence of the depression and width on the Rabi frequency and the coupling constant of the intercomponent density-density interactions. The periodic pattern of the relative phase transforms continuously from a soliton array to a sinusoidal pattern as the period becomes smaller than the soliton width. These patterns become unstable when the localized relative velocity exceeds a critical value. The stability-phase diagram of this system is evaluated with a stability analysis of countersuperflow, by taking into account the finite-size effect owing to the density depression.