How can relevant information be extracted from a quantum information source? In many situations, only some part of the total information content produced by an information source is useful. Can one then find an efficient encoding, in the sense of retaining the largest fraction of relevant information? This paper offers one possible solution by giving a generalization of a classical method designed to retain as much relevant information as possible in a lossy data compression. A key feature of the method is to introduce a second information source to define relevance. We quantify the advantage a quantum encoding has over the best classical encoding in general, and we demonstrate using examples that a substantial quantum advantage is possible. We show analytically, however, that if the relevant information is purely classical, then a classical encoding is optimal.

One of the most fundamental problems in quantum many-body systems is the identification of a mean field in spontaneous symmetry breaking which is usually made in a heuristic manner. We propose a systematic method of finding a mean field based on the Lie algebra and the dynamical symmetry by introducing a class of symmetry-broken phases which we call $\mu$-symmetry breaking. We show that for $\mu$-symmetry breaking the quadratic part of an effective Lagrangian of Nambu-Goldstone modes can be block-diagonalized and that homotopy groups of topological excitations can be calculated systematically.

Interactions between many-body atomic systems in optical lattices and light in cavities induce long-range and correlated atomic dynamics beyond the standard Bose-Hubbard model, due to the global nature of the light modes. We characterize these processes, and show that uniting such phenomena with dynamical constraints enforced by the backaction resultant from strong light measurement leads to a synergy that enables the atomic dynamics to be tailored, based on the particular optical geometry, exploiting the additional structure imparted by the quantum light field. This leads to a range of tunable effects such as long-range density-density interactions, perfectly correlated atomic tunneling, superexchange, and effective pair processes. We further show that this provides a framework for enhancing quantum simulations to include such long-range and correlated processes, including reservoir models and dynamical global gauge fields.

For fermionic fields with nonzero mass, it is shown that the spinor factor of the anticommutation relation between creation and annihilation operators can be justified in a natural way, based on basic properties of Lorentz-invariant inner product in Hilbert space. Furthermore, from the physical point that predictions for measurement results should take real and definite values, we examine the basic requirements for inner product and propose to make certain relaxation to them. Under the relaxed requirements, there exists an alternative way of introducing the anticommutation relation, independent of the mass. In a theory with the latter type of anticommutation relation, the ultraviolet divergence may become less serious than that met in ordinary theories.

Excited-state quantum phase transitions (ESQPTs) are generalizations of quantum phase transitions to excited levels. They are associated with local divergences in the density of states. Here, we investigate how the presence of an ESQPT can be detected from the analysis of the structure of the Hamiltonian matrix, the level of localization of the eigenstates, the onset of bifurcation, and the speed of the system evolution. Our findings are illustrated for a Hamiltonian with infinite-range Ising interaction in a transverse field. This is a version of the Lipkin-Meshkov-Glick (LMG) model and the limiting case of the one-dimensional spin-$\frac{1}{2}$ system with tunable interactions realized with ion traps. From our studies for the dynamics, we uncover similarities between the LMG and the noninteracting XX models.

When two qubits, $A$ and $B$, are in an appropriate state, Alice can remotely steer Bob's system $B$ into different ensembles by making different measurements on $A$. This famous phenomenon is known as quantum steering, or Einstein-Podolsky-Rosen steering. Importantly, quantum steering establishes the correspondence not only between a measurement on $A$ (made by Alice) and an ensemble of $B$ (owned by Bob) but also between each of Alice's measurement outcomes and an unnormalized conditional state of Bob's system. The unnormalized conditional states of $B$ corresponding to all possible measurement outcomes of Alice are called Alice's steering outcomes. We show that, surprisingly, the four-dimensional geometry of Alice's steering outcomes completely determines both the nonseparability of the two-qubit state and its steerability from her side. Consequently, the problem of classifying two-qubit states into nonseparable and steerable classes is equivalent to geometrically classifying certain four-dimensional skewed double cones.

Compared to the quantum noise in the measurement of the translational motion of a suspended mirror using laser light, the quantum noise in the measurement of the angular motion of a suspended mirror has not been investigated intensively despite its potential importance. In this article, an expression for the quantum noise in the angular motion measurement is explicitly derived. The expression indicates that one quadrature of the vacuum field of the first-order Hermite-Gaussian mode of light causes quantum sensing noise and the other causes quantum back-action noise, or in other words the first-order vacuum field is ponderomotively squeezed. It is also shown that the Gouy phase shift the light acquires between the mirror and the position of detection of the light corresponds to the homodyne angle. Therefore, the quantum back-action noise can be canceled and the standard quantum limit can be surpassed by choosing the appropriate position of detection analogously to the cancellation of quantum radiation pressure noise by choosing an appropriate homodyne angle.

We consider entanglement swapping, a key component of quantum network operations and entanglement distribution. Pure entangled states, which are the desired input to the swapping protocol, are typically mixed by environmental interactions, causing a reduction in their degree of entanglement. Thus an understanding of entanglement swapping with partially mixed states is of importance. Here we present a general analytical solution for entanglement swapping of arbitrary two-qubit states. Our result provides a comprehensive method for analyzing entanglement swapping in quantum networks. First, we show that the concurrence of a partially mixed state is conserved when this state is swapped with a Bell state. Then, we find upper and lower bounds on the concurrence of the state resulting from entanglement swapping for various classes of input states. Finally, we determine a general relationship between the ranks of the initial states and the rank of the final state after swapping.

We report a method that exploits a connection between quantum contextuality and graph theory to reveal any form of quantum contextuality in high-precision experiments. We use this technique to identify a graph which corresponds to an extreme form of quantum contextuality unnoticed before and test it using high-dimensional quantum states encoded in the linear transverse momentum of single photons. Our results open the door to the experimental exploration of quantum contextuality in all its forms, including those needed for quantum computation.

We report the energy and angular distribution of ejected electrons from $\mathrm{C}{\mathrm{H}}_4$ and ${\mathrm{H}}_2\mathrm{O}$ molecules impacted by 1 MeV ${\mathrm{H}}^{+}, \mathrm{H}{\mathrm{e}}^{+}$, and 650 keV ${\mathrm{N}}^{+}$ ions. Spectra were measured at different observation angles, from 2 to 2000 eV. The obtained absolute double-differential electron-emission cross sections (DDCSs) were compared with the results of classical trajectory Monte Carlo (CTMC) and continuum distorted wave, eikonal initial state (CDW-EIS) calculations. For the bare ${\mathrm{H}}^{+}$ projectile both theories show remarkable agreement with the experiment at all observed angles and energies. The CTMC results are in similarly good agreement with the DDCS spectra obtained for impact by dressed $\mathrm{H}{\mathrm{e}}^{+}$ and ${\mathrm{N}}^{+}$ ions, where screening effects and electron loss from the projectile gain importance. The CDW-EIS calculations slightly overestimate the electron loss for 1 MeV $\mathrm{H}{\mathrm{e}}^{+}$ impact, and overestimate both the target and projectile ionization at low emitted electron energies for 650 keV ${\mathrm{N}}^{+}$ impact. The contribution of multiple electron scattering by the projectile and target centers (Fermi shuttle) dominates the ${\mathrm{N}}^{+}$-impact spectra at higher electron energies, and it is well reproduced by the nonperturbative CTMC calculations. The contributions of different processes in medium-velocity collisions of dressed ions with molecules are determined.

We have studied the $K^{-2}V$ process corresponding to simultaneous $K$-shell ionization and $K$-shell excitation in the $\mathrm{C}{\mathrm{O}}_2$ molecule. We define these $K^{-2}V$ states as super shake-up, at variance with the “conventional” $K^{-1}{v}^{-1}V$ shake-up states. While the nature and evolution with photon energy of the conventional shake-up satellites has been the object of many studies, no such data on a large photon-energy range were previously reported on super shake-up. The $\mathrm{C}{\mathrm{O}}_2$ molecule is a textbook example because it exhibits two well-isolated $K^{-2}V$ resonances (with V being $2{\pi }_u^{*}$ and $5{\sigma }_g^{*}$) with different symmetries resulting from shake-up processes of different origin populated in comparable proportions. The variation of the excitation cross section of these two resonances with photon energy is reported, using two different experimental approaches, which sheds light on the excitation mechanisms. Furthermore, double-core-hole spectroscopy is shown to be able to integrate and even expand information provided by conventional single-core-hole X-ray Photoelectron Spectroscopy (XPS) and Near-Edge X-ray Absorption Fine Structure (NEXAFS) techniques, revealing, for instance, $g-g$ dipole forbidden transitions which are only excited in NEXAFS spectra through vibronic coupling.

Among many of the nonlinear phenomena induced by strong laser pulses, two of the important processes are the harmonic generation and the creation of neutral atoms in the Rydberg states. We carry out a joint study of the below-threshold high-order-harmonic (BTH) generation and the production of low-lying Rydberg atoms driven by an intense few-cycle midinfrared laser pulse. Our results are based on the numerical solution to the three-dimensional time-dependent Schrödinger equation within the single active electron approximation and a semiclassical simulation. The yields of BTH and low-lying Rydberg atoms are found to have a similar carrier envelope phase dependence. We find that both processes can be faithfully described semiclassically in the deep tunneling regime. The trajectory analysis shows that these two processes share the same series of trajectories and can be simultaneously manipulated by the driving pulse shape. Our finding bridges the below-threshold high-order-harmonic generation and the frustrated tunneling ionization.

Electric-field noise is a major source of motional heating in trapped-ion quantum computation. While the influence of trap-electrode geometries on electric-field noise has been studied in patch potential and surface adsorbate models, only smooth surfaces are accounted for by current theory. The effects of roughness, a ubiquitous feature of surface electrodes, are poorly understood. We investigate its impact on electric-field noise by deriving a rough-surface Green's function and evaluating its effects on adsorbate-surface binding energies. At cryogenic temperatures, heating-rate contributions from adsorbates are predicted to exhibit an exponential sensitivity to local surface curvature, leading to either a large net enhancement or suppression over smooth surfaces. For typical experimental parameters, orders-of-magnitude variations in total heating rates can occur depending on the spatial distribution of adsorbates. Through careful engineering of electrode surface profiles, our results suggests that heating rates can be tuned over orders of magnitudes.

A rigorous theoretical framework is developed for a generalized local-frame-transformation theory (GLFT). The GLFT is applicable to the following systems: Rydberg atoms or molecules in an electric field and negative ions in any combination of electric and/or magnetic fields. A first test application to the photoionization spectra of Rydberg atoms in an external electric field demonstrates dramatic improvement over the first version of the local-frame-transformation theory developed initially by U. Fano [Phys. Rev. A 24, 619 (1981)] and D. A. Harmin [Phys. Rev. A 26, 2656 (1982)]. This revised GLFT theory yields nontrivial corrections because it now includes the full on-shell Hilbert space without adopting the truncations in the original theory. Comparisons of the semianalytical GLFT Stark spectra with ab initio numerical simulations yield errors in the range of a few tens of MHz, an improvement over the original Fano-Harmin theory, whose errors are 10–100 times larger. Our analysis provides a systematic pathway to precisely describe the corresponding photoabsorption spectra that should be accurate enough to meet most modern experimental standards.

The finite-speed-of-light (FSL) effect is a systematic error in atom gravimeters arising from the time delay due to the propagation of the light. It includes the frequency-chirp-independent part and the frequency-chirp-dependent part, which were not considered completely. The FSL effect in atom gravimeters is different from that in corner-cube absolute gravimeters. In the past, this effect has been widely studied in corner-cube absolute gravimeters, whereas little has been discussed about and done with atom gravimeters. In this paper, we mainly propose a complete analytical study based on a coordinate transformation and on a “perturbation” approach to estimate this effect in an atom gravimeter. This also offers the potential to calculate the general relativistic effects in atom gravimeters. In addition, a comparison with a crude “average-path” analysis is given for a particular case of the FSL effect in atom gravimeters.

We study the localization transition of an atom confined by an external optical lattice in a high-finesse cavity. The atom-cavity coupling yields an effective secondary lattice potential, whose wavelength is incommensurate with the periodicity of the optical lattice. The cavity lattice can induce localization of the atomic wave function analogously to the Aubry-André localization transition. Starting from the master equation for the cavity and the atom we perform a mapping of the system dynamics to a Hubbard Hamiltonian, which can be reduced to the Harper's Hamiltonian in appropriate limits. We evaluate the phase diagram for the atom's ground state and show that the transition between extended and localized wave function is controlled by the strength of the cavity nonlinearity, which determines the size of the localized region and the behavior of the Lyapunov exponent. The Lyapunov exponent, in particular, exhibits resonancelike behavior in correspondence with the optomechanical resonances. Finally we discuss the experimental feasibility of these predictions.

We introduce a Hermitian generalization of Pauli matrices to higher dimensions which is based on Heisenberg-Weyl operators. The complete set of Heisenberg-Weyl observables allows us to identify a real-valued Bloch vector for an arbitrary density operator in discrete phase space, with a smooth transition to infinite dimensions. Furthermore, we derive bounds on the sum of expectation values of any set of anticommuting observables. Such bounds can be used in entanglement detection and we show that Heisenberg-Weyl observables provide a first nontrivial example beyond the dichotomic case.

Finding efficient descriptions of how an environment affects a collection of discrete quantum systems would lead to new insights into many areas of modern physics. Markovian, or time-local, methods work well for individual systems, but for groups a question arises: Does system-bath or intersystem coupling dominate the dissipative dynamics? The answer has profound consequences for the long-time quantum correlations within the system. We consider two bosonic modes coupled to a bath. By comparing an exact solution against different Markovian master equations, we find that a smooth crossover of the equations of motion between dominant intersystem and system-bath coupling exists—but it requires a nonsecular master equation. We predict singular behavior of the dynamics and show that the ultimate failure of nonsecular equations of motion is essentially a failure of the Markov approximation. Our findings support the use of time-local theories throughout the crossover between system-bath-dominated and intersystem-coupling-dominated dynamics.

Monogamy is a fundamental property of Bell nonlocality and contextuality. In this article, we study the $n$-cycle noncontextual inequalities and generalized Clauser-Horne-Shimony-Holt (CHSH) inequalities in detail and find sufficient conditions for those inequalities to hold. According to those conditions, we provide several kinds of tradeoff relations: monogamy of generalized Bell inequalities in a nonsignaling framework, monogamy of cycle-type noncontextual inequalities, and monogamy between Bell inequalities and noncontextual inequalities in a general no-disturbance framework. Finally, some generic tradeoff relations of generalized CHSH inequalities for $n$-party physical systems, which are beyond the one-to-many scenario, are discussed.