A major milestone of quantum error correction is to achieve the fault-tolerance threshold beyond which quantum computers can be made arbitrarily accurate. This requires extraordinary resources and engineering efforts. We show that, even without achieving full fault tolerance, quantum error detection is already useful on the current generation of quantum hardware. We demonstrate this experimentally by executing an end-to-end chemical calculation for the hydrogen molecule encoded in the [[4, 2, 2]] quantum error-detecting code. The encoded calculation with logical qubits significantly improves the accuracy of the molecular ground-state energy.

General relativity is a classical field theory and therefore does not predict gravitationally induced entanglement. As such, recent proposals have focused on seeking an empirical demonstration of this feature. We introduce improvements to a spin witness protocol that reduce the highly challenging experimental requirements. After rigorously assessing approximations from the original proposal [S. Bose et al., Phys. Rev. Lett. 119, 240401 (2017)], we focus on entanglement witnessing. We propose a witness which greatly reduces the required interaction time, thereby making the experiment feasible for higher decoherence rates, and we show how statistical analysis can separate the gravitational contribution from other possibly dominant and ill-known interactions. We point out a potential loophole and show how it can be closed using state tomography.

Rigorous mathematical proofs of the security of continuous-variable quantum key distribution (CV QKD) have been obtained recently. Unfortunately, these security proofs rely on assumptions that are hardly met in experimental practice. Here I investigate these issues in detail, and discuss experimentally friendly workarounds to assess the security of CV QKD. The aim of this paper is to show that there are hidden and unsolved issues and to indicate possible partial solutions. To provide a complete and rigorous mathematical security proof is out of the scope of this contribution.

Low-energy collision experiments of ${\mathrm{Ar}}^{8+}$ with acetylene (${\mathrm{C}}_2{\mathrm{H}}_2$) molecules were conducted, and four-body dissociation of highly ionized acetylene was studied focusing on charge-sharing dynamics in two dissociating carbon (C) ions. When the C ions shared three positive charges, the kinetic energy distributions of the two terminal protons, one from the near-site carbon detected as ${\mathrm{C}}^{2+}$ and the other from the other site, were quite similar, indicating equal sharing of the charges by the two C atoms until the C-C bond was elongated to at least about 200 pm. When the carbons had four positive charges to be shared after dissociation by a ${\mathrm{C}}^{3+}$ and a ${\mathrm{C}}^{+}$ pair, the kinetic energy of the ${\mathrm{H}}^{+}$ ion from the $3+$ site was higher than its counterpart, while the difference was much smaller than the pure Coulombic value for ${\mathrm{C}}^{3+}$ and ${\mathrm{C}}^{+}$ sharing from the beginning of dissociation.

We present electric dipole polarizabilities (${\alpha }_d$) of the alkali-metal negative ions, from ${\mathrm{H}}^{-}$ to ${\mathrm{Fr}}^{-}$, by employing four-component relativistic many-body methods. Differences in the results are shown by considering Dirac-Coulomb (DC) Hamiltonian, DC Hamiltonian with the Breit interaction, and DC Hamiltonian with the lower-order quantum electrodynamics interactions. At first, these interactions are included self-consistently in the Dirac-Hartree-Fock (DHF) method, and then electron correlation effects are incorporated over the DHF wave functions in the second-order many-body perturbation theory, random phase approximation, and coupled-cluster (CC) theory. Roles of electron correlation effects and relativistic corrections are analyzed using the above many-body methods with size of the ions. We finally quote precise values of ${\alpha }_d$ of the above negative ions by estimating uncertainties to the CC results, and compare them with other calculations wherever available.

Reduced density matrix equations combined with a cluster molecular-orbital method are formulated to describe resonant core-valence electron excitation by an intense femtosecond x-ray pulse. The electron-hole interaction is treated by the time-dependent unrestricted Hartree-Fock approximation supplemented by a screening correction in the Born approximation. Nonlinear $K$-shell absorption spectra of metallic copper are thereby computed. Numerical results indicate that, in the third-order nonlinear regime, where the fraction of excited electrons increases in proportion to the x-ray intensity, the absorption spectra above the $K$ edge undergo shifts toward high-energy side. The origin of this third-order nonlinearity can be traced to a negative renormalization of the core orbital energy due to strong electron-hole attraction, which offers a sharp contrast to the usual optical nonlinearity due simply to the increment of upper-state populations. For higher intensities, broadening of the absorption edge and saturation of absorption are predicted. These trends are qualitatively consistent with nonlinear spectroscopy experiments using the SACLA x-ray free-electron laser.

Quantum backflow is the classically forbidden effect pertaining to the fact that a particle with a positive momentum may exhibit a negative probability current at some space-time point. We investigate how this peculiar phenomenon extends to many-particle systems. We give a general formulation of quantum backflow for systems formed of $N$ free nonrelativistic structureless particles, either identical or distinguishable. Restricting our attention to bosonic systems where the $N$ identical bosons are in the same one-particle state allows us in particular to analytically show that the maximum achievable amount of quantum backflow in this case becomes arbitrarily small for large values of $N$.

We present diffusion Monte Carlo calculations on the behavior of a mixture of ${}^{173}\mathrm{Yb}$ and ${}^{171}\mathrm{Yb}$ fermionic isotopes in a one-dimensional environment. The interaction parameters between species were modeled by $\delta$ potentials, whose strengths were taken from their experimental scattering lengths and varied by changing the transversal confinement. This implies a repulsive interaction for the ${}^{173}\mathrm{Yb}-{}^{173}\mathrm{Yb}$ pair, a strong attractive one for the ${}^{173}\mathrm{Yb}-{}^{171}\mathrm{Yb}$ set, and a weak attraction between ${}^{171}\mathrm{Yb}-{}^{171}\mathrm{Yb}$ atoms. Those arrangements were described by a corrected geminal multiplied by the appropriate set of Jastrow functions. We found that, for the same number of strong attractive pairs, the width of the cluster decreases when the number of fermionic species increases, the narrower cluster being the one that includes a mixture of six ${}^{173}\mathrm{Yb}$ species and two ${}^{171}\mathrm{Yb}$ spin types.

Passing a photon number state through a balanced beam splitter will produce an entangled state in which the phases of the two output beams are highly correlated. This entangled state can be viewed as a generalized form of a Schrödinger cat state where there is an equal probability amplitude for all possible phases. We show that Bell's inequality can be violated using this entangled state and two distant measuring devices that consist of a single-photon interferometer with a Kerr medium in one path, a set of single-photon detectors, and postselection based on a homodyne measurement. These entangled states are sensitive to photon loss and a violation of Bell's inequality requires either that the losses are inherently small or that their effects have been minimized using linear optics techniques [Micuda et al., Phys. Rev. Lett. 109, 180503 (2012)]. Somewhat surprisingly, the use of the fair sampling assumption is not required for a violation of Bell's inequality despite the use of postselection if the measurements are made in the correct order.

Appearance of adiabatic geometric phase shift in the context of noncommutative quantum mechanics is studied using an exactly solvable model of a two-dimensional simple harmonic oscillator in the Moyal plane, where momentum noncommutativity are also considered along with spatial noncommutativity. For that we introduce a modified form of Bopp's shift, that bridges the noncommutative phase-space operators with their effective commutative counterparts, having their dependence on the noncommutative parameters, and study the adiabatic evolution in the Heisenberg picture. An explicit expression for the geometric phase shift under adiabatic approximation is then found without using any perturbative technique. Lastly, this phase is found to be related to Hannay's angle of a classically analogous system, by studying the evolution of the coherent state of this system.

Hyperentanglement has a higher information density than conventional single-degree-of-freedom entanglement, which has attracted much attention due to its fascinating applications in quantum communication. However, since the inevitable interactions between quantum entangled systems and the environment will drive hyperentangled systems into less hyperentangled states or even mixed hyperentangled states, the efficiency and security of quantum communication will be greatly depressed. The currently existing distillation protocols are not universal, i.e., they only work for the lossy hyperentangled states in specific systems. In this paper, based on local positive-operator-valued measures (POVMs), we present a distillation protocol for lossy hyperentangled photonic Bell and Greenberger-Horne-Zeilinger (GHZ) states. The intrinsic property of our protocol is twofold, i.e., the POVM nature of the protocol guarantees that the protocol is a universal one, and the distillation operation on only one of the two degrees of freedom (DOFs) can enhance the fidelity of the system in both DOFs. Furthermore, in the implementation level, our hyperentanglement distillation protocol (HEDP) has other two merits: no auxiliary local entanglement resources and sophisticated single-photon detectors are required, and only one copy of the lossy state will be operated in each distillation round, which show that our HEDPs are relatively simple and feasible.

Quantum Gibbs state sampling algorithms generally suffer from either scaling exponentially with system size or requiring specific knowledge of spectral properties a priori. These algorithms also require a large overhead of bath or scratch or ancilla qubits. We propose a method, termed the minimal effective Gibbs ansatz (MEGA), which uses a quantum computer to determine a small effective ensemble of pure states that accurately reproduce thermal averages of an objective dynamic correlation function. This technique employs properties of correlation functions that can be split into lesser and greater parts; here, we primarily focus on single-particle Green's functions and density-density correlators. When properly measured, these correlation functions provide a simple test to indicate how close a given pure state or ensemble of pure states is to providing accurate thermal expectation values. Further, we show that, when properties such as the eigenstate thermalization hypothesis hold, this approach leads to accurate results with a sparse ensemble of pure states; sometimes only one suffices. We illustrate the ansatz using exact diagonalization simulations on small clusters for the Fermi-Hubbard and Hubbard-like models. Even if the MEGA becomes as computationally complex as other Gibbs state samplers, it still gains an advantage due to its ease of implementation without any a priori information about the Hamiltonian and in the efficient allocation of available qubits by eliminating bath qubits and using a minimal number of ancillas.

We have observed the process $\mathrm{Rb}ns+\mathrm{Rb}ns+2h\nu \to \mathrm{Rb}n{p}_{1/2}+\mathrm{Rb}n{p}_{3/2}$ from $n=34$ to $n=40$ in a frozen gas of Rb Rydberg atoms. It is resonant when the microwave frequency is halfway between the $ns\to n{p}_{1/2}$ and $ns\to n{p}_{3/2}$ frequencies, which range from 57 to 106 GHz. The process cannot occur in isolated atoms, nor can it occur if the magnetic quantum numbers are unchanged, an implicit assumption of one-dimensional models. A Floquet-Forster model shows that the coupling between the initial and final states involves the absorption of two microwave photons and the dipole-dipole interaction, which leads to a coupling proportional to the product of the density, the microwave field squared, and $n^{*14}$, where $n^{*}$ is the effective quantum number of the $n{p}_{3/2}$ state. We have experimentally verified these dependences. The observed resonances are asymmetric, with a low-frequency tail, which we attribute to the van der Waals shift of the final $n{p}_{1/2}n{p}_{3/2}$ state due to its dipole-dipole interaction with the nearby $ns(n+1)s$ state. While the van der Waals shift is negligible for most of the atoms in the Rydberg gas, it is not for the pairs of close atoms which undergo this transition.

High-energy scattering spectroscopy is a widely established technique for probing the characteristic properties of complex physical systems. Motivated by the recent observation of long-sought supersolid states in dipolar quantum Bose gases, I investigate the general relationships existing between the density contrast, the superfluid fraction, and the response to a high-energy scattering probe of density-modulated states within a classical-field approach. I focus on the two extreme regimes of shallow and deep supersolids, which are of particular interest in describing the phase transitions of the supersolid to a uniform superfluid and an incoherent crystal state, respectively. Using relevant Ansätze for the fields of dipolar supersolid states in these regimes, I specify and illustrate the scaling laws relating the three observables. This work was first prompted to develop an intuitive understanding of a concomitant study based on experiments and mean-field numerical simulations. Beyond this specific application, this works provides a simple and general framework to describe density-modulated states and in particular the intriguing case of supersolids. It describes key properties characterizing the supersolid order and highlights possibilities for probing such properties based on high-energy scattering response.

We consider a two-dimensional octagonal-diamond network with a fine-tuned diagonal coupling inside the diamond-shaped unit cell. Its linear spectrum exhibits coexistence of two dispersive bands (DBs) and two flat bands (FBs), touching one of the DBs embedded between them. Analogous to the kagome lattice, one of the FBs will constitute the ground state of the system for a proper sign choice of the Hamiltonian. The system is characterized by two different flat-band fundamental octagonal compactons, originating from the destructive interference of fully geometric nature. In the presence of a nonlinear amplitude (on-site) perturbation, the single-octagon linear modes continue into one-parameter families of nonlinear compact modes with the same amplitude and phase structure. However, numerical stability analysis indicates that all strictly compact nonlinear modes are unstable, either purely exponentially or with oscillatory instabilities, for weak and intermediate nonlinearities and sufficiently large system sizes. Stabilization may appear in certain ranges for finite systems and, for the compacton originating from the band at the spectral edge, also in a regime of very large focusing nonlinearities. In contrast to the kagome lattice, the latter compacton family will become unstable already for arbitrarily weak defocusing nonlinearity for large enough systems. We show analytically the existence of a critical system size consisting of 12 octagon rings, such that the ground state for weak defocusing nonlinearity is a stable single compacton for smaller systems, and a continuation of a nontrivial, noncompact linear combination of single compacton modes for larger systems. Investigating generally the different nonlinear localized (noncompact) mode families in the semi-infinite gap bounded by this FB, we find that, for increasing (defocusing) nonlinearity the stable ground state will continuously develop into an exponentially localized mode with two main peaks in antiphase. At a critical nonlinearity strength a symmetry-breaking pitchfork bifurcation appears, so that the stable ground state is single peaked for larger defocusing nonlinearities. We also investigate numerically the mobility of localized modes in this regime and find that the considered modes are generally immobile both with respect to axial and diagonal phase-gradient perturbations.

In this work, we establish the relationship existing between astigmatic Gaussian beams and Bessel-modulated Gaussian beams with quadratic radial dependence. We introduce an alternative representation of quadratic Bessel-Gaussian beams. This result permits us to expand the astigmatic Gaussian beams in a Fourier series with respect to the polar azimuthal angle with coefficients that are expressible in terms of Bessel-modulated Gaussian beams with quadratic radial dependence. The analysis presented also includes an analytic derivation of the power azimuthal spectral distribution associated with the decomposition in orbital angular momentum eigenmodes and a comprehensive characterization of the properties of this distribution as the beam parameters are varied.

We study quantum non-Markovian dynamics of the Caldeira-Leggett model, a prototypical model for quantum Brownian motion describing a harmonic oscillator linearly coupled to a reservoir of harmonic oscillators. Employing the exact analytical solution of this model one can determine the size of memory effects for arbitrary couplings, temperatures, and frequency cutoffs. Here, quantum non-Markovianity is defined in terms of the flow of information between the open system and its environment, which is quantified through the Bures metric as distance measure for quantum states. This approach allows us to discuss quantum memory effects in the whole range from weak to strong dissipation for arbitrary Gaussian initial states. A comparison of our results with the corresponding results for the spin-boson problem show a remarkable similarity in the structure of non-Markovian behavior of the two paradigmatic models.

In recent work, Arora and Asadian have proposed a sophisticated physical structure for testing the macroscopic Clauser-Horne-Shimony-Holt (CHSH) inequality of two entangled particles using a multislit Young experiment that employs classical-like modular variables and measurements. By imposing the algebraic CHSH constraint on the Wigner representations of these observables, they found that a strong connection exists between the non-negative Wigner function of a quantum state and having the macroscopic CHSH inequality hold. The entangled states with negative Wigner functions violate the macroscopic CHSH inequality when the number of slits is $N\ge 8$ and the maximum violation, in principle, requires $N\to +\infty$. In this paper, we further study this macroscopic local-realism test by analyzing the eigenvalues of the classical-like modular variables when $N$ is finite. Through this analysis, we find that one can modify the classical boundary for the macroscopic CHSH inequality when $N$ is finite, which makes it possible to demonstrate macroscopic Bell nonlocality for entangled states with $N<8$. More interestingly, we find another form of an entangled state that violates the macroscopic CHSH inequality under the modified boundaries when the number of slits is $N=2$. But the violation of the macroscopic CHSH inequality under the modified classical boundaries with a finite $N$ does not necessarily correspond to states with a non-positive-definite Wigner function.

Multiphase estimation is a paradigmatic example of a multiparameter problem. When measuring multiple phases embedded in interferometric networks, specially tailored input quantum states achieve enhanced sensitivities compared with both single-parameter and classical estimation schemes. Significant attention has been devoted to defining the optimal strategies for the scenario in which all of the phases are evaluated with respect to a common reference mode, in terms of optimal probe states and optimal measurement operators. Also, the strategies assume unlimited external resources, which is experimentally unrealistic. Here, we optimize a generalized scenario that treats all of the phases on an equal footing and takes into account the resources provided by external references. We show that the absence of an external reference mode reduces the number of simultaneously estimable parameters, owing to the immeasurability of global phases, and that the symmetries of the parameters being estimated dictate the symmetries of the optimal probe states. Finally, we provide insight for constructing optimal measurements in this generalized scenario. The experimental viability of this paper underlies its immediate practical importance beyond fundamental physics.