Randomized measurement protocols such as classical shadows represent powerful resources for quantum technologies, with applications ranging from quantum state characterization and process tomography to machine learning and error mitigation. Recently, the notion of measurement dual frames, in which classical shadows are generalized to dual operators of positive operator-valued measure (POVM) effects, resurfaced in the literature. This brought attention to additional degrees of freedom in the postprocessing stage of randomized measurements that are often neglected by established techniques. In this work, we leverage dual frames to construct improved observable estimators from informationally complete measurement samples. We introduce novel classes of parametrized frame superoperators and optimization-free dual frames based on empirical frequencies, which offer advantages over their canonical counterparts while retaining computational efficiency. Remarkably, this comes at almost no quantum or classical cost, thus rendering dual frame optimization a valuable addition to the randomized measurement toolbox.

With the recent development of quantum information theory, some attempts have been made to construct information theory beyond quantum theory. Here, we consider hypothesis-testing relative entropy and one-shot classical capacity, that is, the optimal rate of classical information transmitted by using a single channel under the constraint of a certain error probability, in general physical theories where states and measurements are operationally defined. Then we obtain the upper bound of the one-shot classical capacity by generalizing the method given by Wang and Renner [Phys. Rev. Lett. 108, 200501 (2012)]. Also, we derive the lower bound of the capacity by showing the existence of a good code that can transmit classical information with a certain error probability. Applying the above two bounds, we prove the asymptotic equivalence between classical capacity and hypothesis-testing relative entropy in any general physical theory.

In this work we address the problem of quantum Fisher information (QFI) maximization in an unbalanced lossy Mach-Zehnder interferometer. We implement the scheme from Escher et al. [Nat. Phys. 7, 406 (2011)] allowing us to obtain in closed form the lossy QFI for all involved scenarios. Then, mirroring the lossless case Ataman [Phys. Rev. A 105, 012604 (2022)], by optimizing the transmission coefficient of the first beam splitter, we maximize each QFI in question. We consider this problem for both single- and two-parameter QFI, i.e., for the scenarios with or without access to an external phase reference. Contrary to the lossless case, calculations are much more involved, however, we are able to put forward a large number of results in closed form. We also introduce two concepts, the balanced penalty and the QFI loss rate. Finally, we thoroughly discuss our results through a number of examples, including both Gaussian and non-Gaussian input states.

Measurements of isotope shifts have recently been attracting considerable attention due to their potentials in searching for new forces. We report on the isotope shifts of the $4f^{14}6s^2 {}^1{S}_0–4f^{13}5d6s^2(J=2)$ transition at 431 nm in Yb, based on absolute frequency measurements with an accuracy of $\approx 10$ kHz. With these data, the hyperfine constants for ${}^{173}\mathrm{Yb}$ are determined. To analyze these data further, electronic structure of ytterbium is theoretically calculated. The nuclear charge radii are estimated together with some previously reported isotope-shift data for other transitions. An analysis of the King plot for the $4f^{14}6s^2 {}^1{S}_0–4f^{13}5d6s^2(J=2)$ transition shows a good consistency with other transitions, resulting in a constraint on the existence of new bosons mediating the force between an electron and a neutron. The analysis motivates further precision measurements on isotope shifts of the narrow-linewidth transitions in ytterbium, not only for the even-mass isotopes but also for the odd-mass isotopes.

Here we theoretically demonstrate the generation of spinning linearly polarized harmonics through the combination of polarization shaping with high-order harmonic generation. Specifically, two orthogonally polarized 800-nm femtosecond pulses with precisely controlled relative peak amplitude were combined to obtain a spinning linearly polarized driving field, with which we show a successful chirality transfer from the driving field to the resultant harmonics through its interaction with isotropic Ar atoms. Systematic investigations of the influence from the polarization rotational speed and the peak amplitude of the driving field were conducted, which reveal that the angular frequency and the harmonic order of spinning linearly polarized harmonics can be manipulated independently. The proposed strategy extends the photon energy of the laser fields with twisted polarization into the extreme ultraviolet region, which paves the way for exploring ultrafast dynamics on the attosecond timescale.

Recently, the possibility of the generation and interaction of unipolar half-cycle electromagnetic pulses with quantum systems has been the subject of active research. Such pulses can find many different and interesting applications. They are able to excite quantum systems very fast. Based on the numerical solution of Maxwell-Bloch equations, this paper studies theoretically the possibility of guiding and ultrafast controlling population difference gratings by a sequence of half-cycle attosecond pulses in a three-level resonant medium. The parameters of the model medium (transition frequencies and transition dipole moments) match those in a hydrogen atom. We show the possibility of guiding periodic gratings and dynamic microcavities on different resonant transitions in the medium. We also consider the superradiance of polarization waves and atomic gratings produced by half-cycle pulses.

Atomic four-wave mixing (FWM) is an important nonlinear process in ultracold physics. Despite numerous works on atomic FWM, the phase coherence effect has not been extensively studied. Here, by preparing multiple spin-momentum modes with ultracold ${}^{87}\mathrm{Rb}$ atoms in a crossed dipole trap and applying an external magnetic field to regulate the atomic motions and interactions, we extensively investigate how the coherence fluctuation affects the atomic FWM process. We observe that the atomic motion and spin-exchange collision involve a periodic collapse and revival of the yield fraction of the atomic FWM. The oscillation period is mainly determined by the spin-exchange rate and thus the atomic scattering cross section. Our work demonstrates that atomic FWM can be used to probe the coherence and the atomic interactions, which should benefit various areas related to multicomponent atomic interactions and spin dynamics in the future.

We propose a general mechanism for generating limit cycle (LC) oscillations by coupling a linear bosonic mode to a dissipative nonlinear bosonic mode. By analyzing the stability matrix, we show that LCs arise due to a supercritical Hopf bifurcation. We find that the existence of LCs is independent of the sign of the effective nonlinear interaction. The bosonic model can be realized in three-level systems interacting with a quantized light mode as realized in atom-cavity systems. Using such a platform, we experimentally observe LCs in an atom-cavity system with attractive optical pump lattice, thereby confirming our theoretical predictions for the minimal model and interactions needed to generate LCs for a class of driven-dissipative systems.

The fast dynamics of molecular polaritonics is scrutinized theoretically through the implementation of two-dimensional spectroscopy protocols. We derive conceptually simple and computationally efficient formulas to calculate two-dimensional spectra for molecules, each of them modeled as a system of two electronic states including vibrational relaxation, immersed in an optical cavity, thus coupled to quantized radiation. Cavity photon losses and molecular relaxation are incorporated into the Hamiltonian dynamics to form an open quantum system that is solved through a master equation. In the collective case, the relaxation dynamics into dark states is revealed to be the crucial factor to explain the asymmetries in both the diagonal and cross peaks of two-dimensional spectra for long waiting times between excitation and detection, a feature shown by recent experiments. Our theoretical method provides a deeper insight in those processes that yield relevant signals in multidimensional molecular spectroscopy.

Macrorealism formalizes the seemingly intuitive notion that, in contrast with the principles of quantum mechanics, a physical system can be in a definite state at any given time and moreover its dynamical evolution is independent of the measurements performed on it. In this study, we carry out a comparative analysis between three-time Leggett–Garg-type inequalities and the conditions of no-signaling-in-time and arrow-of-time for macrorealism within the context of meson oscillations. Our findings indicate that, under given initial conditions, no violations of Leggett–Garg inequalities are observed. However, no-signaling-in-time conditions are found to be violated, thereby revealing the impossibility of applying a macrorealistic description to the physics of meson oscillations.

The blinking statistics of quantum emitters and their corresponding Markov models play an important role in high-resolution microscopy of biological samples as well as in nano-optoelectronics and many other fields of science and engineering. Current methods for analyzing the blinking statistics like the full counting statistics and the Viterbi algorithm break down for low photon rates. We present an evaluation scheme that eliminates the need for both a minimum photon flux and the usual binning of photon events which limits the measurement bandwidth. Our approach is based on higher-order spectra of the measurement record which we model within the recently introduced method of quantum polyspectra from the theory of continuous quantum measurements. By virtue of this approach we can determine on- and off-switching rates of a semiconductor quantum dot at light levels 1000 times lower than in a standard experiment and 20 times lower those than achieved with a scheme from full counting statistics. Thus, a very powerful high-bandwidth approach to the parameter-learning task of single-photon hidden Markov models is established with applications in many fields of science.

In a previous paper [Phys. Rev. A 105, 042205 (2022)], the distribution of resonance poles in the complex plane of the wave number $k$ associated to the multiple scattering of a quantum particle in a random point field was numerically discovered. This distribution presented two distinctive structures: a set of peaks at small $k$ when the wavelength is larger than the interscatterer distance and a band almost parallel to the real axis at larger $k$. In this paper, a theoretical study based on wave transport theory is proposed to explain the origin of these structures and to predict their distribution in the complex $k$ plane. First, it is shown that the peaks at small $k$ can be understood using the effective wave equation for the average wave function over the disorder. Then, that the band at large $k$ can be described by the Bethe-Salpeter equation for the square modulus of the wave function. This study is supported by careful comparisons with numerical simulations.

Attenuation and amplification are the most common processes for optical communications. Amplification can be used to compensate the attenuation of the complex amplitude of an optical field, but is unable to recover the coherence lost, provided that the attenuation channel and the amplification channel are independent. In this paper, we show that the quantum coherence of an optical field can be regained if the attenuation channel and the amplification channel share correlated noise. We propose an all-optical correlated noisy channel relying on the four-wave mixing process and demonstrate its capability of recovering quantum coherence within continuous-variable systems. We quantitatively investigate the coherence recovery phenomena for coherent states and two-mode squeezed states. Moreover, we analyze the effect of other photon losses that are independent from the recovery channel on the performance of recovering coherence. Different from correlated noisy channels previously proposed based on electro-optic conversions, the correlated noisy channel in our protocol is all-optical and thus owns larger operational bandwidths.

Quantum error-correcting codes (QECCs) and decoherence-free subspace (DFS) codes provide active and passive means, respectively, to address certain types of errors that arise during quantum computation. The latter technique is suitable to correct correlated errors with certain symmetries and the former to correct independent errors. The concatenation of a QECC and a DFS code results in a degenerate code that splits into actively and passively correcting parts, with the degeneracy impacting either part, leading to degenerate errors as well as degenerate stabilizer operators. The concatenation of the two types of code can aid universal fault-tolerant quantum computation when a mix of correlated and independent errors is encountered. In particular, we show that for sufficiently strongly correlated errors, the concatenation with the DFS as the inner code provides better entanglement fidelity, whereas for sufficiently independent errors, the concatenation with the QECC as the inner code is preferable. As illustrative examples, we examine in detail the concatenation of a two-qubit DFS code and a three-qubit repetition code or five-qubit Knill-Laflamme code, under independent and correlated errors.

In recent years, informationally complete measurements have attracted considerable attention, especially in the context of classical shadows. In the particular case of informationally overcomplete measurements, for which the number of possible outcomes exceeds the dimension of the space of linear operators in Hilbert space, the dual positive operator-valued measure operators used to interpret the measurement outcomes are not uniquely defined. In this paper, we propose a method to optimize the dual operators after the measurements have been carried out in order to produce sharper, unbiased estimations of observables of interest. We discuss how this procedure can produce zero-variance estimations in cases where the classical shadows formalism, which relies on so-called canonical duals, incurs exponentially large measurement overheads. We also analyze the algorithm in the context of quantum simulation with randomized Pauli measurements, and show that it can significantly reduce statistical errors with respect to canonical duals on multiple observable estimations.

In contrast to the classical optimization process required by the quantum approximate optimization algorithm, FALQON, a feedback-based algorithm for quantum optimization [A. B. Magann et al., Phys. Rev. Lett. 129, 250502 (2022)], enables one to obtain approximate solutions to combinatorial optimization problems without any classical optimization effort. In this study, we leverage the specifications of a recent experimental platform for the neutral-atom system [Z. Fu et al., Phys. Rev. A 105, 042430 (2022)] and present a scheme to implement an optimally tuned small-angle controlled-phase gate. By examining the two- to four-qubit FALQON algorithms in the MaxCut problem and considering the spontaneous emission of the neutral atomic system, we observe that the performance of FALQON implemented with small-angle controlled-phase gates exceeds that of FALQON utilizing controlled-$Z$ gates. This approach has the potential to significantly simplify the logic circuit required to simulate FALQON and effectively address the MaxCut problem, which may pave the way for the experimental implementation of near-term noisy intermediate-scale quantum algorithms with neutral-atom systems.

We design variational pulse sequences tailored for neutral atom quantum simulators and show that we can engineer layers of single-qubit and multiqubit gates. As an application, we discuss how the proposed method can be used to perform refocusing algorithms, swap networks, and ultimately quantum chemistry simulations. While the theoretical protocol we develop still has experimental limitations, it paves the way, with further optimization, for the use of analog quantum processors for variational quantum algorithms, including those not previously considered compatible with analog mode.

We present phase-shift calculations for positron collisions with positive ions using a complex scaling method (CSM) in which the phase shifts are derived only from the complex eigenenergies of the CSM Hamiltonian. Based on the findings of this study [R. Suzuki, T. Myo, and K. Katō, Prog. Theor. Phys. 113, 1273 (2005)], we propose a modification of the phase shift in the CSM calculation for application to few-body scattering problems. This modification is based on the fact that the contributions of high-lying complex eigenenergies to the phase shift can be approximated as a constant value in the case of small collision energy, where neither target excitation nor positronium formation occurs. The proposed modification limits the contribution of the complex eigenenergies to the vicinity of the collision energy, which is intuitively acceptable. We present a geometrical formulation of the modification and demonstrative calculations of positron scattering off positive ions. Our results agree well with those reported in the literature for the targets Ne, Ar, Kr, Xe, H, He, ${\mathrm{He}}^{+}$, and ${\mathrm{Li}}^{2+}$. The phase shifts of positron scattering off a ${\mathrm{Li}}^{+}$ ion are also reported.

Is there a saddle-point mechanism for ionization in intermediate-energy ion-atom collisions? Since Olson [Phys. Rev. A 33, 4397 (1986)] proposed the idea that the electrons stranded in the potential saddle between the two Coulomb centers dominate the ejected-electron spectra, multiple experimental and theoretical attempts have been made to answer this question. However, the topic has remained controversial. Here we provide a theoretical analysis of this question which can contribute significantly to a definitive answer, at least for intermediate and large projectile energies. To this end we calculate the energy and angular distribution of electrons emitted in proton-helium collisions. We use the two-center four-body wave-packet convergent close-coupling method based on the correlated two-electron structure for the helium target. The doubly differential cross sections obtained at 52 and 103 keV show no sign of a hump near one-half the relative velocity of the collision, which is expected according to the saddle-point ionization theory. At the same time, the results are in excellent agreement with measurements by Meckbach et al. [J. Phys. B 24, 3763 (1991)]. Two mechanisms for the production of electrons are clearly identified: direct ionization (direct knockout) and electron capture to the continuum (ECC) of the projectile. The electron speed (equivalently, energy) where direct ionization peaks is found to be practically independent of the ejection angle. However, the ECC peak is shown to shift towards one-half the relative velocity with increasing electron angle. It is concluded that the signatures of the suggested saddle-point mechanism may actually be due to a shift of the well-known ECC peak when electrons are emitted into angles away from the forward direction. Thus, the answer to the question is in the negative.