An important problem in the coherent resource theory is the convertibility of coherent states by free operations. In this paper we consider such a problem from a mixed coherent state into a pure one by using both stochastic incoherent operations and incoherent operations. We prove that stochastic incoherent operations can transform a mixed coherent state into a pure coherent state if and only if the density matrix of the initial state contains a singular principal submatrix. Then we provide two sufficient conditions with explicit expressions for the probabilistic transformation and the deterministic transformation. These two sufficient conditions facilitate the construction of concrete operators of stochastic incoherent operations and incoherent operations. These results demonstrate that incoherent operations are strictly more powerful than strictly incoherent operations within the probabilistic transformation as well as the deterministic transformation.

The quantum extreme reservoir computation (QERC) is a versatile quantum neural network model that combines the concepts of extreme machine learning with quantum reservoir computation. Key to QERC is the generation of a complex quantum reservoir (feature space) that does not need to be optimized for different problem instances. Originally, a periodically driven system Hamiltonian dynamics was employed as the quantum feature map. In this work we capture how the quantum feature map is generated as the number of time-steps of the dynamics increases by a method to characterize unitary matrices in the form of weighted networks. Furthermore, to identify the key properties of the feature map that has sufficiently grown, we evaluate it with various weighted network models that could be used for the quantum reservoir in image classification situations. At last, we show how a simple Hamiltonian model based on a disordered discrete time crystal with its simple implementation route provides nearly optimal performance while removing the necessity of programming of the quantum processor gate by gate.

Using optimal control, we establish and link the ultimate bounds in time (referred to as the quantum speed limit) and energy of two- and three-level quantum nonlinear systems which feature 1:2 resonance. Despite the unreachable complete inversion, by using the Pontryagin maximum principle, we determine the optimal time, pulse area, or energy for a given arbitrary accuracy. We show that the third-order Kerr terms can be absorbed in the detuning in order to lock the dynamics to the resonance. In the two-level problem, we determine the nonlinear counterpart of the optimal $\pi$-pulse inversion for a given accuracy. In the three-level problem, we obtain an intuitive pulse sequence similar to the linear counterpart but with different shapes. We prove the (slow) logarithmic increasing of the optimal time as a function of the accuracy.

Entanglement purification is a crucial technique for promising the effective entanglement channel in noisy large-scale quantum networks, yet complicated in designing protocols in multi-degree of freedom (DoF). To execute the above tasks easily and effectively, developing a learning framework for designing the entanglement purification with multi-DoF is a promising way and still an open research question. Inspired by variational quantum circuit (VQC) with remarkable advantage in learning optimal quantum operations with near-term quantum devices, in this paper we propose an effective VQC framework for the entanglement purification in multi-DoF and exploit it to learn the optimal purification protocols of the objective function which are based on postselection. By properly introducing additional circuit lines for representing each of the ancillary DoFs of all the particles, e.g., space and time, the parametrized quantum circuit can effectively simulate scalable entanglement purification. To verify our framework, the well-known protocols in linear optics are learned well with alternative operations in low-depth quantum circuit. Moreover, we simulate the multipair cases with multi-DoF to show the scalability and discover one-round protocols. Our work provides an effective way for exploring the entanglement purification protocols in multi-DoF and multipair with near-term quantum devices.

We measured the branching ratios of the ${\mathrm{He}}^{+}+{\mathrm{H}}^{-}$ and ${\mathrm{He}}^{+}+{\mathrm{D}}^{-}$ mutual neutralization at a collision energy below 25 meV. Those are correctly reproduced using the Landau-Zener model applied to potential energy curves computed by an anion-centered asymptotic model. The analyticity of both models allows getting a deeper insight into the reaction. It allows defining a low collision energy regime for the mutual neutralization at which the collision energy no longer affects the branching ratios. Using those models, we explain how heavier isotopes favor the production of higher excited states.

We report on mutual neutralization measurements between ${}^7\mathrm{Li}^{+}$ and ${}^1\mathrm{H}^{-}$ at effective center-of-mass collision energies in the range of 100 to 350 meV. We find that final states of lithium with principal quantum number $n=3$ dominate with $3s$ separated from the unresolved $3p$ and $3d$ states. We measure the $3s$ branching fraction to be 0.665(12) at 100(16) meV and no significant dependence on collision energy is observed in the studied range. Comparing to previous results on mutual neutralization between ${}^7\mathrm{Li}^{+}$ and ${}^2\mathrm{H}^{-}$ [G. Eklund et al., Phys. Rev. A 102, 012823 (2020)], we find that ${}^7\mathrm{Li}^{+}$ collisions with ${}^1\mathrm{H}^{-}$ result in a significantly higher $3s$ branching fraction than collisions with ${}^2\mathrm{H}^{-}$. The difference is 0.087(14). The $3s$ branching fraction of ${}^7\mathrm{Li}^{+} + {}^1\mathrm{H}^{-}$ and the determined isotope difference are in agreement with results from extended full quantum calculations based on the same input data and numerical method as in Croft et al. [H. Croft, A. S. Dickinson, and F. X. Gadéa, J. Phys. B 32, 81 (1999)]. These calculations reveal strong Stueckelberg oscillations of the $3s$ branching fraction for both isotopes.

The linear response approach to the relativistic coupled-cluster (RCC) theory has been extended to estimate contributions from the parity and time-reversal violating pseudoscalar-scalar (Ps-S) and scalar-pseudoscalar (S-Ps) electron-nucleus interactions along with electric dipole moments (EDMs) of electrons ($d_e$) interacting with internal electric and magnetic fields. The random phase approximation (RPA) is also employed to produce results to compare with the earlier reported values and demonstrate the importance of the non-RPA contributions arising through the RCC method. It shows that contributions from the S-Ps interactions and $d_e$ arising through the hyperfine-induced effects are very sensitive to the contributions from the high-lying virtual orbitals. Combining atomic results with the nuclear shell-model calculations, we impose constraints on the pion-nucleon coupling coefficients, and the EDMs of a proton and a neutron. These results are further used to constrain EDMs and chromo-EDMs of the up- and down-quarks by analyzing particle physics models.

The effect of optically driven spin precession discovered by Bell and Bloom [W. E. Bell and A. L. Bloom, Phys. Rev. Lett. 6, 280 (1961)] is widely used nowadays as a basis for numerous experiments in fundamental physics and for diverse applications. In this paper we consider a much less popular version of the light-induced spin precession that does not imply coherent precession of the spin-system magnetization and is excited by linearly (rather than circularly) polarized light. Pump-probe measurements performed on the $D_2$ line of cesium vapor show that the magnitude of the signal of the optically driven spin-alignment precession, in “vacuum” cells (with no buffer gas) is close to that of classical spin-orientation precession. In the presence of buffer gas, however, the signal of spin-alignment precession appears to be strongly suppressed. The discovered effect is ascribed to spin mixing of excited states of cesium atoms in the cycle of optical pumping.

Multichannel quantum-defect theory (MQDT) provides a powerful toolkit for describing and understanding collisions of cold alkali-metal atoms. Various MQDT approximations differ primarily in how they characterize the so-called short-ranged $K$ matrix ${\mathbf{K}}_{\text{sr}}$, which encapsulates the short-ranged physics into a handful of low-energy parameters that exhibit simple and smooth dependence on energy and field. Here, we compare three different methods for computing ${\mathbf{K}}_{\text{sr}}$ for homonuclear collisions of alkali-metal atoms, from lithium to cesium. The MQDT calculations are benchmarked against numerically converged coupled-channels calculations that use a log-derivative propagator out to the asymptotic region. We study how well these approximations reproduce positions of $s$-wave magnetic Feshbach resonances, comparing with experiment where possible, and identify the limitations of various approximations.

We investigate the localization-delocalization transition (LDT) in an electromagnetically induced photonic lattice. A four-level tripod-type scheme in atomic ensembles is proposed to generate an effective photonic moiré lattice through the electromagnetically induced transparency (EIT) mechanism. By taking advantage of the tunable atomic coherence, we show that both periodic (commensurable) and aperiodic (incommensurable) structure can be created in such a photonic moiré lattice via adjusting the twist angle between two superimposed periodic patterns with square primitive. Furthermore, we also find that by tuning the amplitudes of these two superimposed periodic patterns, the localization-delocalization transition occurs for the light propagating in the aperiodic moiré lattice. Such localization is shown to link the fact that the flat bands of moiré lattice support quasi-nondiffracting localized modes and thus induce the localization of the initially localized beam. It would provide a promising approach to control the light propagation via the electromagnetically induced photonic lattice.

We employ a time-dependent variational approach with the multiple Davydov $D_2$ ansatz and two approximate analytical methods to study the spontaneous emission of a V-type artificial atom in the strong-coupling regime, where the decay rate of the emitter becomes a considerable fraction of its transition frequencies, and focus on quantum-interference-induced effects. The variational approach is found to be accurate in certain strong-coupling regimes and is used as the benchmark to address the validity of the analytical methods: the rotating-wave approximation (RWA) and the transformed RWA (TRWA). It is found that the TRWA is fairly accurate in the strong-coupling regime where the RWA breaks down. By using the numerical and analytical methods, we illustrate that there are dark lines and line narrowing in the emission spectra in the strong-coupling regime and in a wide accessible range of the emitter parameters. We also illustrate how the emission spectrum is altered by the counter-rotating couplings. The present results offer insights into the experimental observation of the quantum-interference-induced effect in the strong-coupling regime and in the context of artificial atoms.

When a coherent field is combined with the phase-matched output of an atomic ensemble, the second-order correlation function of the total field can exhibit superbunching or antibunching. Homodyning the reference field with the atomic emission can amplify the nonclassical characteristics of the atomic emission. A theoretical description of these phenomena is presented. It is pointed out that, even if the number of excitations in the ensemble is much less than unity, truncating a factorized state to have at most two excitations can lead to errors in calculating the second-order correlation function. We also include the effects of dephasing produced by Rydberg-Rydberg interactions and show how they modify the bunching and antibunching that occur in the absence of atom-atom interactions. It is shown that the particle separation probability distribution and the joint particle separation probability distribution play critical roles in determining the effects of dephasing.

Up to now, experiments involving Mössbauer nuclei have been restricted to the low-excitation regime (LER). The reason for this is the narrow spectral linewidth of the nuclei. This defining feature enables Mössbauer spectroscopy with remarkable resolution and convenient control and measurements in the time domain, but at the same time implies that only a tiny part of the photons delivered by accelerator-based x-ray sources with orders-of-magnitude larger pulse bandwidth are resonant with the nuclei. X-ray free-electron lasers promise a substantial enhancement of the number of nuclear-resonant photons per pulse, such that excitations beyond the LER come within reach. This raises the question of how the onset of nonlinear excitations could be experimentally verified. Here, we develop and explore a method to detect an excitation of nuclear ensembles beyond the LER for ensembles of nuclei embedded in x-ray waveguides. It relies on the comparison of the x rays coherently and incoherently scattered off of the nuclei. As a key result, we show that the ratio of the two observables is constant within the LER, essentially independent of the details of the nuclear system and the characteristics of the exciting x rays. Conversely, deviations from this equivalence serve as a direct indication of excitations beyond the LER. Building upon this observation, we develop a variety of experimental signatures both, for near-instantaneous impulsive and for temporally extended nonimpulsive x-ray excitation. Correlating coherently and incoherently scattered intensities further allows one to compare theoretical models of nonlinear excitations more rigorously to corresponding experiments.

We establish rigorously in this work a measurement uncertainty relation (MUR) for three unbiased qubit observables, which was previously shown to hold true under some presumptions. The triplet MUR states that the uncertainty, which is quantified by the total statistical distance between the target observables and the jointly implemented observables, is lower bounded by an incompatibility measure that reflects the joint measurement conditions. We derive a necessary and sufficient condition for the triplet MUR to be saturated and the corresponding optimal measurement. To facilitate experimental tests of MURs we propose a straightforward implementation of the optimal joint measurements. Lastly, by a symmetry argument, the exact values of incompatibility measure are analytically calculated for some symmetric triplets. We anticipate that our work may enrich the understanding of quantum incompatibility in terms of MURs and inspire further applications in quantum information science. This work presents a complete theory relevant to a parallel work [Y.-L. Mao et al., Testing Heisenberg-type measurement uncertainty relations of three observables, Phys. Rev. Lett. 131, 150203 (2023)] on experimental tests.

Recent advances in quantum thermodynamics have been focusing on ever more elementary systems of interest, approaching the limit of a single qubit, with correlations, strong coupling, and far-from-equilibrium environments coming into play. Under such scenarios, it is clear that fundamental physical quantities must be revisited. This article questions whether a universal definition of internal energy for open quantum systems can be devised, setting limits on its possible properties. We argue that, for such a definition to be regarded as local, it should be determined by using only local resources, i.e., the open system's reduced density operator $\varrho$ and its time derivatives. The simplest construction, then, would be a functional $U(\varrho ,\dot{\varrho })$. We adopt the minimalist implementation of a bipartite quantum universe, namely, two qubits in a pure joint state, and show that the functional relationship cannot be that simple if it is to generally recover the well-established internal energy of the universe. No further hypothesis or approximation scheme was assumed. An illustrative counterexample is explored, and possible implications of the general constraint are discussed.

A random access code (RAC) is a communication task in which the sender encodes a random message into a shorter one to be decoded by the receiver so that a randomly chosen character of the original message is recovered with some probability. Both the message and the character to be recovered are assumed to be uniformly distributed. In this paper, we extend this protocol by allowing more general distributions of these inputs, which alters the encoding and decoding strategies optimizing the protocol performance, with either classical or quantum resources. We approach the problem of optimizing the performance of these biased RACs with both numerical and analytical tools. On the numerical front, we present algorithms that allow a numerical evaluation of the optimal performance over both classical and quantum strategies and provide a Python package designed to implement them, called RAC-tools. We then use this numerical tool to investigate single-parameter families of biased RACs in the $n^2\mapsto 1$ and $2^d\mapsto 1$ scenarios. For RACs in the $n^2\mapsto 1$ scenario, we derive a general upper bound for the cases in which the inputs are not correlated, which coincides with the quantum value for $n=2$ and in some cases for $n=3$. Moreover, it is shown that attaining this upper bound self-tests pairs or triples of rank-1 projective measurements, respectively. An analogous upper bound is derived for the value of RACs in the $2^d\mapsto 1$ scenario, which is shown to be always attainable using mutually unbiased measurements if the distribution of input strings is unbiased.

In this work we develop a theory of fractional stimulated Raman adiabatic passage (FSTIRAP) using frequency-chirped pulses (CFSTIRAP). We analyze the CFSTIRAP as a method to create a coherent superposition state maximizing coherence between the initial and the target state in the presence of the two-photon detuning. We demonstrate that the pulse chirping permits relaxation of the condition of the two-photon resonance required for adiabatic passage in STIRAP and FSTIRAP. The choice of the chirp rate $\left|\alpha \right|=\left|\delta \right|/(t_p-t_s)$ enables adiabatic passage to a predetermined state between two nearly degenerate final states within a broad range of values of the two-photon detuning and the chirp rate. The proposed schemes will expand the scope of quantum control methods and contribute to the further improvement of quantum imaging, sensing, and metrology.

We prove a general class of continuous variable entanglement criteria based on the Husimi $Q$ distribution, which represents a quantum state in canonical phase space, by employing a theorem by Lieb and Solovej. We discuss their generality, which roots in the possibility to optimize over the set of concave functions, from the perspective of continuous majorization theory and show that with this approach families of entropic as well as second moment criteria follow as special cases. All derived criteria are compared with corresponding marginal based criteria, and the strength of the phase-space approach is demonstrated for a family of prototypical example states where only our criteria flag entanglement. Furthermore, we explore their optimization prospects in two experimentally relevant scenarios characterized by sparse data: Finite detector resolution and finite statistics. In both scenarios optimization leads to clear improvements enlarging the class of detected states and the signal-to-noise ratio of the detection, respectively.