We derive a generalization of the Ehrenfest theorem valid for open quantum systems. From this result, we identify three contributions to the evolution of expected values: (i) the explicit time dependence of the observable, (ii) the incompatibility between the observable and an operator which plays the role of an effective Hamiltonian, and (iii) entropy changes. Considering the local Hamiltonian as the observable, and adopting a specific interpretation of the nature of thermal interactions, we obtain an alternative version of the first law of thermodynamics. Within this framework, we show that in some cases the power performed by the system can be considered as a quantum observable. As an application, the pure-dephasing process is reinterpreted from this perspective.

We theoretically investigate the role of chiral transitions in the quantum friction force that acts on a two-level atom that moves with relative velocity $v$ parallel to a planar metallic surface. We find that the friction force has a component that is sensitive to the handedness of the atomic transition dipole moment. In particular, we show that the friction force can be enhanced by an atomic transition with a dipole moment with a certain handedness and can almost be suppressed by the dipole moment with the opposite handedness. Curiously, the handedness of the transition dipole moment that boosts the ground-state friction force is the opposite of what is classically expected from the spin-momentum locking. We explain this discrepancy in terms of the interaction between positive- and negative-frequency oscillators.

We investigate the topological-to-nontopological quantum phase transitions (QPTs) occurring in the Kitaev code under local perturbations in the form of a local magnetic field and spin-spin interactions of the Ising-type using fidelity susceptibility (FS) and entanglement as the probes. We assume the code to be embedded on the surface of a wide cylinder of height $M$ and circumference $D$ with $M\ll D$. We demonstrate a power-law divergence of FS across the QPT and determine the quantum critical points via a finite-size-scaling analysis. We verify these results by mapping the perturbed Kitaev code to the two-dimensional Ising model with nearest- and next-nearest-neighbor interactions and computing the single-site magnetization as the order parameter using the quantum Monte Carlo technique. We also demonstrate a finite-size odd-even dichotomy in the occurrence of the QPT in the Kitaev ladder with respect to the odd and even values of $D$, when the system is perturbed with only Ising interaction. Our results also indicate a higher robustness of the topological phase of the Kitaev code against local perturbations if the boundary is made open along one direction. We further consider a local entanglement witness operator designed specifically to capture a lower bound to the localizable entanglement on the vertical nontrivial loop of the code. We show that the first derivative of the expectation value of the witness operator exhibits a logarithmic divergence across the QPT and perform the finite-size-scaling analysis. We demonstrate similar behavior of the expectation value of the appropriately constructed witness operator also in the case of a locally perturbed color code with open boundaries.

Stabilizer codes lie at the heart of modern quantum-error-correcting codes (QECCs). Of particular importance is a class called Calderbank-Shor-Steane (CSS) codes, which includes many important examples such as toric codes, color codes, and fractons. Recent studies have revealed that the decoding transition for these QECCs could be intrinsically captured by calculating information-theoretic quantities from the mixed state. Here we perform a simple analytic calculation of the coherent information for general CSS codes under local incoherent Pauli errors via diagonalization of the density matrices and mapping to classical statistical mechanical (SM) models. Our result establishes a rigorous connection between the decoding transition of the quantum code and the phase transition in the random classical SM model. It is also directly confirmed for CSS codes that exact error correction is possible if and only if the maximum-likelihood decoder always succeeds in the thermodynamic limit. Thus, the fundamental threshold is saturated by the optimal decoder.

The atom-optics realization of the quantum kicked rotor represents one of the most well-studied experimental platforms for the physics of Anderson localization. In this work, we show that the same platform can be used to implement a quantum algorithm to perform quantum amplitude amplification (AA), a generalization of Grover's search algorithm. This is done using the usual kick sequence in combination with the well established technique of Raman velocity selection. We argue that this platform is well suited to implement AA, as its characteristic property of localization can be exploited to enhance the performance of the amplitude amplification algorithm by reducing its average runtime. We also introduce a kick potential which asymptotically leads to the optimal quantum speedup, constituting a complementary approach. Finally, we demonstrate that the scheme is fairly robust to noise in the kicks and discuss the experimental feasibility of each component of our proposal

Spin-exchange relaxation-free magnetometers based on dense ensembles of alkali-metal spins are precision quantum sensors that hold the record of measured and projected sensitivity to magnetic fields, in the microgauss to milligauss range. At geomagnetic fields however, these sensors quickly lose their magnetic sensitivity due to spin decoherence by random spin-exchange collisions. Here we discover that atoms with nuclear spin $I=\frac{1}{2}$ can operate in the spin-exchange relaxation-free regime even at high magnetic field. We counterintuitively show that frequent collisions between a dense and optically inaccessible $(I=\frac{1}{2})$ gas with another optically accessible spin gas ($I>\frac{1}{2}$) improve the fundamental magnetic sensitivity of the latter. We analyze the performance of a dual-species potassium and atomic hydrogen magnetometer and project a fundamental sensitivity of about $10\mathrm{aT}{\left({\mathrm{cm}}^3\text{/}\mathrm{Hz}\right)}^{1/2}$ at geomagnetic fields for feasible experimental conditions.

Accurate calculations of electric dipole polarizabilities (${\alpha }_d$), quadrupole moments ($\mathrm{\Theta }$), and quadrupole polarizabilities (${\alpha }_q$) for the clock states of the singly charged calcium (${\mathrm{Ca}}^{+}$) and ytterbium (${\mathrm{Yb}}^{+}$) ions are presented using the general-order relativistic coupled-cluster (RCC) theory. Precise knowledge of these quantities is immensely useful for estimating uncertainties caused by major systematic effects such as the linear and quadratic Stark shifts and black-body radiation shifts in the optical ${\mathrm{Ca}}^{+}$ and ${\mathrm{Yb}}^{+}$ clocks. A finite-field approach is adopted for estimating these quantities in which the first-order and second-order energy level shifts are analyzed by varying strengths of externally applied electric field and field- gradient. To achieve high-accuracy results in the heavier ${\mathrm{Yb}}^{+}$ ion, we first calculate these properties in a relatively lighter clock candidate ${\mathrm{Ca}}^{+}$, which involves similar clock states. From these analyses, we learn that electron correlation effects arising from triple excitations in the RCC theory contribute significantly to the above properties, and are decisive factors in bringing the calculated values closer to the experimental results.

We report enhanced accuracy in isotope-shift (IS) measurement using sympathetic cooling, demonstrated with ${}^{170,172,174,176}\mathrm{Yb}^{+}$ transitions at 369 and 935 nm. Considering only type-A uncertainties, sympathetic cooling achieves 30- and 200-fold improvements in IS measurement accuracy at 369 and 935 nm compared with previous single-ion results. Our measurements remain the most accurate to date including type-B uncertainties. King-plot analysis yields model-independent IS factors for these transitions [$F_{369}=-12.3\left(8\right)$ GHz/${\mathrm{fm}}^2, K_{369}=-1800\left(1400\right)$ GHz u, $F_{935}=30.7\left(2.0\right)$ GHz/${\mathrm{fm}}^2$, and $K_{935}=12900\left(3000\right)$ GHz u] and their ratio [$\frac{F_{935}}{F_{369}}=-2.498\left(4\right)$] along with $K_{935}-K_{369}\frac{F_{935}}{F_{369}}=8410\left(90\right)$ GHz u, representing a 17-fold improvement. More reliable nuclear charge radii for ${}^{170–174,176}\mathrm{Yb}$ are also determined with an accuracy of 0.01 ${\mathrm{fm}}^2$. This paper complements collinear laser spectroscopy, introduces a robust approach for researching unstable isotopes, and supports applications of sympathetic cooling in trapped-ion quantum computers and quantum frequency standards.

A key hallmark of quantum Hall physics is the existence of topological chiral states at the system boundary. Signatures of these edge states have been experimentally observed in cold atoms by using different approaches, including notably that of “synthetic dimensions” in which internal states are coupled together and reinterpreted as sites along an artificial spatial dimension. However, previous atomic synthetic dimension implementations have been limited to relatively small system sizes with inflexible boundaries. In this paper, we propose instead how to use a synthetic dimension of atomic trap states to observe chiral edge states in a large quantum Hall system with a tunable edge. We present numerical simulations for relevant experimental parameters, showing how this scheme may be used to probe the properties and robustness of the edge states to defects. Our work opens the way for future experiments in topological physics with synthetic dimensions, while also providing new ways to manipulate and control highly excited trap states.

We have developed a theory of the first- and second-harmonic-generated extinction coefficients in plasmonic nanohybrids. We consider that a nanohybrid is made of an ensemble of interacting metallic nanoparticles (MNPs). The surface plasmon polaritons (SPPs) for the MNPs and the dipole-dipole interaction (DDI) between nanoparticles are calculated. Using the quantum mechanical density matrix method, we have obtained analytical expressions for the first- and second-harmonic-generated extinction coefficients in the presence of the SPP and DDI fields. These analytical expressions can be useful for scientists and engineers to compare their experiments and make new plasmonic devices. We have predicted that there is a noticeable enhancement in the extinction coefficients due to an extra contribution from the SPPs present in the nanohybrid. We found that there are two types of contributions to the extinction coefficients. The first is called the photonic extinction coefficient induced by the probe field. The second is called the polaritonic extinction coefficient produced by the SPP field. The enhancement phenomenon can be used to fabricate the nanoamplifiers and nanosensors from plasmonic nanohybrids. Next, we have compared theory with experimental data of the Au-MNPs and Au/Ag core-shell metallic nanorods for the first harmonic extinction coefficient. Similarly, we have also compared our theory with experimental data of the Au/Ag core-shell MNPs for the second harmonic extinction coefficient. Good agreement between theory and experiments is found. Further, we predicted the phenomenon of the electromagnetically induced transparency in the first- and second-harmonic-generated extinction coefficients due to DDI coupling. In other words, the nanohybrid becomes transparent for the first- and second-harmonic-generated extinction processes. Additionally, we found that a peak in the extinction coefficient splits into two peaks due to DDI coupling. Due to the strong coupling between the exciton and DDI polaritons, the excitonic state splits into two states and produces two excitons. These two excitons are responsible for the two peaks. This finding can be used to fabricate nanoswitches (i.e., ON = one peak, OFF = two peaks) and nanosensors using plasmonic nanohybrids.

A fundamental problem in quantum information is to understand the operational significance of quantum resources. Quantum resource theories (QRTs) provide a powerful theoretical framework that aids in the analysis and comprehension of the operational meaning of these resources. Early resource theories primarily focused on analyzing static quantum resources. Recently, interest in the study of dynamic quantum resources has been growing. In this paper, we utilize superchannel theory to describe the dynamic resource theory of quantum coherence. In this dynamic resource theory, we treat classical channels as free channels and consider two classes of free superchannels that preserve channel incoherence [maximally incoherent superchannels (MISCs) and dephasing-covariant incoherent superchannels (DISCs)] as free resources. We regard the quantum Fourier transform as the golden unit of dynamic coherence resources. We first establish the one-shot theory of dynamic coherence cost and dynamic coherence distillation, which involves converting the quantum Fourier transform into an arbitrary quantum channel using MISCs and DISCs. Next, we introduce a class of free superchannels known as $\delta$-MISCs, which asymptotically generate negligible dynamic coherence. Finally, we provide upper and lower bounds for the one-shot catalytic dynamic coherence cost of quantum channels under the action of these $\delta$-MISC superchannels.

The traditional Coherent-Population-Trapping (CPT) approach to atomic signal generation in chip-scale atomic clocks (CSACs) requires circularly polarized light, which creates spin polarization in the vapor and leads to reduced CSAC signal-to-noise ratios. Though various strategies have been developed to mitigate this problem, there is only a superficial and/or empirical understanding of these strategies’ efficacies due to the difficulty of measuring ground-state population distributions among hyperfine Zeeman sublevels. Here, we demonstrate an optical technique to measure the first three (density-matrix) state multipole moments of a single ground-state hyperfine manifold. Using this technique, we have discovered that ground-state angular momentum alignment (i.e., the quadrupole moment) can play an important role in CPT signal-to-noise ratios.

Nonclassical features of quantum systems can degrade when subjected to environment and noise. Here, we ask a fundamental question: What is the minimum amount of time it takes for a quantum system to exhibit nonclassical features in the presence of noise? Here, we prove distinct speed limits on the quantumness of observable as the norm of the commutator of two given observables. The speed limit on such quantumness measures sets the fundamental upper bound on the rate of change of quantumness, which provides the lower bound on the time required to change the quantumness of a system by a given amount. Additionally, we prove the speed limit for the nonclassical features such as quantum coherence that captures the amount of superposition in the quantum systems. We demonstrate the attainability of the upper bounds for processes of physical interest and verify their tightness through illustrated cases.

Quantum resources may provide an advantage over their classical counterparts in communication tasks. We refer to this as quantum advantage. Here, we consider a single communication task to study different approaches of observing quantum advantage. We call this setting a unified scenario. Our task is described as the following. There are three parties—the Manager, Alice, and Bob. The Manager sends a value of a random variable to Alice, and at the same time Bob receives some partial information regarding that value. Initially, neither Alice nor Bob knows the input of the other, which is received from the Manager. The goal of the task is achieved if and only if the value of the random variable, sent to Alice by the Manager, is identified by Bob with a success probability greater than half all the time. Here, nonzero error probability is allowed. However, to help Bob, Alice sends a limited amount of classical or quantum information to him (cbit or qubit). We show that the goal of the task can be achieved when Alice sends a qubit. On the other hand, a cbit communication is not sufficient for achieving the goal. Thus, it establishes quantum advantage. We further show that the optimal success probability in the overall process for a qubit communication can be higher than the optimal success probability for a cbit communication. In fact, this success probability is higher for qubit communication even if along with cbit communication Alice and Bob share randomness which allows mixing of classical strategies. Clearly, it not only establishes quantum advantage, it also demonstrates a more prominent nonclassical feature. Actually, we obtain higher success probability compared to other tasks. This also suggests the experiment-friendly nature of our task. For applications, we connect our task with semi-device-independence and show how our task can be useful to detect quantumness of a communication in a secure way. Moreover, within the same setting, we provide a way to detect universal coherence present in an ensemble. For a high-dimensional random variable, to achieve the goal, it may require a high-dimensional classical communication, while it can be achieved with only a qubit communication. This establishes a large separation between the quantum and the classical communication.

Variational quantum algorithms (VQAs) employ parametrized quantum circuits optimized using classical methods to minimize a cost function. While VQAs have found broad applications, certain challenges persist. Notably, a significant computational burden arises during parameter optimization. The prevailing “parameter shift rule” mandates a double evaluation of the cost function for each parameter. In this paper, we introduce an optimization approach named “learning to learn with an evolutionary strategy” (LLES). LLES unifies “learning to learn” and “evolutionary strategy” methods. Learning to learn treats optimization as a learning problem, utilizing recurrent neural networks to iteratively propose VQA parameters. Conversely, evolutionary strategy employs gradient searches to estimate function gradients. Our optimization method is applied to two distinct tasks: determining the ground state of an Ising Hamiltonian and training a quantum neural network. The obtained results underscore the efficacy of this approach. Additionally, we identify a key hyperparameter that significantly influences gradient estimation using the evolutionary strategy method.

Device-independent quantum key distribution (DIQKD) aims to mitigate adversarial exploitation of imperfections in quantum devices by providing an approach for secret key distillation with modest security assumptions. Advantage distillation, a two-way communication procedure in error correction, has proven effective in raising noise tolerances in both device-dependent and device-independent QKD. Previously, device-independent security proofs against independent and identically distributed (IID) collective attacks were developed for an advantage distillation protocol known as the repetition-code protocol, based on security conditions involving the fidelity between some states in the protocol. However, there exists a gap between the sufficient and necessary security conditions, which hinders the calculation of tight noise-tolerance bounds based on the fidelity. We close this gap by presenting an alternative proof structure that replaces the fidelity with the quantum Chernoff divergence, a distinguishability measure that arises in symmetric hypothesis testing. Working in the IID collective attacks model, we derive matching sufficient and necessary conditions for the repetition-code protocol to be secure (up to a natural conjecture regarding the latter case) in terms of the quantum Chernoff divergence, hence indicating that this serves as the relevant quantity of interest for this protocol. Furthermore, using this security condition we obtain some improvements over previous results on the noise tolerance thresholds for DIQKD. Our results provide insight into a fundamental question in quantum information theory regarding the circumstances under which DIQKD is possible.

The photon momentum transfer in the one-photon single ionization (1PSI) of helium is theoretically and experimentally studied. The influence of electron correlations is found to be displayed in the dimensionless photon momentum-transfer factor $F$, which takes a value of $8/5$ for the 1PSI of the $1s$ state of hydrogen. For the ground state of helium, we find that $F$ first decreases and then increases with the energy of the photoelectron, which is drastically different from the monotonic behavior predicted by the mean-field approximation. When resonances due to the doubly excited states are accessible, the parameter shows dramatic fluctuations. We report experimental results for F in the energy region of the ${\left(2s2p\right)}^1{P}_1$ and ${\left(2p^2\right)}^1{D}_2$ autoionizing states with a photon energy resolution of around 12 meV, a factor of approximately 1.7 better than the resolution reported for the pioneering data of Krässig et al. [Phys. Rev. Lett. 88, 203002 (2002)]. These high-resolution data agree very well with our theoretical predictions. Our study shows that $F$ is sensitive to effects of electron correlations.

In nonlinear topological physics, Thouless pumping of nonlinear excitations is a central topic, often illustrated by scalar solitons. Vector solitons, with the additional spin degree of freedom, exhibit phenomena absent in scalar solitons due to the enriched interplay between nonlinearity and topology. Here, we theoretically investigate Thouless pumping of vector solitons in a two-component Bose-Einstein condensate confined in spin-dependent optical superlattices, using both numerical solutions of the Gross-Pitaevskii equation and the Lagrangian variational approach. The spin-up and spin-down components experience superlattice potentials that are displaced by a tunable distance $d_r$, leading to a vector soliton state with a relative shift between its components. We demonstrate that $d_r$, as an independent degree of freedom, offers a novel control parameter for manipulating the nonlinear topological phase transition of vector solitons. Specifically, when $d_r=0$, both components are either pumped or arrested, depending on the interaction strength. When fixing the interaction strength and varying $d_r$, remarkably, we find that an arrested vector soliton can reenter the pumped regime and exhibits a quantized shift. As $d_r$ continues to increase, the vector soliton transitions into a dynamically arrested state; however, with further increases in $d_r$, the quantized shift revives. Our work paves new routes for engineering nonlinear topological pumping of solitons in spinor systems by utilizing the relative motion degrees of freedom between different spin components.

The ability to efficiently characterize the spatial correlations of entangled states of light is critical for applications of many quantum technologies such as quantum imaging. Here, we demonstrate highly efficient theoretical and experimental characterization of the spatial Schmidt modes and the Schmidt spectrum of bright multiphoton entangled states of light produced from high-gain parametric down-conversion. In contrast to previous studies, we exploit the approximate quasihomogeneity and isotropy of the signal field and dramatically reduce the numerical computations involved in the experimental and theoretical characterization procedures. In our particular case where our experimental datasets consist of 5000 single-shot images of $256\times 256$ pixels each, our method reduced the overall computation time by 2 orders of magnitude. This speedup would be even more dramatic for larger input sizes. Consequently, we are able to rapidly characterize the Schmidt modes and the Schmidt spectrum for a range of pump amplitudes and study their variation with increasing gain. Our results clearly reveal the broadening of the Schmidt modes and the narrowing of the Schmidt spectrum for increasing gain with agreement between theory and experiment.