We propose a quantum game based on coin-based quantum walks. Given a quantum walk and a Hermitian operator on the coin-position composite space, winning this game involves choosing an initial coin state such that the given quantum walk leads to a composite state in which the expectation value of the given Hermitian operator is greater than a certain value. Parrondo's paradox is a phenomenon where a combination of losing strategies becomes a winning strategy. We give a deterministic scheme for identifying Parrondo's paradox in our game, in the sense that, given a collection of distinct quantum steps, we identify initial coin states which happen to be losing states for all quantum walks comprised solely of these steps individually, but turn out to be winning states for a quantum walk comprised of all the given steps taken in a sequence. Unlike traditional quantum steps that allow for equal magnitude forward and backward strides based on the outcome of the coin toss, the steps of the quantum walks employed here, though still contingent upon coin toss, permit the strides to be of unequal magnitude, and not necessarily in opposite directions. We believe the results presented here will contribute to a deeper understanding of evolution of expectation values of observables in quantum walks, and facilitate the development of novel quantum algorithms.

Search and state transfer between hubs, i.e., fully connected vertices, on otherwise arbitrary connected graph is investigated. Motivated by a recent result of Razzoli et al. [J. Phys. A: Math. Theor. 55, 265303 (2022)] on the universality of hubs in continuous-time quantum walks and spatial search, we extend the investigation to state transfer and also to the discrete-time case. We show that the continuous-time quantum walk allows for perfect state transfer between multiple hubs if the numbers of senders and receivers are close. Turning to the discrete-time case, we show that the search for hubs is successful provided that the initial state is locally modified to account for a degree of each individual vertex. Concerning state transfer using discrete-time quantum walk, it is shown that between a single sender and a single receiver one can transfer two orthogonal states in the same run time. Hence, it is possible to transfer an arbitrary quantum state of a qubit between two hubs. In addition, if the sender and the receiver know each other location, another linearly independent state can be transferred, allowing for exchange of a qutrit state. Finally, we consider the case of transfer between multiple senders and receivers. In this case we cannot transfer specific quantum states. Nevertheless, quantum walker can be transferred with high probability in two regimes—either when there is a similar number of senders and receivers, which is the same as for the continuous-time quantum walk, or when the number of receivers is considerably larger than the number of senders. Our investigation is based on dimensional reduction utilizing the invariant subspaces of the respective evolutions and the fact that for the appropriate choice of the loop weights the problem can be reduced to the complete graph with loops.

Partial differential equations frequently appear in the natural sciences and related disciplines. In this work, we explore the potential for enhancing a classical deep-learning-based method for solving high-dimensional nonlinear partial differential equations with suitable quantum subroutines. In a first approach, we construct a deep-learning architecture based on variational quantum circuits without provable guarantees. In a second approach, tailored towards fault-tolerant quantum computers, find that quantum-accelerated Monte Carlo methods offer the potential to speed up the estimation of the loss function. In addition, we identify and analyze the trade-offs when using quantum-accelerated Monte Carlo methods to estimate the gradients with different methods, including a recently developed backpropagation-free forward gradient method. Finally, we discuss the usage of a suitable quantum algorithm for accelerating the training of feed-forward neural networks. Hence, this work provides different avenues with the potential for polynomial speedups for deep-learning-based methods for nonlinear partial differential equations.

We experimentally implement circuits of one- and two-mode operations on two motional modes of a single trapped ion. This is achieved by implementing the required displacement, squeezing, two-mode squeezing, and beam-splitter operations using oscillating electric potentials applied to the trap electrodes. The resulting electric fields drive the modes resonantly or parametrically without the need for optical forces. As a demonstration, we implement SU(2) and SU(1,1) interferometers with phase sensitivities near the Cramér-Rao bound. We report a maximum sensitivity of a SU(2) interferometer within 0.67(5) dB of the standard quantum limit (SQL) as well as a single- and two-mode SU(1,1) sensitivity of 5.9(2) dB and 4.5(2) dB below the SQL, respectively.

Relativistic coupled-cluster (RCC) theory at the singles and doubles approximation has been implemented to estimate nuclear-spin-dependent (NSD) parity-violating (PV) electric dipole ($E1$) transition amplitudes ($E{1}_{\mathrm{PV}}^{\mathrm{NSD}}$) among hyperfine levels of the $6s{}^{2}S_{1/2}\to 7s{}^{2}S_{1/2}$ transition in ${}^{133}\mathrm{Cs}$. To validate our calculations, we reproduce the Dirac-Hartree-Fock values and results from the combined coupled-Dirac-Hartree-Fock and random phase approximation (CPDF-RPA) method reported earlier. Contributions from the double-core-polarization (DCP) effects with the CPDF-RPA method were found to be between 3% and 12% among different hyperfine levels. We derived a generalized expression for $E{1}_{\mathrm{PV}}^{\mathrm{NSD}}$, which helped incorporate both the NSD PV Hamiltonian and $E1$ operator simultaneously in the perturbative approach to account for the DCP contributions. The RCC method subsumes the CPDF-RPA and DCP effects in addition to contributions from the Brückner pair correlations and normalization of the wave functions and correlations among them. To improve accuracy of the $E{1}_{\mathrm{PV}}^{\mathrm{NSD}}$ amplitudes further, we replace the ab initio values of the $E1$ matrix elements and energies by their experimental values via a sum-over-states approach.

The analytical calculation of the complete $\alpha {\left(Z\alpha \right)}^6$ one-loop radiative correction to energies of two-body systems with the angular momenta $l>0$, consisting of a pointlike particle and an extended-size nucleus with arbitrary masses and spin 1/2, is presented. The obtained results apply to a wide variety of two-body systems, such as hydrogen, muonium, positronium, and antiprotonic atoms.

We consider construction of effective Hamiltonians for periodically driven interacting systems in the case of resonant driving. The standard high-frequency expansion is not expected to converge due to the resonant creation of collective excitations, and one option is to resort to the application of degenerate perturbation theory (DPT) in the Floquet-Hilbert space. We propose an extension of DPT whereby the degenerate subspace includes not only the degenerate levels of interest but rather all levels in a Floquet zone. The resulting approach, which we call extended DPT (EDPT), is shown to resemble a high-frequency expansion, provided the quasienergy matrix is constructed such that each $m\mathrm{th}$ diagonal block contains energies reduced to the $m\mathrm{th}$ Floquet zone. The proposed theory is applied to a driven Bose-Hubbard model and is shown to yield more accurate quasienergy spectra than the conventional DPT. The computational complexity of EDPT is intermediate between DPT and the numerically exact approach, thus providing a practical compromise between accuracy and efficiency.

Recently achieved chiral condensates open intriguing avenues for the study of the chiral properties induced by current-density interactions. An attempt to include these features in a spinor system is presented, which gives rise to a nonlinear, effective spin-orbit coupling that emerges from the differential orbital currents, along with constraints in the conserved quantities due to the linear coupling between spin components. Chirality pervades the resulting spectrum of stationary states and their dynamical stability, which are explored in plane waves, dark and bright solitons, and Josephson vortices. Our analytical and numerical results reveal the destabilizing role of polarization and Josephson currents and support the existence of stable nonlinear states built of linear superpositions of plane waves.

The stimulated Raman adiabatic passage (STIRAP) allows selective, coherent population transfer in a three-level quantum system by the adiabatic control of two suitably chosen envelopes and delayed laser pulses. However, the long operation time involved with the adiabatic protocols makes them more susceptible to decay and decoherence. A shortcut-to-adiabaticity technique, namely, counterdiabatic driving (CD), suppresses the decoherence-induced loss by speeding up the STIRAP process, thereby enhancing the efficiency and fidelity of population transfer. The superadiabatic STIRAP (saSTIRAP) method requires the application of a shortcut drive or CD pulse, which couples the coherently trapped states in a three-level quantum system. Hence, the closed-loop $\mathrm{\Lambda }$ system consisting of all electric dipole-allowed transitions is an essential requirement for saSTIRAP, which is rarely admissible in a natural atom. This paper theoretically investigates an experimentally feasible model for implementing saSTIRAP using a closed-loop $\mathrm{\Lambda }$ system with doubly dressed polariton states in a driven circuit QED system. We show a population transfer with efficiencies close to $80.75\%$ and $98.10\%$ with fidelities of $89.86\%$ and $99.04\%$ for the resonant STIRAP and saSTIRAP protocols, respectively, with experimentally feasible parameters. The efficiency of the population transfer can be further increased by improving the coherence times of the cavity and the transmon qubit. This work may be useful in designing fast, efficient quantum gates for applications in quantum technologies.

The Einstein-Podolsky-Rosen (EPR) paradox gives an argument for the incompleteness of quantum mechanics based on a plausible criterion for reality, as well as the assumption of locality. A general view is that the argument is compromised, because EPR's premises are falsified by Greenberger-Horne-Zeilinger (GHZ) and Bell experiments. In this paper, we present an EPR argument based on premises not falsified by these experiments. First, we consider macroscopic EPR-Bohm, Bell, and GHZ experiments using spins ${\widehat{S}}_{\theta }$ defined by two macroscopically distinct states. The analyzers that realize the unitary operations $U_{\theta }$ determining the measurement settings $\theta$ are nonlinear devices creating macroscopic superposition states. We note two definitions of macroscopic realism (MR). For a system with two macroscopically distinct states available to it, MR posits a predetermined outcome for the measurement ${\widehat{S}}_{\theta }$ distinguishing between the states. Deterministic macroscopic realism assumes MR for the system defined prior to the interaction $U_{\theta }$ being carried out but is falsifiable by the macroscopic Bell and GHZ proposals. Motivated by arguments to uphold MR (without resorting to decoherence), as well as no-signaling and the properties of a meter, we define a set of premises referred to as weak macroscopic realism (wMR). Weak macroscopic realism (wMR) posits MR for the system after $U_{\theta }$, at the time $t_f$—when the system is prepared with respect to the measurement basis, ready for a “pointer” measurement and readout. For this system, wMR posits that the outcome of ${\widehat{S}}_{\theta }$ is determined and not changed by interactions that might subsequently occur at a remote system $B$. The premise wMR also posits a weaker version of EPR's criterion for reality. Importantly, we show that the GHZ and Bell predictions are consistent with wMR. Yet, an EPR paradox arises for a macroscopic EPR-Bohm state, based on wMR. As considered by Schrödinger, it is possible to measure two complementary spins of system $A$ simultaneously, “one by direct, the other by indirect measurement”: If we assume wMR, then once both settings are fixed, the outcomes of the two spins are both determined. We revisit the original EPR paradox and find a similar result: An EPR argument can be based on a set of premises, weak local realism, which we show are not falsifiable by GHZ or Bell experiments.

Wigner's friend paradoxes highlight contradictions between measurements made by friends inside a laboratory and superobservers outside the laboratory, who have access to an entangled state of the measurement apparatus. Where there are two separated laboratories, the contradictions lead to no-go theorems for observer-independent facts, thus challenging concepts of objectivity. Here, we examine the paradoxes from the perspective of establishing consistency with macroscopic realism. We present versions of the Brukner-Wigner's-friend and Frauchiger-Renner paradoxes in which the spin-$1/2$ systems measured by the friends correspond to two macroscopically distinct states. The local unitary operations $U_{{\theta }_j}$ that determine the measurement settings ${\theta }_j$ at each laboratory are carried out using nonlinear interactions, which are tailored to ensure that measurements need only distinguish between the macroscopically distinct states. The macroscopic paradoxes are perplexing, seemingly suggesting there is no objectivity in a macroscopic limit. However, we demonstrate consistency with a contextual weak form of macroscopic realism (wMR): The premise wMR asserts that each system $j$ can be considered to have a definite spin outcome ${\lambda }_{{\theta }_j}$, at the time after the system has undergone the local unitary rotation $U_{{\theta }_j}$ to prepare it in a suitable measurement basis. We further show that the paradoxical outcomes imply failure of deterministic macroscopic local realism and arise when there are unitary interactions $U_{{\theta }_j}$ occurring due to a change of measurement setting at both laboratories, with respect to the state prepared by each friend. In models which validate wMR, there is a breakdown of a subset of the assumptions that constitute the Bell-locality premise. A similar interpretation involving a contextual weak form of local realism exists for the original paradoxes.

Since both coherence and quantum correlations arise from the superposition principle and can be regarded as resources in quantum information tasks, it is of significance to investigate the interplay between them from different perspectives. In this work we focus on the basis-dependent correlations in a bipartite state defined by the coherence difference between global state and local state relative to a local basis and characterize bipartite states with vanishing basis-dependent correlations. Using the relative entropy of coherence, the structure of such states has been determined by Yadin et al. [Phys. Rev. X 6, 041028 (2016)], which we call block-diagonal product states here. The first result of this work is to demonstrate that the set of block-diagonal product states can also be characterized by the property of possessing vanishing basis-dependent correlations using the coherence measure based on skew information. As a by-product of this result, we describe the structure of quantum ensembles saturating the convexity inequality in the resource theory of coherence using the coherence measure based on skew information, which may be of independent interest. Next, we characterize the set of bipartite states with vanishing basis-dependent correlations using the $l_1$ norm of coherence, and show that the set of block-diagonal product states is a subset of it. Furthermore, we provide an operational interpretation of block-diagonal product states in an interference model. Finally, we compare the amount of basis-dependent correlations using the three mentioned coherence measures through several examples such as Werner states, isotropic states, Bell-diagonal states, and a family of classical-quantum states.

Entanglement subject to noise cannot be shielded against decaying. But, in case of many noisy channels, the degradation can be partially prevented by using local unitary operations. We consider the effect of local noise on shared quantum states and evaluate the amount of entanglement that can be preserved from deterioration. The amount of saved entanglement not only depends on the strength of the channel but also on the type of the channel, and in particular, it always vanishes for the depolarizing channel. The main motive of this work is to analyze the reason behind this dependency of saved entanglement by inspecting properties of the corresponding channels. In this context, we quantify and explore the biasnesses of channels towards the different states on which they act. We postulate that all biasness measures must vanish for depolarizing and unitary channels, and subsequently introduce a few measures of biasness. We also consider the entanglement capacities of channels. We observe that the joint behavior of the biasness quantifiers and the entanglement capacity explains the nature of saved entanglement. Furthermore, we find a pair of upper bounds on saved entanglement which are noticed to imitate the graphical nature of the latter.

Quantum Fisher information (QFI) may exhibit the irregular behavior at the critical point of phase transitions of a physical system and be very sensitive to slight variations of some controlling parameters. This parameter sensitivity may be used for quantum parameter estimation or quantum sensing. In this study, taking the quantum Rabi model as an example, we investigate the critical properties of the QFI for the parameter estimation at the critical point of the SU(1,1) dynamic systems. We show that the QFI goes divergently in the sixth power law $\left(T^6\right)$ of the parameter coding time around the critical point. After taking into the consumption of energy during the dynamic evolution, we find that the variation of the QFI around the critical point is scaled by the Heisenberg scaling $T^2$. It is noticed that for nonclassical initial probe states the scaling of QFI can beat the standard quantum limit $\left(n_0\right)$ as a function of the initial mean phonon number $n_0$. The homodyne and phonon-number measurement schemes are compared. We find that the quantum Cramér-Rao bound can be reached by use of the phonon-number detection scheme. However, it is more sensitive to the noise than the homodyne detection scheme. We extend the investigation to a two-mode non-Hermitian system and show that the QFI exhibits the same irregular properties at the exceptional point, revealing that for the SU(1,1) dynamic systems the QFI universally diverges as $T^6$ at the critical point.

Non-Rydberg resonant states are a special type of resonant states with open-shell electronic configurations that cannot be partitioned into a quasi-two-body system of a tightly coupled ion target and a loosely coupled projectile electron as the case of Rydberg states, which is an important type of resonant processes in atomic and molecular systems. Previous treatments of non-Rydberg resonances in the context of multichannel quantum defect theory (MQDT) were to introduce these states as resonances in the smoothly varied MQDT parameters, and the main merit of the MQDT method for Rydberg states would be lost. To reconcile the efficiency and numerical accuracy for the calculation of non-Rydberg states, a nonperturbative calculation approach is proposed in this paper. In this approach, the smooth-varying short-range scattering matrices are obtained by applying the eigenchannel $R$-matrix method to the subsystem excluding the non-Rydberg states. Subsequently, the non-Rydberg states are restored using the configuration-interaction formalism. The scattering matrices with resonant structures can then be obtained directly using simple linear algebra operations. Since the ingredients of the procedure are all smooth functions of energy, only a sparse energy grid is required for the time-consuming ab initio calculations. This makes our method highly computationally efficient and can be considered as an extension of the traditional MQDT. To demonstrate the efficacy of our method, the resonant $e+{\mathrm{O}}^{+}$ collisional complex in the $1^{-}$ partial wave is calculated. In addition, we demonstrate that the numerical accuracy of the scattering matrices is significantly affected by the non-Rydberg states.

The approach of photoemission orbital tomography (POT), i.e., the orbital density reconstruction from photoemission of planar molecular layers, is applied to measurements of the partial cross section from gas-phase methane $\left({\mathrm{CH}}_4\right)$. Within a central-field and one-electron model, the method previously validated on neon is tested on ${\mathrm{CH}}_4$'s molecular orbitals $2a_1$ and $1t_2$ with the goal to reconstruct absolute radial orbital densities. The reconstruction method is based on a Markov chain Monte Carlo optimization method, employing Bayesian inference, which additionally offers a reliable uncertainty evaluation. Applying the method to ${\mathrm{CH}}_4$, we aim to bridge the gap between simple single atoms and molecular layers, and to find a practical reference standard for the determination of orbital densities within POT.

Motivated by discrepancies between recent cold-atom experiments and the associated theory, we explore the effect of immobile holes on the quantum dynamics of $x\text{−}z$ spin helices in the one-dimensional $XX$ model. We calculate the exact spin dynamics by mapping onto a system of noninteracting fermions, averaging over the distribution of holes. At small hole densities we find that the helical spin pattern decays exponentially, with a pitch dependence that agrees with the experiments. At large hole densities we instead find persistent oscillations. While our analytic approach does not generalize to the $XXZ$ model with arbitrary anisotropies, we validate a matrix-product-state technique which might be used to model the experiments in those settings.