Quantum resource theories provide a unified framework to quantitatively analyze inherent quantum properties as resources for quantum information processing. So as to investigate the best way for quantifying resources, desirable axioms for resource quantification have been extensively studied through axiomatic approaches. However, a conventional way of resource quantification by resource measures with such desired axioms may contradict rates of asymptotic transformation between resourceful quantum states due to an approximation in the transformation. In this paper we establish an alternative axiom, asymptotic consistency of resource measures, and we investigate asymptotically consistent resource measures, which quantify resources without contradicting the rates of the asymptotic resource transformation. We prove that relative entropic measures are consistent with the rates for a broad class of resources, i.e., all convex finite-dimensional resources, e.g., entanglement, coherence, and magic, and even some nonconvex or infinite-dimensional resources such as quantum discord, non-Markovianity, and non-Gaussianity. These results show that consistent resource measures are widely applicable to the quantitative analysis of various inherent quantum-mechanical properties.

The diverging responses to parameter variations of systems at quantum critical points motivate schemes of quantum critical metrology (QCM), which feature sub-Heisenberg scaling of the sensitivity with the system size (e.g., the number of particles). This sensitivity enhancement by quantum criticality is rooted in the formation of Schrödinger cat states, or macroscopic superposition states at the quantum critical points. The cat states, however, are fragile to decoherence caused by coupling to local environments, since the local decoherence of any particle would cause the collapse of the whole cat state. Therefore, it is unclear whether the sub-Heisenberg scaling of QCM is robust against the local decoherence. Here we study the effects of local decoherence on QCM, using a one-dimensional transverse-field Ising model as a representative example. We find that the standard quantum limit is recovered by single-particle decoherence. Using renormalization group analysis, we demonstrate that the noise effects on QCM is general and applicable to many universality classes of quantum phase transitions whose low-energy excitations are described by a ${\varphi }^4$ effective field theory. Since in general the many-body entanglement of the ground states at critical points, which is the basis of QCM, is fragile to quantum measurement by local environments, we conjecture that the recovery of the standard quantum limit by local decoherence is universal for QCM using phase transitions induced by the formation of long-range order. This work demonstrates the importance of protecting macroscopic quantum coherence for quantum sensing based on critical behaviors.

Entanglement witnesses form an effective method to locally detect entanglement in the laboratory without having the prior knowledge of the full density matrix. However, separable states can be erroneously indicated as entangled in such detections in the presence of wrong measurements or loss in detectors. Measurement-device-independent entanglement witnesses (MDI-EWs) never detect fake entanglement even under wrong measurements and for a particular kind of lossy detectors. A crucial assumption in the case of faithful detection of entanglement employing MDI-EWs is that the preparation devices producing “quantum inputs”—which are inputs additional to the quantum state whose entanglement is to be detected—are perfect and there is no noise during their transmission. Here we relax these assumptions and provide a general framework for studying the effect of noise on the quantum inputs, invoking uniform and nonuniform noise models. We derive sufficient conditions on the uniform noisy map for retaining the characteristic of MDI-EWs. We find that in the context of nonuniform and entangling noise, fake entanglement detection is possible even by MDI-EWs. We also investigate various paradigmatic models of local noise and find conditions of revealing entanglement in the class of Werner states.

Continuous-variable (CV) cluster states are a universal resource for fault-tolerant quantum computation when supplemented with the Gottesman-Kitaev-Preskill (GKP) bosonic code. We generalize the recently introduced subsystem decomposition of a bosonic mode [G. Pantaleoni et al., Phys. Rev. Lett. 125, 040501 (2020)], and we use it to analyze CV cluster-state quantum computing with GKP states. Specifically, we decompose squeezed-vacuum states and approximate GKP states to reveal their encoded logical information, and we decompose several gates crucial to CV cluster-state quantum computing. Then, we use the subsystem decomposition to quantify damage to the logical information in approximate GKP states teleported through noisy CV cluster states. Each of these studies uses the subsystem decomposition to circumvent complications arising from the full CV nature of the mode in order to focus on the encoded qubit information.

Continuous-variable cluster states (CVCSs) can be supplemented with Gottesman-Kitaev-Preskill (GKP) states to form a hybrid cluster state with the power to execute universal, fault-tolerant quantum computing in a measurement-based fashion. As the resource states that comprise a hybrid cluster state are of a very different nature, a natural question arises: Why do GKP states interface so well with CVCSs? To answer this question, we apply the recently introduced subsystem decomposition of a bosonic mode, which divides a mode into logical and gauge-mode subsystems, to three types of cluster state: CVCSs, GKP cluster states, and hybrid continuous-variable (CV)-GKP cluster states. We find that each of these contains a “hidden” qubit cluster state across their logical subsystems, which lies at the heart of their utility for measurement-based quantum computing. To complement the analytical approach, we introduce a simple graphical description of these CV-mode cluster states that depicts precisely how the hidden qubit cluster states are entangled with the gauge modes, and we outline how these results would extend to the case of finitely squeezed states. This work provides important insight that is both conceptually satisfying and helps to address important practical issues like when a simpler resource (such as a Gaussian state) can stand in for a more complex one (like a GKP state), leading to more efficient use of the resources available for CV quantum computing.

Given their potential for fault-tolerant operations, topological quantum states are currently a focus of intense activity. Of particular interest are topological quantum error correction codes, such as the surface and planar stabilizer codes that are equivalent to the celebrated toric code. While every stabilizer state maps to a graph state under local Clifford operations, the graphs associated with topological stabilizer codes remain unknown. We show that the toric code graph is composed of only two kinds of subgraphs: star graphs (which encode Greenberger-Horne-Zeilinger states) and half graphs. The topological order is identified with the existence of multiple star graphs, which reveals a connection between the repetition and toric codes. The graph structure readily yields a log-depth quantum circuit for state preparation, assuming geometrically nonlocal gates, which can be reduced to a constant depth including ancillae and measurements at the cost of increasing the circuit width. The results provide a graph-theoretic framework for the investigation of topological order and the development of topological error correction codes.

The electron affinity (EA) of the superheavy element Og is calculated by the use of the relativistic Fock-space coupled cluster (FSCC) and configuration interaction methods. The FSCC cluster operator expansion includes single, double, and triple excitations treated in a nonperturbative manner. The Gaunt and retardation electron-electron interactions are taken into account. Both methods yield the results that are in agreement with each other. The quantum electrodynamics correction to the EA is evaluated using the model Lamb-shift operator approach. The electron affinity of Og is obtained to be 0.076(4) eV.

An approach to translational, rotational, and vibrational temperatures of small metal clusters (${\mathrm{Ga}}_M{\mathrm{Sn}}_N, M=0,1$ and $N=6–16$) in a molecular beam from a cryogenically cooled laser vaporization source is presented. The velocity distribution in the molecular beam is measured with a mechanical shutter at a fixed photoionization delay which gives an estimate of the lower bound of the translational temperature $T_{\text{trans}}$. These values of $T_{\text{trans}}$ are found to be considerably smaller than the corresponding nozzle temperatures $T_{\text{nozzle}}=16–300\mathrm{K}$. The rotational temperature $T_{\text{rot}}$ is estimated from the comparison of an electric deflection experiment with molecular dynamics simulations and from magnetic deflection experiments to be in the range $T_{\text{rot}}=5–20\mathrm{K}$ for $T_{\text{nozzle}}=16\mathrm{K}$. The vibrational temperature $T_{\text{vib}}$ is studied by comparing magnetic deflection experiments with a microscopic model based on avoided level crossings between vibrational, rotational, and Zeeman energy levels. For $T_{\text{nozzle}}\ge 50\mathrm{K}, T_{\text{vib}}\approx T_{\text{nozzle}}$ is observed, while for lower temperatures, $T_{\text{vib}}>T_{\text{nozzle}}$. Thus, $T_{\text{trans}}\le T_{\text{rot}}<T_{\text{vib}}$ is found at least for $N=11,12$ and the lowest nozzle temperature of 16 K.

A continuous excitation band of a free-bound photoassociation transition of ytterbium atoms is observed as a red wing of the ${}^{1}S_0\text{−}{}^{1}P_1$ atomic line at 399 nm for a hot thermal vapor. The excitation to the $0_u^{+}$ molecular state is observed by monitoring fluorescence from the ${}^{3}P_1$ state atoms, which allows us to detect the production of ${\mathrm{Yb}}_2$ molecules with high sensitivity. The photoassociation is characterized in comparison with transitions to atomic Rydberg states. The time profile of the fluorescence signal suggests that the $0_u^{+}$ molecular state predissociates with states correlating to the ${}^{1}S_0+{}^{3}D_2$ atomic states.

We propose a method of generating and detecting entanglement via spin squeezing in an exciton-polariton condensate. Spin squeezing is a sensitive detector of entanglement because any squeezing below shot noise implies entanglement. In our scheme, two polariton spin species are resonantly pumped, forming a particle number fluctuating effective spin. The naturally occurring nonlinear interactions between the polaritons produce an effective one-axis squeezing interaction, which drives the system toward a spin-squeezed state at steady-state. We investigate the squeezing level that is attainable at the steady state for realistic experimental parameters and show the favorable parameters for strong squeezing. The amount of squeezing tends to improve with larger pumping, due to the bosonic enhancement of the one-axis twisting Hamiltonian. Using number-fluctuating versions of the Wineland squeezing criterion and optimal spin inequalities, we show how multipartite entanglement can be detected.

An actively correlated Mach-Zehnder interferometer (ACMZI) renders a number of significant advantages over a conventional Mach-Zehnder interferometer (MZI) with a squeezed vacuum state input such as an active output readout, loss tolerant detection, and multiarms for multiparameter estimation. We theoretically studied the quantum Cramér-Rao bound of an ACMZI, where the quantum Fisher information obtained by the phase-averaging method can give the conclusive phase-sensing sensitivity without any external phase reference. We numerically calculate the phase sensitivities with the method of homodyne detection and intensity detection in the presence of losses. Under lossless and very low loss conditions, the ACMZI is operated in a balanced case to beat the standard quantum limit (SQL). As the loss increases, the reduction in sensitivity increases. Fortunately, within a certain range, we can adjust the gain parameters of the beam recombination process to reduce the reduction in sensitivity and realize the sensitivity can continue to beat the SQL in an unbalanced situation. Our scheme provides an optimization method of phase estimation in the presence of losses.

We report measurements of the branching fraction, hyperfine constant, and second-order Zeeman coefficient of the $D_{5/2}$ level in ${}^{171}\mathrm{Yb}^{+}$ with up to a two-orders-of-magnitude reduction in uncertainty compared to previously reported values. We estimate the electric quadrupole reduced matrix element of the $S_{1/2}\leftrightarrow D_{5/2}$ transition to be 12.5(4) $e{a}_0^2$. Furthermore, we determine the transition frequency of the $F_{7/2}\leftrightarrow {}^{1}D{[3/2]}_{3/2}$ at 760 nm with a $\sim$25-fold improvement in uncertainty. These measurements provide benchmarks for quantum-many-body atomic-physics calculations and provide valuable data for efforts to improve quantum information processors based on ${}^{171}{\text{Yb}}^{+}$.

We provide an algorithm for preparing the thermofield double (TFD) state of the Sachdev-Ye-Kitaev (SYK) model without the need for an auxiliary bath. Following previous work, the TFD can be cast as the approximate ground state of a Hamiltonian, $H_{\text{TFD}}$. Using variational quantum circuits, we propose and implement a gradient-based algorithm for learning parameters that find this ground state, an application of the variational quantum eigensolver. Concretely, we find shallow quantum circuits that prepare the ground state of $H_{\text{TFD}}$ for the $q=4$ SYK model for $N=8$ Majoranas per side. For $N=12$, we achieve a variational energy within 1% of the true ground-state energy.

We evaluate analytically the quantum discord for a large family of multiqubit states. It is interesting to note that the quantum discord of three qubits and five qubits is the same, as is the quantum discord of two qubits and six qubits. We discover that the quantum discord of this family of states can be classified into three categories. The level surfaces of the quantum discord in the three categories are shown through images. Furthermore, we investigated the dynamic behavior of quantum discord under decoherence. For the odd partite systems, we prove the frozen phenomenon of quantum discord does not exist under the phase flip channel, while it can be found in the even partite systems.

Nonadiabatic holonomic gates provide an effective means to perform high-speed and error-resilient manipulation of quantum states. It is practically important to realize nonadiabatic holonomic multiqubit controlled gates since multiqubit controlled gates are widely used in quantum information processing. Rydberg atoms are an appealing physical system for the realization of nonadiabatic holonomic multiqubit controlled gates as the Rydberg-mediated interaction is beneficial to couple two qubits. In this paper, we put forward a scheme for the realization of nonadiabatic holonomic multiqubit controlled gates based on Rydberg atoms, where an $(n+1)$-qubit controlled-$\left(\mathrm{n}·\mathbf{\sigma }\right)$ gate can be realized by $(2n-1)$ basic operations. Moreover, the effective coupling between two qubits is in the first-order strength of Rabi frequencies, which allows for the implementation of quantum gates within a short duration.

Nonstoquastic Hamiltonians are hard to simulate due to the sign problem in quantum Monte Carlo simulation. It is, however, unclear whether nonstoquasticity can lead to advantage in quantum annealing. Here we show that $YY$ interactions between the qubits make the adiabatic path during quantum annealing, and therefore the performance, dependent on spin-reversal transformations. With the right choice of spin-reversal transformation, a nonstoquastic Hamiltonian with $YY$ interaction can outperform stoquastic Hamiltonians with similar parameters. We introduce an optimization protocol to determine the optimal transformation and discuss the effect of suboptimality.

We consider theoretically the process of two-electron one-photon (TEOP) transitions to the ground state with the emission of a single $K_{\alpha \alpha }$ photon in a He-like sequence of atomic ions: from boron to uranium. The corresponding transition probabilities and transition energies are calculated within the QED theory. The calculations of the transition probabilities are performed in various gauges. The intensity ratios between the TEOP transitions and the other major transitions are presented.

In this study, we investigate the three-body recombination (TBR) rates on both sides of the interspecies $d$-wave Feshbach resonance in the ${}^{85}\mathrm{Rb}$ -${}^{87}\mathrm{Rb}-{}^{87}\mathrm{Rb}$ system using the $R$-matrix propagation method in the hyperspherical coordinate frame. Our calculations are based on the Lennard-Jones model potential for the Rb-Rb interaction. Two different mechanisms of recombination-rate enhancement for positive and negative ${}^{85}\mathrm{Rb}$ -${}^{87}\mathrm{Rb} d$-wave scattering lengths are analyzed. On the positive-scattering-length side, recombination-rate enhancement occurs due to the existence of three-body shape resonance, while on the negative-scattering-length side, the coupling between the lowest entrance channel and the highest recombination channel is crucial to the appearance of the enhancement. In addition, our study shows that the intraspecies interaction has a significant role in determining the emergence of recombination-rate enhancements. Compared to the case in which the three pairwise interactions are in $d$-wave resonance, when the ${}^{87}\mathrm{Rb}-{}^{87}\mathrm{Rb}$ interaction is near the $d$-wave resonance, the values of the interspecies scattering length that produce the recombination enhancement shift. In particular, when the ${}^{87}\mathrm{Rb}-{}^{87}\mathrm{Rb}$ interaction is away from the $d$-wave resonance, the enhancement disappears on the side with negative interspecies scattering length.