We propose a scheme for the sharing of quantum steering among three observers, Alice, Bob, and Charlie, using standard projective measurements. We show that in the unilateral sequential scenario, Alice can steer Bob's and Charlie's states and conversely, Bob and Charlie can steer Alice's state. Unlike the quantum steering sharing achieved through weak measurements, we use the standard projective measurements to enable quantum steering sharing. Quantum steering is demonstrated by the violations of the linear steering inequality among different observer combinations. We find that Alice can simultaneously steer both Bob's and Charlie's states, and Bob and Charlie can simultaneously steer Alice's state, regardless of whether they are in maximally entangled states or partially entangled states. The maximum double violation of the linear steering inequalities obtained from partially entangled states may not be greater in some cases than that obtained from maximally entangled states. Additionally, we verify hybrid quantum correlation sharing through the double violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality and the linear steering inequality. Our results provide an alternative perspective for studying quantum steering and hybrid quantum correlation and may lead to applications in quantum random access code, randomness certification, and self-testing processes.

Quantum network nonlocality sharing provides a unique perspective for constructing large-scale quantum networks and holds promise for numerous potential applications. In this paper we demonstrate the network nonlocality sharing via unsharp measurements in a two-forked $n$-layer tree-shaped network, which features $2^n-2$ independent sources and $2^n-1$ nodes. We investigate the $(2^n-2)$-local scenarios via any $m$-sided sequential measurements, and conclude that arbitrarily many independent observers on each sequential side can share the non-$(2^n-2)$-locality for a sufficiently large value of $n$. For a finite $n$, we present a method that enables directly obtaining the number of observers on each sequential side, who can share the non-$(2^n-2)$-locality simultaneously. To interpret our results more intuitively, we discuss the simplest case of $n=3$, and find that at most 30, 6, 3, and 2 sequential observers per sequential side can simultaneously share the non-6-locality in $m$-sided cases for $m=1,2,3,4$, respectively.

Resisting diverse noise effects is crucial for the accurate manipulation of quantum systems. For static or slowly varying noises, many efficient noise mitigation strategies have been developed, such as composite pulses and dynamical decoupling. However, for fast fluctuating noise in the Markovian limit, whether and to what extent coherent quantum control can enhance quantum engineering tasks remains unclear and less explored. Here, we propose a robust quantum optimal control method to tackle Markovian noises. The basic idea is that, regarding the Markovian noise channel as perturbation, we quantitatively characterize the noise-induced error evolution by the perturbative expansion term, and then take them as the objective functions to be suppressed. During optimization, the optimal controls are obtained by maximizing the control target function and meanwhile minimizing the perturbative terms due to Markovian noise order by order. As demonstration examples, we first apply our method to quantum state transfer tasks on two-level and three-level $\mathrm{\Lambda }$ systems, then use it to design quantum gates in two-level and three-level ladder systems, all under Markovian noises. The simulation results illustrate that our method can notably enhance quantum state transfer fidelities and have very limited improvement on gate fidelities. The method presented here is versatile and can be extended to enhance the performance of various control tasks under Markovian noise in multilevel or multiqubit quantum systems.

We introduce a class of entangled subspaces: completely entangled subspaces of entanglement depth $k$ $\left(k\text{−}\text{CESs}\right)$. These are subspaces of multipartite Hilbert spaces containing only pure states with an entanglement depth of at least $k$. We present an efficient construction of $k\text{−}\text{CESs}$ of any achievable dimensionality in any multipartite scenario. Further, we discuss the relation between these subspaces and unextendible product bases (UPBs). In particular, we establish that there is a nontrivial bound on the cardinality of a UPB whose orthocomplement is a $k\text{−}\text{CES}$. Further, we discuss the existence of such UPBs for qubit systems.

Variational quantum algorithms have emerged as a cornerstone of contemporary quantum algorithms research. Practical implementations of these algorithms, despite offering certain levels of robustness against systematic errors, show a decline in performance due to the presence of stochastic errors and limited coherence time. In this work, we develop a recipe for mitigating quantum gate errors using zero-noise extrapolation. We introduce an experimentally amenable method to control error strength in the circuit. We utilize the fact that gate errors in a physical quantum device are distributed inhomogeneously over different qubits and qubit pairs. As a result, one can achieve different circuit error sums based on the manner in which abstract qubits in the circuit are mapped to a physical device. We apply the proposed protocol to variational quantum algorithms and find that the estimated energy is approximately linear with respect to the circuit error sum (CES). Consequently, a linear fit through the energy-CES data, when extrapolated to zero CES, can approximate the energy estimated by a noiseless variational algorithm. We demonstrate this numerically and investigate the applicability range of the technique.

Multipartite entanglement includes not only the genuine entanglement but also the $k$-entanglement $(k⩾2)$. It is known that the most bipartite entanglement measures have been shown to be monogamous, but the monogamy relation is involved in the bipartite entanglement measures rather than the multipartite ones. So how we can explore the monogamy relation for $k$-entanglement becomes a basic open problem. In this paper we establish an axiomatic definition of the monogamy relation for the $k$-entanglement measure based on the coarser relation of the system partition. We also present the axiomatic definition of the complete $k$-entanglement measure and the associated complete monogamy relation according to the framework of the complete multipartite entanglement measure we established in [Phys. Rev. A 101, 032301 (2020)], which is shown to be an efficient tool for characterizing the multipartite quantum correlation as complementary to the monogamy relation associated with the bipartite measure. Consequently, the relation and the difference between monogamy, complete monogamy, and tightly complete monogamy are clearly depicted in light of the three types of coarser relation of the system partition. We then illustrate our approach with two classes of $k$-entanglement measures in detail. We find that all these $k$-entanglement measures are monogamous if the reduced function is strictly concave, they are not completely monogamous, and they are not complete generally.

Equivalence between positive partial transpose (PPT) entanglement and bound entanglement is a long-standing open problem in quantum information theory. Limited progress has been made so far, even on the seemingly simple case of the bound entanglement of Werner states. The primary challenge is to give a concise mathematical representation of undistillability. To this end, we propose a decomposition of the $N$-undistillability verification into $\text{log}\left(N\right)$ repeated steps of 1-undistillability verification. For Werner states' $N$-undistillability verification, a parameter interval for $N$-undistillability is given, which is independent of the dimensionality of Werner states. Equivalent forms of inequalities for both rank 1 and 2 matrices are presented, before transforming the 2-undistillability case into a matrix analysis problem. A new perspective is also attempted by seeing it as a nonconvex multivariable function, proving its critical points and conjecturing Hessian positivity, which would make them local minimums.

The investigation of many-body interactions holds significant importance for both quantum foundations and information. Hamiltonians coupling multiple particles at once, beyond other applications, can lead to faster entanglement generation, multiqubit gate implementation, and improved error correction. As an increasing number of quantum platforms can enable the realization of such physical settings, it has become interesting to study the verification of many-body-interaction resources. In this work, we explore the possibility of higher-order coupling detection through the quantum Fisher information. For a family of normalized symmetric $k$-body Ising-like Hamiltonians, we derive bounds on the quantum Fisher information in product states. Due to its ordering with respect to the order of interaction, we demonstrate the possibility of detecting many-body couplings for a given Hamiltonian from the discussed family by observing violations of an appropriate bound. As a possible extension to these observations, we further analyze an example concerning three-body-interaction detection in the $XY$ model.

The quadrature coherence scale (QCS) is a recently introduced measure that was shown to be an efficient witness of nonclassicality. It takes a simple form for pure and Gaussian states, but a general expression for mixed states tends to be prohibitively unwieldy. In this paper we introduce a method for computing the quadrature coherence scale of quantum states characterized by Wigner functions expressible as linear combinations of Gaussian functions. Notable examples within this framework include cat states, Gottesman-Kitaev-Preskill states, and states resulting from Gaussian transformations, measurements, and breeding protocols. In particular, we show that the quadrature coherence scale serves as a valuable tool for examining the scalability of nonclassicality in the presence of loss. Our findings lead us to put forth a conjecture suggesting that, subject to 50% loss or more, all pure states lose any QCS-certifiable nonclassicality. We also consider the quadrature coherence scale as a measure of quality of the output state of the breeding protocol.

Quantum kernel methods have been actively examined from both theoretical and practical perspectives due to the potential of quantum advantage in machine learning tasks. Despite a provable advantage of fine-tuned quantum kernels for specific problems, widespread practical usage of quantum kernel methods requires resolving the so-called vanishing similarity issue, where exponentially vanishing variance of the quantum kernels causes implementation infeasibility and trainability problems. In this work, we analytically and numerically investigate the vanishing similarity issue in projected quantum kernels with alternating layered Ansätze. We find that variance depends on circuit depth, the size of local unitary blocks, and the initial state, indicating the issue is avoidable if shallow alternating layered Ansätze are used and the initial state is not highly entangled. Our work provides some insight into design principles of projected quantum kernels and implies the need for caution when using highly entangled states as input to quantum kernel-based learning models.

The telecloning protocol distributes quantum states from a single sender to multiple receivers via a shared entangled state by exploiting the notions of teleportation and approximate cloning. We investigate the optimal telecloning fidelities obtained using both Gaussian and non-Gaussian shared resources. When the shared non-Gaussian state is created by subtracting photons from both the modes of the Gaussian two-mode squeezed vacuum state, we demonstrate that higher telecloning fidelities can be achieved in comparison with its Gaussian counterpart. To quantify this advantage, we introduce a quadrature-based nonclassicality measure, which is capable of estimating the fidelity of the clones, both with Gaussian and non-Gaussian resource states. We further provide a linear optical setup for asymmetric telecloning of continuous variable states using a multimode entangled state.

The resource theory of quantum thermodynamics has emerged as a powerful tool for exploring the out-of-equilibrium dynamics of microscopic and highly correlated systems. Recently, it has been employed in photoisomerization, a mechanism facilitating vision through the isomerism of the photoreceptor protein rhodopsin, to elucidate the fundamental limits of efficiency inherent in this physical process. Limited attention has been given to the impact of energetic quantum coherences in this process, as these coherences do not influence the energy-level populations within an individual molecule subjected to thermal operations. However, a specific type of energetic quantum coherences can impact the energy-level populations in the scenario involving two or more molecules. In this study, we examine the case of two molecules undergoing photoisomerization to show that energetic quantum coherence can function as a resource that amplifies the efficiency of photoisomerization. These insights offer evidence for the role of energetic quantum coherence as a key resource in the realm of quantum thermodynamics at mesoscopic scales.

Quantifying the effect of noise on unitary operations is an essential task in quantum information processing. We propose the quantum Wasserstein distance between unitary operations, which shows an explanation for quantum circuit complexity and characterizes the local distinguishability of multiqudit operations. We show analytical calculations of the distance between identity and widely used quantum gates including swap, cnot, and other controlled gates. As an application, we estimate the closeness between quantum gates in a circuit and show that the noisy operation simulates the ideal one well when they become close under the distance. Further, we introduce the $W_1$ error rate by the distance and establish the relation between the $W_1$ error rate and two practical cost measures of recovery operations in quantum error correction under typical noise scenarios. These applications allow the distance to quantify the effect of noise on unitary operations from the perspective of experiment resources, which cannot be achieved by existing distance.

Multisqueezed states, also known as generalized squeezed states, are valuable quantum non-Gaussian resources, because they can feature nonclassical properties such as large phase-space Wigner negativities. In this paper, we introduce a shortcuts to adiabaticity (STA) method for the fast preparation of multisqueezed states. In contrast to previous STA methods, which rely on the use of counterdiabatic control to suppress unwanted nonadiabatic effects, our method simplifies the process and accelerates state preparation by selecting an appropriate sampling along a quantum evolution path. We demonstrate the high fidelity and fast preparation of multisqueezed states, as well as hybrid entangled states between a bosonic mode and a qubit.

A method, termed controlled injection, is proposed for compiling three-qubit controlled gates within the non-Abelian Fibonacci anyon model. Building on single-qubit compilation techniques with three Fibonacci anyons, the approach showcases enhanced accuracy and reduced braid length compared to the conventional decomposition method for the controlled three-qubit gates. This method necessitates only four two-qubit gates for decomposition, a notable reduction from the conventional five. In conjunction, the study introduces a class of controlled three-qubit gates and conducts a numerical simulation of the topological $i\mathrm{Toffoli}$ gate to validate the approach. In addition, we propose an optimization method for single-qubit gate approximation using algebraic relations and numerical methods, including distributed computing.

Efficient decomposition of multiqubit operators is critical in the execution of quantum algorithms. In this paper, we introduce decompositions of the multiple controlled-$Z$ (ccz and cccz) gates tailored to various qubit-coupling graphs. Specifically, we demonstrate that the ccz gate is realized with cz-depth 4 on a square-shaped qubit-coupling graph utilizing one auxiliary qubit. As for the cccz gate, previous research indicated that the decomposition requires 14 cz gates in a fully connected topology. However, our findings reveal that only four specific qubit couplings are needed to achieve a decomposition using the same number of cz gates, 14. Our research employs an optimization method to improve the alignment of parametrized quantum circuits with their intended quantum gates, which facilitates these efficient decompositions. This methodology is versatile and can be applied to decompose any quantum gates, not just the ccz and cccz gates. These advancements in decomposing multiqubit gates, coupled with our ccz and cccz decompositions, are poised to reduce quantum circuit execution times and enhance the efficiency of complex quantum algorithms in imminent quantum computing applications.

Highly charged ions of heavy actinides from uranium to einsteinium are studied theoretically to find optical transitions sensitive to the variation of the fine-structure constant. A number of promising transitions have been found in ions with ionization degree $\sim$ 10. All these transitions correspond in single-electron approximation to the $6p-5f$ transitions. Many of the transitions are between ground and excited metastable states of the ions, which means that they can probably be used as optical clock transitions. Some of the ions have more than one clock transition with different sensitivity to the variation of the fine-structure constant $\alpha$. The most promising systems include the ${\mathrm{Np}}^{10+}$, ${\mathrm{Np}}^{9+}$, ${\mathrm{Pu}}^{11+}$, ${\mathrm{Pu}}^{10+}$, ${\mathrm{Pu}}^{9+}$, ${\mathrm{Pu}}^{8+}$, ${\mathrm{Bk}}^{15+}$, ${\mathrm{Cm}}^{12+}$, and ${\mathrm{Es}}^{15+}$ ions.

Numerical calculations of the sensitivity coefficients, $Q_{\mu }$, of microwave molecular transitions in the ground torsion-rotation state of deuterated methanol $({\mathrm{CH}}_3\mathrm{OD},$ ${\mathrm{CD}}_3\mathrm{OH}, \text{and} {\mathrm{CD}}_3\mathrm{OD})$ to small variations in the fundamental physical constant $\mu =m_e/m_p$—the electron-to-proton mass ratio—are reported. Theoretical motivation for changes in $\mu$ comes from a variety of models beyond the standard model of particle physics which are invoked to explain the nature of dark matter and dark energy that dominate the Universe. The calculated values of $Q_{\mu }$ range from $-300$ to $+73$ and, thus, make deuterated methanol promising for searches for small space-time changes in $\mu$. It is also shown that, among the calculated sensitivity coefficients $Q_{\mu }$ using different Hamiltonians in the present and previous works, there are several pronounced outliers of unclear nature.

We experimentally investigate the Rydberg-state excitation (RSE) process induced by a strong near-infrared (NIR) laser field for nitrogen dioxide $\left({\mathrm{NO}}_2\right)$ molecules which are initially excited in the ${\tilde{A}}^2{B}_2$ state by a UV laser field. Both the neutral parent ${\mathrm{NO}}_2$ and the fragments are observed to survive the strong laser field in high Rydberg states. It is found that the RSE yield of ${\mathrm{NO}}_2$ $\left({\tilde{A}}^2{B}_2\right)$ molecules depends on the intensity of the strong NIR laser, as well as the relative polarization and delay time between the NIR and the UV laser fields. Distinct different behaviors between RSE and strong-field ionization of ${\mathrm{NO}}_2$ $\left({\tilde{A}}^2{B}_2\right)$ are observed. Analysis indicates that the probability of recapturing the tunneling electron to form high Rydberg states is affected by the molecular orbitals of the excited state, and the RSE process can qualitatively reflect the changes of molecular structure during ultrafast dynamics of the excited state of molecules.