Hybrid classical-quantum systems are of interest in numerous fields from quantum chemistry to quantum information science. A fully quantum effective description of them is straightforward to formulate when the classical subsystem is discrete. But it is not obvious how to describe them in the general case. We propose a probability-based approach starting with four axioms for hybrid classical-quantum probability measures that readily generalize the usual ones for classical and quantum probability measures. They apply to discrete and nondiscrete classical subsystems and to finite- and infinite-dimensional quantum subsystems. A generalized Gleason theorem that gives the mathematical form of the corresponding hybrid states is shown. This form simplifies when the classical subsystem probabilities are described by a probability density function with respect to a natural reference measure, for example the familiar Lebesgue measure. We formulate a requirement for the transformations, that is, the finite-time evolutions, of hybrid probability measures analogous to the complete positive assumption for quantum operations. For hybrid systems with reference measure, we prove a generalized Kraus theorem that fully determines the considered transformations provided they are continuous with respect to an appropriate metric. Explicit expressions for these transformations are derived when the classical and quantum subsystems are noninteracting, the classical subsystem is discrete, or the Hilbert space of the quantum subsystem is finite dimensional. We also discuss the quantification of the correlations between the classical and quantum subsystems and a generalization of the quantum operations usually considered in the study of quantum entanglement.

Measurement backaction inherently alters observed dynamics in quantum physics. In the realm of quantum synchronization, this backaction induces a phase bias, making the assessment of synchronization critically dependent on the choice of the observables. In this study we extend the quantum phase reduction approach [W. Setoyama and Y. Hasegawa, Phys. Rev. Lett. 132, 093602 (2024)] into heterodyne detection, offering a comprehensive theoretical framework for analyzing quantum synchronization dynamics through uniform continuous measurement over all possible quadrature observables. This method averages out the backaction, allowing for unbiased evaluation of synchronization between quantum oscillators while avoiding measurement-induced phase bias. Furthermore, by defining the phase and limit-cycle solution independently of specific observables, our proposed method consistently adapts to the scenario where the observables are freely modified during the time evolution. Through simulations of noise-induced synchronization, our method reveals that the number of phase clusters between oscillators is restricted by their bosonic levels.

The quantum alternating operator ansatz (QAOA) represents a branch of quantum algorithms for solving combinatorial optimization problems. A specific variant, the Grover-mixer (GM) QAOA, ensures uniform amplitude across states that share equivalent objective values. This property makes the algorithm independent of the problem structure, focusing instead on the distribution of objective values within the problem. In this work we provide an alternative proof for the upper bound on the probability of measuring a computational basis state from a GM QAOA circuit with a given depth, which is a critical factor in QAOA cost. Using this, we derive the upper bounds for the probability of sampling an optimal solution and for the approximation ratio of maximum optimization problems, both dependent on the objective value distribution. Through numerical analysis, we link the distribution to the problem size and build the regression models that relate the problem size, QAOA depth, and performance upper bound. Our results suggest that the GM QAOA provides a quadratic enhancement in sampling probability and requires circuit depth that scales exponentially with problem size to maintain consistent performance.

Dissipation is usually considered a negative factor for observing quantum effects and for harnessing them for quantum technologies. Here, we propose a scheme for conditionally speeding up the generation of quantum entanglement between two coupled qubits by introducing a strong dissipation channel to one of these qubits. The maximal entanglement is established by evenly distributing a single excitation between these two qubits in a probabilistic manner. When the excitation is initially held by the qubit with stronger dissipation, the dissipation accelerates the excitation redistribution process for the quantum state trajectory without quantum jumps. Our results show that the time needed to conditionally attain the maximal entanglement is monotonously decreased as the dissipative rate is increased, at the price of a quickly decreasing success probability. We further show that this scheme can be generalized to accelerate the production of the $W$ state for the three-qubit system, where one qubit with strong dissipation is symmetrically coupled to two qubits with weak dissipation.

Quantum algorithms such as dynamical decoupling can be used to improve the sensitivity of a quantum sensor to a signal while suppressing sensitivity to noise. Atomic clocks are among the most sensitive quantum sensors, with recent improvements in clock technology allowing for unprecedented precision and accuracy. These clocks are highly sensitive to variations in fundamental constants, making them ideal probes for local ultralight scalar dark matter. Further improvements to the sensitivity are expected in proposed nuclear clocks based on a nuclear transition in the thorium-229 isotope. We investigate the use of various quantum metrology algorithms in the search for dark matter using quantum clocks. We propose a broadband dynamical decoupling algorithm and compare it with quantum metrology protocols that have been previously proposed and demonstrated, namely, differential spectroscopy and narrowband dynamical decoupling. We conduct numerical simulations of scalar dark matter searches with realistic noise sources and accounting for dark matter decoherence. Finally, we propose an alternative thorium nuclear transition excitation method that bypasses the technical challenges associated with vacuum ultraviolet lasers.

Measurement-device-independent quantum secret sharing (MDI-QSS) can resist all attacks on imperfect measuring devices. However, limited by the exponential increase in fiber loss, MDI-QSS has a low key rate and short communication distance. In this paper, we introduce quantum memory (QM) in MDI-QSS to increase the success probability of the three-photon synchronous projection measurement and propose a memory-assisted (MA) MDI-QSS protocol. In this protocol, the heralded single-photon source and the decoy-state method are also explored. This MA-MDI-QSS protocol has three advantages. First, the QM used here is all optical, and this protocol is feasible under current experimental conditions. Second, combined with the decoy-state method, our protocol can guarantee the security of the transmitted keys under practical experimental conditions. Third, numerical simulation results show that our protocol has a higher secure key rate and longer photon transmission distance than existing MDI-QSS protocols without QM. Our protocol provides a promising way for implementing the long-distance MDI-QSS in the near future.

Quantum secret sharing (QSS) enables a dealer to securely distribute keys to multiple players. Device-independent (DI) QSS can resist all possible attacks from practical imperfect devices and provide QSS the highest level of security in theory. However, DI QSS requires high-performance devices, especially for low-noise channels, which is a big challenge to demonstrate experimentally. We propose a DI QSS protocol with the advanced random key generation basis strategy, which combines the random key generation basis with the noise preprocessing and postselection strategies. We develop the methods to numerically simulate the key generation rate in an acceptable time. Our DI QSS protocol has some advantages. First, it can increase the noise tolerance threshold from an initial 7.147% to 9.231% (29.16% growth) and reduce the global detection efficiency threshold from 96.32% to 93.41%. The maximal distance between any two users increases to 1.43 km, which is about 5.5 times the initial value. Second, by randomly selecting two basis combinations to generate the key, our DI QSS protocol can reduce the entanglement resource consumption. Our protocol has potential for the experimental demonstration of DI QSS and application in the future.

High-fidelity and decoherence-insensitive quantum gates are essential for achieving universal quantum computing. In quantum information processing, decoherence arising from excited states significantly contributes to the scheme's infidelity. Therefore, minimizing the average population of the excited state is crucial when designing quantum protocols. A promising approach involves utilizing capture-and-release dynamics to induce a complex phase on the ground state in a two-level system, effectively suppressing the integrated excited-state population. By applying this dynamics protocol to a $\mathrm{\Lambda }$ three-level system, we propose a scheme to construct arbitrary decoherence suppressed single-qubit and nontrivial two-qubit gates; meanwhile, by incorporating the Zeno dynamics process in the construction of two-qubit logic gates, the large detuning and excitation of virtual photons render the scheme insensitive to qubit decoherence and cavity dissipation. Applying our scheme to the nitrogen-vacancy (NV) center as an example, we prove our scheme with higher fidelity than conventional nonadiabatic non-Abelian geometric gates while significantly enhancing the robustness against decoherence and frequency shift errors. These studies provide alternative approaches for constructing robust quantum gate operations. We also emphasize that the scheme is feasible for three-level quantum systems, not limited to NV center systems.

We present a study of the scattering of a monochromatic helical laser beam, described by a Laguerre-Gauss solution of the Maxwell equations, on an electron sheet, initially at rest in the focal plane of the laser; the interaction is described in the framework of a local plane-wave approximation. We calculate the scattered electromagnetic field observed in an arbitrary point at a large distance from the laser focal spot, by adding coherently the contributions of each point in the electron sheet. Due to the interference effects, the radiation is emitted only into the forward direction, within a narrow cone, and it has a spatial structure that we analyze theoretically and numerically. For circularly polarized incident fields, the structure is also helical, with a helical index which depends on the helical index of the incident radiation and the harmonic order. These structures can be observed experimentally, as each harmonic order is emitted with a different frequency, and within cones of different opening angles. Our findings are in agreement with experimental results in the literature which demonstrate the generation of orbital angular momentum carrying photons by radiation scattering on electrons.

We investigate the stability of a vortex ring in a miscible two-component Bose-Einstein condensate confined in a harmonic potential, where the vortex cores in the two components are initially overlapped. Solving the Gross-Pitaevskii equation numerically, we find that the overlapped vortex rings in the two components are dynamically unstable against separation and that they can form linked vortex rings, resulting in a three-dimensional skyrmion. The parameter range for spontaneous skyrmion generation is determined by the Bogoliubov analysis.

The sensitivity of an interferometer depends on its readout scheme. However, little attention has been paid to the readout schemes of atom interferometers from the viewpoint of their sensitivity. The difference in sensitivity between readout schemes or their optimization has not been considered in the literature. Herein we analytically calculate the sensitivities of an atom interferometer with typical readout schemes by applying the two-photon formalism, which was developed for optical interferometers to deal with quantum noise. Our calculations reveal that by using sinusoidal phase modulation, the sensitivity can surpass that obtained by the conventional phase sweeping scheme. The superiority of this phase modulation scheme for both cold and thermal atomic beams is demonstrated. In addition, we show that the phase modulation scheme is advantageous for atom-flux fluctuation and resists atom-flux drift. This study performs a general analysis of the sensitivity of atom interferometers and identifies an advantageous readout scheme.

We propose fault-tolerant quantum encoders for Calderbank-Shor-Steane (CSS) and non-CSS codes over qudits by utilizing $g$-partite maximally entangled states. The qudits are grouped into $g$ contiguous blocks such that entangled states are shared across the blocks, and multiqudit gates are applied locally to restrict the error propagation within each block. We also propose a transversal fault-tolerant block decoder to decode the blocks individually and recover the complete encoded quantum information. The optimum value of $g$ to obtain an improvement in the probability of error propagation of the proposed encoders against non-fault-tolerant schemes is analytically determined for application in the encoding circuit. The proposed fault-tolerant scheme with entanglement assistance scales linearly with the number of $g$-partite entangled states and overcomes the limitations of diminishing coding rates for higher levels of concatenation within the concatenated coding scheme. We validate the proposed ideas by constructing fault-tolerant encoding circuits for the non-CSS ${\left[[5,1,3]\right]}_3$ code and the ${\left[[7,1,3]\right]}_3$ CSS code through illustrative examples. We reduced the probability of error propagation from 0.248 to 0.212 for the ${\left[[5,1,3]\right]}_3$ code and from 0.207 to 0.174 for the ${\left[[7,1,3]\right]}_3$ code. For example, over ${\left[[100,70]\right]}_2$ quantum code without any fault tolerance, using three-partite entangled pairs, one can get two orders of improvement (1e-2) in the probability of error propagation compared to the non-fault-tolerant encoder by encoding over 190 physical qubits with the same number of stabilizers.

For many applications the presence of a quantum advantage crucially depends on the availability of resourceful states. Although the resource typically depends on the particular task, in the context of multipartite systems entangled quantum states are often regarded as resourceful. We propose an algorithmic method to find maximally resourceful states of several particles for various applications and quantifiers. We discuss in detail the case of the geometric measure, identifying physically interesting states and delivering insights to the problem of absolutely maximally entangled states. Moreover, we demonstrate the universality of our approach by applying it to maximally entangled subspaces, the Schmidt-rank, the stabilizer rank as well as the preparability in triangle networks.

The question of which resources drive the advantages in quantum algorithms has long been a fundamental challenge. While entanglement and coherence are critical to many quantum algorithms, our results indicate that they do not fully explain the quantum advantage achieved by the Grover search algorithm. By introducing a generalized Grover search algorithm, we demonstrate that the success probability depends not only on the querying number of oracles but also on the coherence fraction, which quantifies the fidelity between an arbitrary initial quantum state and the equal superposition state. Additionally, we explore the role of the coherence fraction in the quantum minimization algorithm, which offers a framework for solving complex problems in quantum machine learning. These findings offer insights into the origins of quantum advantage and open pathways for the development of new quantum algorithms.

Nonadiabatic holonomic quantum computation (NHQC) based on non-Abelian geometric phases can possess potential robustness advantages due to its intrinsic error-resilient features. However, rigorous geometric conditions, including cyclic evolution and parallel transport conditions, typically demand complex and error-prone control and also involve additional auxiliary resources. Moreover, the limitations of optional evolution paths in previous NHQC schemes make it difficult to avoid path segments that are heavily affected by systematic errors, thereby weakening the error resilience of holonomic gates. To address this problem, we propose a multipath NHQC scheme, which can sufficiently improve the robustness of quantum gates by flexibly correcting geometric evolution paths. Numerical simulation results show that our scheme surpasses previous NHQC schemes in suppressing systematic errors for arbitrary gate types. In addition, we provide a physical implementation based on superconducting quantum circuits, with the decoherence-free-subspace encoding and an experiment-friendly two-body exchange interaction, demonstrating the excellent compatibility of our scheme. Therefore, our scheme offers a promising alternative for future fault-tolerant quantum computation.

It was shown in Phys. Rev. Lett. 108, 170402 (2012) that quantum tunneling is instantaneous using a time-of-arrival (TOA) operator constructed by Weyl quantization of the classical TOA. However, there are infinitely many possible quantum images of the classical TOA, leaving it unclear if one is uniquely preferred over the others. This raises the question on whether instantaneous tunneling time is simply an artifact of the chosen ordering rule. Here, we demonstrate that tunneling time vanishes for all possible quantum images of the classical arrival time, irrespective of the ordering rule between the position and momentum observables. The result still holds for TOA-operators that are constructed independent of canonical quantization, while still imposing the correct algebra defined by the time-energy canonical commutation relation.

We propose a quantum metrology protocol based on a two-step joint evolution of the probe system and an ancillary qubit and quantum measurement. With a proper initial state of the ancillary qubit and an optimized evolution time, the quantum Fisher information (QFI) about the phase parameter encoded in the probe system is found to be determined by the expectation value of the square of a phase generator, irrespective of the probe initial state. Consequently, even if the probe is prepared as a finite-temperature state, faraway from the so-called resource state, e.g., the squeezed spin state or the Greenberger-Horne-Zeilinger state in atomic systems, the QFI in our protocol can approach the Heisenberg scaling $N^2$ with respect to the probe size $N$. This quadratic scaling behavior shows robustness against the imperfections about the initial state of the ancillary qubit and the optimized evolution time of the whole system. Also it is not sensitive to the deviation in system parameters and the qubit decoherence. Using the time-reversal strategy and a single-shot projective measurement, the classical Fisher information (CFI) in our metrology protocol is saturated with its quantum counterpart. Our work thus provides an economical method to reach the Heisenberg limit in metrology precision with no input of entanglement or squeezing.

A key concept of quantum information theory is that accessing information encoded in a quantum system requires us to discriminate between several possible states the system could be in. A natural generalization of this problem, namely, quantum sequence discrimination, appears in various quantum information processing tasks, the objective being to determine the state of a finite sequence of quantum states. Since such a sequence is a composite quantum system, the fundamental question is whether an optimal measurement is local, i.e., comprising measurements on the individual members, or collective, i.e., requiring joint measurement(s). In some known instances of this problem, the optimal measurement is local, whereas in others, it is collective. But, so far, a definite prescription based solely on the problem description has been lacking. In this paper, we prove that if the members of a given sequence are secretly and independently drawn from an ensemble or even from different ensembles, the optimum success probability is achievable by fixed local measurements on the individual members of the sequence, and no collective measurement is necessary. This holds for both minimum-error and unambiguous state discrimination paradigms.