Entanglement is a cornerstone of quantum information theory, yet efficiently generating entangled quantum states remains a significant challenge. In this work, we present a algebraic framework for constructing entangled states from systems of linear equations over the finite field ${\mathbb{F}}_d$, where $d$ is a prime number. We introduce the notion of an entanglement-producing system of linear equations and show how each can be systematically mapped to quantum circuits using only Hadamard and $d$-cnot gates with linear gate complexity in terms of the number of variables for the system. We formalize the criteria for when a system of equations produces genuine multipartite entanglement and provide constructive algorithms for synthesizing quantum circuits. Furthermore, we characterize that every entanglement-producing linear system is equivalent to structured simplex entanglement, which can be formulated in linear gate complexity in terms of the number of variables. By bridging abstract and linear algebraic techniques with practical circuit synthesis, this low-complexity approach provides a structured, efficient, and scalable entanglement generation.

Entropic uncertainty relations quantify the limits on the predictability of quantum measurements. When the measured system is correlated with a quantum memory, these limits are described by the memory-assisted entropic uncertainty relation (MA-EUR). We examine the behavior of MA-EUR when the memory qubit undergoes noisy dynamics implemented via high-order controlled processes, namely, the quantum switch and the quantum time flip. We consider a setting in which the control qubit is the very system on which the measurements are performed, while the target qubit serves as a noisy quantum memory. Focusing on Pauli channels, we show that feeding them into the quantum switch and the quantum time flip can significantly reduce the total entropic uncertainty as compared to their direct application. Our results reveal that indefinite causal order and input-output direction can serve as resources to mitigate the effects of noise in the context of MA-EUR and its applications.

We propose cascaded spontaneous four-wave mixing (SFWM) in microring resonators as a scalable and efficient approach for directly generating non-Gaussian states of light. Focusing on the well-understood “low-gain” regime, we demonstrate that triplet generation through cascaded SFWM can be achieved with high efficiency and favorable spectral characteristics using realistic microring sources in AlGaAs. The ability to achieve the generation of light in a single set of supermodes—and the predicted accessibility of the “high-gain” regime at realistic pump powers—makes this source a promising candidate as a direct and deterministic source of non-Gaussian light for photonic quantum information processing.

We propose a protocol to generate entanglement between two remote magnon modes by coupling two macroscopic Kerr yttrium iron garnet (YIG) spheres and an atom to an odd-numbered cavity chain. The atom is placed in the middle cavity chain, while the two YIG spheres are symmetrically positioned on opposite sides. We derive the master equation of the YIG spheres and the atom and obtain its analytical solution. If the dissipations of the cavity chain, of the YIG spheres, and of the atom can all be ignored, a pure two-mode squeezed Schrödinger-cat state is obtained by measuring the atomic level. We also show that the Kerr nonlinearity, on the one hand, improves the entanglement and, on the other hand, enhances the mean magnon number.

Young's double-slit experiment has often been used to illustrate the concept of complementarity in quantum mechanics. If information can in principle be obtained about the path of the photon, then the visibility of the interference fringes is reduced or even destroyed. This Gedanken experiment discussed by Bohr and Einstein can be realized when the slit is replaced by individual atoms sensitive to the transferred recoil momentum of a photon which “passes through the slit”. Early pioneering experiments were done with trapped ions and atom pairs created via photodissociation. Recently, it became possible to perform interference experiments with single neutral atoms cooled to the absolute ground state of a harmonic oscillator potential. The slits are now single atoms representing a two-level system, and the excitation in the harmonic oscillator potential is the which-way marker. In this article, we analyze and generalize two recent experiments performed with single atoms and emphasize the different ways they record which-way information.

A set of orthogonal quantum states is said to be locally indistinguishable if they cannot be perfectly distinguished by local operations and classical communication (LOCC). Otherwise, the states are locally distinguishable. Interestingly, locally indistinguishable states can have productive applications in quantum information processing protocols. In this sense, locally indistinguishable states are useful. On the other hand, it is usual to consider that locally distinguishable states are useless. Nevertheless, recent works suggest that locally distinguishable states should be given due consideration, as in certain situations these states can be converted to locally indistinguishable states under orthogonality-preserving LOCC (OP-LOCC). Such a counterintuitive phenomenon motivates us to ask when the aforesaid conversion is possible and when it is not. In this work, we provide different structures of locally distinguishable product and entangled states which do not allow the aforesaid conversion. We also provide certain structures of locally distinguishable states which allow the aforesaid conversion. In this way, we classify the locally distinguishable sets by introducing hierarchies among them. In a multipartite system, this study becomes more involved, as there exist multipartite locally distinguishable sets which cannot be converted to locally indistinguishable sets by OP-LOCC across any bipartition. We call this “no activation across bipartitions.”

We investigate continuous quantum error correction, comparing performance under a Markovian error model to two distinct non-Markovian models. The first non-Markovian model involves an interaction Hamiltonian between the system and an environmental qubit via an $X\text{−}X$ coupling, with a “cooling” bath acting on the environment qubit. This model is known to exhibit abrupt transitions between Markovian and non-Markovian behavior [S. Pang et al., arXiv:1712.10109]. The second non-Markovian model uses the post-Markovian master equation (PMME), which represents the bath correlation through a memory kernel; we consider an exponentially decaying kernel and both underdamped and overdamped dynamics. We systematically compare these non-Markovian error models against the Markovian case and against each other, for a variety of different codes. We start with a single qubit, which can be solved analytically. We then consider the three-qubit repetition code and the five-qubit “perfect” code. In all cases, we find that the fidelity decays more rapidly in the Markovian case than in either non-Markovian model, suggesting that continuous quantum error correction has enhanced performance against non-Markovian noise. We attribute this difference to the presence of a quantum Zeno regime in both non-Markovian models.

In this work, we investigate the role of functionals of generalized fidelity measures in deriving quantum speed limits (QSLs) within a geometric approach. We establish a general theoretical framework and show that, once a specific generalized fidelity is selected, the resulting Margolus-Levitin and Mandelstam-Tamm QSLs for both unitary and nonunitary (Lindblad-type) dynamics depend solely on the chosen fidelity measure. We prove that any monotone, differentiable reparametrization of the chosen fidelity yields exactly the same Margolus-Levitin and Mandelstam-Tamm-type QSL, rendering the QSLs invariant under such transformations and thereby unifying fidelity- and metric-induced geometric formulations. This result highlights the limitations of improving QSLs through functional transformations of fidelity and indicates that genuine improvements must arise from alternative fidelity definitions. We further show that several QSLs reported in the literature are encompassed by our framework and discuss possible extensions based on other generalized fidelity measures beyond those explicitly analyzed. In addition, we consider the damped Jaynes-Cummings model as a concrete physical setting to explore the behavior of the QSLs discussed in this work and analyze their regime-dependent features.

We establish two inequalities, the weighted strong monogamy (WSM) and the maximum residual strong monogamy (MRSM), which sharpen the generalized Coffman-Kundu-Wootters inequality for multiqubit states. The WSM inequality distinguishes itself from the strong monogamy (SM) conjecture [B. Regula et al., Phys. Rev. Lett. 113, 110501 (2014)] by using coefficients rather than exponents to modulate the weight allocated to various $m$-partite contributions. In contrast, the MRSM inequality is formulated using only the maximum $m$-partite entanglement. We find that the residual entanglement of the MRSM inequality can effectively distinguish the separable states. We also compare the tightness of various SM inequalities and provide examples using a four-qubit mixed state and a five-qubit pure state to illustrate the MRSM inequality. These examples characterize the trade-off relations among entanglement components involving varying numbers of qubits. Our results provide a rigorous framework to characterize and quantify the monogamy of multipartite entanglement.

Quantum conditional entropies play a fundamental role in quantum information theory. In quantum key distribution, they are exploited to obtain reliable lower bounds on the secret-key rates in the finite-size regime, against collective attacks and coherent attacks under suitable assumptions. Here we consider continuous-variable communication protocols, where the sender Alice encodes information using a discrete modulation of phase-shifted coherent states, and the receiver Bob decodes by homodyne or heterodyne detection. We compute the Petz-Rényi and sandwiched Rényi conditional entropies associated with these setups, assuming either a passive eavesdropper or one that injects thermal photons into the channel, who gathers the quantum information leaked through a lossy communication line of known or bounded transmittance. Whereas our results do not directly provide reliable key-rate estimates, they do represent useful ballpark figures. We obtain analytical or semianalytical expressions that do not require intensive numerical calculations. These expressions serve as bounds on the key rates that may be tight in certain scenarios. We compare different estimates, including known bounds that have already appeared in the literature and bounds that we determine. The latter are found to be tighter for very short block sizes.

The Greenberger-Horne-Zeilinger (GHZ) state is a typical maximally entangled state which is pursued in both fundamental research and emerging quantum technologies. Preparing large-scale GHZ states in lattice spin systems is particularly appealing for quantum advantages, but conventional schemes face great challenges in scalability. Here we propose a universal and scalable scheme to generate large-scale GHZ-like states, which share similar entanglement and metrological properties with standard GHZ states, in lattice spin systems through global Floquet engineering. Our scheme requires only global operations and shows great advantages for large particle number. It is applicable to systems with arbitrary interaction ranges, offering a practical pathway for large-scale implementation of many-body entangled states in various systems.

In the accompanying Letter of Koizumi et al., Phys. Rev. Lett. 136, 080605 (2026), we presented a generalized scheme of the adaptive quantum gradient estimation algorithm and further proposed two practical variants which not only achieve doubly quantum enhancement in query complexity regarding estimation precision and number of observables but also enable minimal cost to estimate $k$-body  reduced density matrix ($k$-RDMs) in fermionic systems among existing quantum algorithms. Here we provide full descriptions on the algorithm and provide theoretical guarantee for the estimation precision in terms of the root-mean-squared error. Furthermore, we analyze the performance of the quantum amplitude estimation algorithm, another variant of the Heisenberg-limited scaling algorithm, and show how the estimation error is minimized under the circuit structure that resembles the phase estimation algorithm. We finally describe the details for the numerical evaluation of the query complexity of the Heisenberg-limited algorithms and sampling-based methods to make a thorough comparison in the task of estimating fermionic $k$-RDMs.

We develop a framework for constructing unitary propagators for ensemble states of a quantum system characterized by a continuous distribution of resonance frequencies. The evolution of quantum states is realized through time-dependent electromagnetic control fields. The ensemble members evolve under distinct Hamiltonians, and their evolution is uniquely dependent on their resonance frequencies. The aim of this article is to develop the theory and technique for designing control pulse sequences that generate identical rotations of angular momentum or equivalently the magnetic moments for all members of the quantum ensemble about an arbitrarily chosen axis, regardless of their individual resonance frequencies, while simultaneously preserving the angular momentum component along that axis for every ensemble member. In this way, the control pulse sequence enforces an engineered symmetry in the ensemble dynamics. The control pulse sequence as a whole thereby functions as a universal operator, an engineered ensemble propagator that implements uniform evolutions of the ensemble states while preserving the angular momentum component along a specified axis, for all members across the continuous spectrum of resonance frequencies.

Electronic bridge mechanisms driving the ${}^{229}\mathrm{Th}$ nuclear clock transition in the vacuum-ultraviolet-transparent crystals ${}^{229}\text{Th:LiCAF}$ (${\mathrm{LiCaAlF}}_6$) and ${}^{229}\text{Th:LiSAF}$ (${\mathrm{LiSrAlF}}_6$) are investigated theoretically. Due to doping-induced symmetry breaking within the host crystal, electronic defect states emerge around the thorium nucleus and can facilitate nuclear (de)excitation via laser-assisted electronic bridge mechanisms. We investigate spontaneous and laser-assisted electronic bridge schemes for different charge compensation mechanisms. While the calculated spontaneous electronic bridge rates are very low, laser-assisted electronic bridge schemes for nuclear (de)excitation turn out to be significantly more efficient than both spontaneous nuclear decay and direct laser excitation, offering promising prospects for future clock operation.

Apparently disordered at large scales, aperiodic materials may manifest complex structural correlations at mesoscopic scales, which, in turn, substantially affect their optical properties. Despite theoretical and numerical progress, the precise role of structural correlations has yet to be plainly established experimentally. Here, we use a novel composite scattering medium where the macroscopic concentration of strongly scattering particles can be kept constant while their structural correlations can be controllably adjusted via a small amount of nanoextenders. Using inelastic and elastic spectroscopies we probe both the local and the global consequences of tuning the properties of structural correlations and we are able to observe and characterize multiple phases in the way light diffuses through disordered media. We demonstrate that both the incipient anomalous transport and the extent of subsequent anomalous diffusion depend on the extent of these structural correlations.

The control of interactions among quantum emitters through nanophotonic structures offers significant opportunities for quantum technologies. However, a rigorous theoretical description of the interaction of multiple quantum emitters with complex, dispersive dielectric objects remains challenging. Here, we introduce an approach based on the modified Langevin noise formalism that unveils the roles of both the noise polarization currents of the dielectrics and the vacuum fluctuations of the electromagnetic field scattered by the dielectrics. This work extends [G. Miano et al., Nanophotonics 14, 4019 (2025); Phys. Rev. A 112, 033712 (2025)] to the general case of an arbitrary number of emitters. The proposed approach allows us to describe the dynamics of the quantum emitters for arbitrary initial quantum states of the electromagnetic environment, consisting of two independent bosonic reservoirs, a medium-assisted reservoir, and a scattering-assisted reservoir, each characterized by its own spectral density matrix. Specifically, we examine situations where both reservoirs are initially in thermal quantum states but have different temperatures. Understanding how these reservoirs shape the dynamics of the emitters is crucial for understanding light–matter interactions in complex electromagnetic environments and for improving intrinsic emitter properties within structured environments.

Quantum sensing near exceptional points (EPs) in non-Hermitian systems has shown promising sensitivity enhancements. However, practical applications are often hindered by structural complexity and strict parameter constraints. In this work, we introduce a simplified anti-parity-time ($\mathcal{PT}$) symmetric platform consisting of two independent cavities, which are indirectly coupled to each other by a shared dissipative environment. We demonstrate a significantly enhanced sensing response at the EPs compared to non-EP configurations. This improvement is attributed to the dominant second-order term in the Laurent series expansion of the eigenvalue response to external perturbations—a characteristic feature of higher-order singularities at EPs. This mechanism not only reinforces the foundation for sensitivity enhancement but also offers a structurally compact and robust strategy for quantum sensing. Our results underscore the potential of anti-$\mathcal{PT}$ symmetric systems in enabling high-precision sensing technologies and bridging non-Hermitian physics with scalable photonic device platforms.