We present several analytical approaches to the Dicke superradiance problem, which involves determining the time evolution of the density operator for an initially inverted ensemble of $N$ identical two-level systems undergoing collective spontaneous emission. This serves as one of the simplest cases of open quantum system dynamics that allows for a fully analytical solution. We explore multiple methods to tackle this problem, yielding a solution valid for any time and any number of emitters. These approaches range from solving coupled rate equations and identifying exceptional points in non-Hermitian evolution to employing combinatorial and probabilistic techniques, as well as utilizing a quantum jump unraveling of the master equation. The analytical solution is expressed as a residue sum obtained from a contour integral in the complex plane, suggesting the possibility of fully analytical solutions for a broader class of open quantum system dynamics problems.

Classical thermodynamics is a theory based on coarse graining, meaning that the thermodynamic variables arise from discarding information related to the microscopic features of the system at hand. In quantum mechanics, however, where one has a high degree of control over microscopic systems, information theory plays an important role in describing the thermal properties of quantum systems. Recently, a new approach has been proposed in the form of quantum thermodynamic gauge theory, where the notion of redundant information arises from a group of physically motivated gauge transformations called the thermodynamic group. In this work, we explore the geometrical structure of quantum thermodynamics. In particular, we do so by explicitly constructing the relevant principal fiber bundle. We then show that there are two distinct (albeit related) geometric structures associated with the gauge theory of quantum thermodynamics. In this way, we express thermodynamics in the same mathematical (geometric) language as the fundamental theories of physics. Finally, we discuss how the geometric and topological properties of these structures may help explain fundamental properties of thermodynamics.

Quantum machine learning (QML) leverages quantum computing for classical inference, furnishes the processing of quantum data with machine-learning methods, and provides quantum algorithms adapted to noisy devices. Typically, QML proposals are framed in terms of the circuit model of quantum computation. The alternative measurement-based quantum computing (MBQC) paradigm can exhibit lower circuit depths, is naturally compatible with classical coprocessing of midcircuit measurements, and offers a promising avenue towards error correction. Despite significant progress on MBQC devices, QML in terms of MBQC has been hardly explored. We propose the multiple-triangle Ansatz (MuTA), a universal quantum neural network assembled from MBQC neurons featuring bias engineering, monotonic expressivity, tunable entanglement, and scalable training. We numerically demonstrate that MuTA can learn a universal set of gates in the presence of noise, a quantum-state classifier, as well as a quantum instrument, and classify classical data using a quantum kernel tailored to MuTA. Finally, we incorporate hardware constraints imposed by photonic Gottesman-Kitaev-Preskill qubits. Our framework lays the foundation for versatile quantum neural networks native to MBQC, allowing one to explore MBQC-specific algorithmic advantages and QML on MBQC devices.

EPR steering is a crucial quantum resource that lies intermediate between entanglement and Bell nonlocality. Gaussian channels, meanwhile, play a foundational role in diverse quantum protocols, secure communication, and related fields. In this paper we focus on several classes of Gaussian channels associated with EPR steering: Gaussian steering-annihilating channels, Gaussian steering-breaking channels, Gaussian unsteerable channels, and maximal Gaussian unsteerable channels. We give the concepts of these channels, derive the necessary and sufficient conditions for a Gaussian channel to belong to each class, and explore the intrinsic relationships among them. Additionally, since quantifying the steering capability of Gaussian channels in continuous-variable systems requires an understanding of the structure of free superchannels, we also provide a detailed characterization of Gaussian unsteerable superchannels and maximal Gaussian unsteerable superchannels.

Quantum algorithms typically demand prohibitively complex circuits to solve practical problems. Previous studies have shown that classical randomness can accelerate some specific quantum algorithms. In this work, we introduce the randomized truncated series (RTS), which enables all quantum algorithms relying on truncated series approximations to enjoy such acceleration. RTS offers twofold accelerations: it quadratically suppresses truncation errors and allows continuous adjustment of the effective truncation order. By leveraging random mixing between two quantum circuits, RTS ensures that their probabilistic combination accurately realizes the desired algorithm, while significantly reducing the average circuit size. We demonstrate the versatility of RTS through concrete applications. Our results shed light on a path toward practical quantum advantage.

Closed quantum systems with degenerate spectra or sparse couplings often trap conventional Lyapunov or gradient controllers on invariant sets, yielding low final fidelities. We propose a hybrid control strategy that uses a number-theoretic exploration phase followed by a Lyapunov refinement. In the low-fidelity regime, the control signal is a bounded, aperiodic drive formed by a Littlewood-Ramanujan modulation multiplied by a bandwidth-limited multitone comb built from divisors of a highly composite number. This prime-driven signal provides persistent excitation across Bohr gaps without phase locking and activates the noncommuting directions needed to escape degenerate subspaces. Once a preset fidelity threshold is reached, the controller switches to a Lyapunov law with logarithmic shaping, ensuring monotonic fidelity increase under amplitude constraints. We prove finite hitting time to the threshold and asymptotic convergence under bounded-input, detectability, and persistence-of-excitation conditions, and provide practical tuning rules. Simulations on multilevel systems show high-fidelity state preparation and consistent improvements over standard Lyapunov control.

The indistinguishability of many bosons undergoing passive linear transformations followed by number basis measurements is fully characterized by the visible state of the bosons. However, measuring all the parameters in the visible state is experimentally demanding. In this work, we seek to perform partial characterization of the visible state by measuring properties of it that are available after randomization. First, we study the case where the occupied visible modes are randomly permuted, and second, we study the case where Haar random linear optical unitaries are applied. In each case, we find that the generalized bunching probability—which is the probability that all the input bosons arrive in a given subset of the output modes—obeys monotonicity with respect to some partial order of distinguishability of the input bosons. As an intermediate result, we show that Lieb's permanental-dominance conjecture for immanants is equivalent to the following statement: for states that are invariant under permutations of the occupied visible modes, the generalized bunching probability is maximized when the bosons are perfectly indistinguishable. We also prove that a consequence of the monotonicity of the generalized bunching probability after Haar averaging is that this average is maximized when the bosons are perfectly indistinguishable. Finally, we discuss applications of our results to thermometry of cold-atom systems.

We investigate the influence of $3p\to 3d$ core-to-core resonance on the transient level populations of Kr driven by x-ray free-electron laser pulses, using rate-equation approaches. The process begins with the predominant photoionization of $3d$ electrons, creating transient $3d^{-1}$ core holes. These holes can then be resonantly filled by $3p$ electrons via $3p\to 3d$ excitations, a pathway that competes directly with the ultrafast Auger decay of the $3d^{-1}$ state. The signature of this resonant process is monitored through the resulting $3p^{-1}$ Auger electron spectra. Our calculated spectra show distinct resonant features which are in good agreement with recent experimental measurements of Fushitani et al. [Phys. Rev. A 107, L021101 (2023)]. At relatively low intensities ($\sim 7.0\times {10}^{13}{\mathrm{W}/\mathrm{cm}}^2$), the $3p\to 3d$ resonance suppresses the ${\mathrm{Kr}}^{2+}$ population by 2.5%, a suppression that increases to 8.6% at $5.0\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$. For intensities beyond $5.0\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$, the resonance saturates, yielding a maximum reduction in ${\mathrm{Kr}}^{2+}$ population of approximately 10%. Our work offers practical guidelines for the quantum control of innershell processes in future ultrafast x-ray experiments.

We investigate the ferromagnetic-paramagnetic phase transition in coherently (Rabi-)coupled Bose-Einstein condensates at zero and finite temperatures, exploring different routes to the transition by tuning the Rabi coupling or increasing the temperature at a fixed coupling. Using the Hartree-Fock-Bogoliubov theory within the Popov approximation, we map out the finite-temperature phase diagram of a three-dimensional homogeneous condensate. The critical line is identified from the softening of the spin gap, which at finite temperature does not strictly close but exhibits a discernible minimum. Magnetization and the spin dispersion branch reveal the progressive suppression of the ferromagnetic order with increasing temperature. In quasi-one-dimensional harmonic traps, the transition, driven by Rabi coupling, does not correspond to a sharply defined critical point. To this end, we use the softening of the spin breathing mode as an operational indicator of the transition, whose minimum shifts to lower coupling strengths with increasing temperature. Notably, the thermally driven transition causes monotonic hardening of all the spin modes. For both coupling and the temperature-driven transition, the hybridized “density” modes in the ferromagnetic phase acquire more density character while approaching the critical point.

Randomness is fundamental for secure communication and information processing. While continuous-variable optical systems offer an attractive platform for this task, certifying genuine quantum randomness in such setups remains challenging. We present a semi-device-independent scheme for randomness certification tailored to continuous-variable implementations, where the dimension assumption is operationally implemented by restricting state preparations to the two-level Fock subspace. Using standard homodyne and displacement-based measurements, we show that simple optical setups can achieve dimension-witness violations that certify positive min-entropy, even in the presence of realistic losses and misaligned reference frames. These results demonstrate that practical and scalable quantum randomness generation is achievable with minimal experimental complexity on continuous-variable platforms.

We discuss quantum speed limits (QSLs) for finite-dimensional quantum systems undergoing general physical processes. These QSLs were obtained using two families of entropic measures, namely, the square root of the Jensen-Shannon divergence, which in turn defines a faithful distance of quantum states, and the square root of the quantum Jeffreys divergence. The results apply to both closed and open quantum systems and are evaluated in terms of the Schatten speed of the evolved state, as well as cost functions that depend on the smallest and largest eigenvalues of both initial and instantaneous states of the quantum system. To illustrate our findings, we focus on the unitary and nonunitary dynamics of mixed single-qubit states. In the first case, we obtain speed limits à la Mandelstam-Tamm that are inversely proportional to the variance of the Hamiltonian driving the evolution. In the second case, we set the nonunitary dynamics to be described by the noisy operations: depolarizing channel, phase damping channel, and generalized amplitude damping channel. We provide analytical results for the two entropic measures, present numerical simulations to support our results on the speed limits, comment on the tightness of the bounds, and provide a comparison with previous QSLs. Our results may find applications in the study of quantum thermodynamics, entropic uncertainty relations, and the complexity of many-body systems.

Many optimally scaling quantum simulation algorithms employ controlled time evolution of the Hamiltonian, which is typically the major bottleneck for their efficient implementation. This work establishes a compression protocol for encoding the controlled time evolution operator of translationally invariant local Hamiltonians into a quantum circuit. It achieves a near-optimal in time $t$ scaling for circuit depth $\mathcal{O}\left[t\text{polylog}\right(tN/\epsilon \left)\right]$, while reducing the control overhead from a multiplicative to an additive factor. We report that this compression protocol enables the implementation of iterative quantum phase estimation with as few as 414 controlled-not gates for a frustrated quantum spin system on a $6\times 6$ triangular lattice and delivers ground-state energy errors below 1% (with $\pm 1.5$% variation, calculated with a hardware noise-aware pipeline) on a $4\times 4$ triangular lattice using the noisy emulator of the Quantinuum H2 trapped ion device.