Papers

Solving interacting multi-particle systems is a central challenge in quantum chemistry and condensed matter physics. In this work, we investigate the computation of ground states and ground-state energies for the He-H+ and H2O molecules using quantum computing techniques. We employ the variational quantum eigensolver (VQE), implemented both on a quantum computer simulator and on an IBM quantum device. The resulting energies are benchmarked against exact ground-state energies obtained via classical methods. Simulations of the H2O molecule were performed on Nottingham's High Performance Computing (HPC) facilities.

Collisional gates in optical superlattices have recently achieved record fidelities, but their operation times are typically limited by tunneling. Here we propose and analyze an alternative route to a fast $\sqrt{\mathrm{SWAP}}$ gate for two fermionic atoms in an optical superlattice based on optimized, time-dependent control of the short and long lattice depths. The gate is implemented by transiently releasing the atoms into a quasi-harmonic confinement centered between the two sites. With an appropriately chosen contact interaction strength, a controlled collision accumulates the exchange phase required for $\sqrt{\mathrm{SWAP}}$ and generates entanglement. We employ a continuum, time-dependent Schrödinger-equation simulation that goes beyond a two-site Fermi–Hubbard description and benchmark it against experimentally implemented tunneling-based protocols, reproducing the observed single-particle tunneling and spin-exchange dynamics. For experimentally accessible lattice depths, we find that the proposed gate operates in $\sim 21\,\mu\mathrm{s}$, more than an order of magnitude faster than tunneling-based implementations, while achieving fidelities $\gtrsim 99\%$. We further analyze sensitivity to lattice-depth variations and show that a composite sequence improves robustness. Our results establish fast, collision-mediated entangling gates in superlattices as a promising building block for scalable neutral-atom quantum computation.

Quantum computing holds potential for accelerating the simulation of fluid dynamics. However, hardware noise in the noisy intermediate-scale quantum era significantly distorts simulation accuracy. Although error magnitudes are frequently quantified, the specific physical effects of quantum noise on flow simulation results remain largely uncharacterized. We investigate the influence of gate noise on the quantum simulation of one-dimensional scalar convection. By employing a quantum spectral algorithm where ideal time advancement affects only Fourier phases, we isolate and analyze noise-induced artifacts in spectral magnitudes. We derive a theoretical transition matrix based on Hamming distances between computational basis states to predict spectral decay, and then validate this model against density-matrix simulations and experiments on a superconducting quantum processor. Furthermore, using data-driven sparse regression, we demonstrate that quantum noise manifests in the effective partial differential equation primarily as artificial diffusion and nonlinear source terms. These findings suggest that quantum errors can be modeled as deterministic physical terms rather than purely stochastic perturbations.

Accurate phase estimation plays a pivotal role in quantum metrology, yet its precision is significantly affected by noise, particularly phase-diffusive noise caused by phase drift. To address this challenge, the joint estimation of phase and phase diffusion has emerged as an effective approach, transforming the problem into a multi-parameter estimation task. However, the incompatibility between optimal measurements for different parameters prevents single-copy measurements from reaching the fundamental precision limits defined by the quantum Cramer-Rao bound. Meanwhile, collective measurements performed on multiple identical copies can mitigate this incompatibility and thus enhance the precision of joint parameter estimation. This work experimentally demonstrates joint phase and phase-diffusion estimation using deterministic Bell measurements on a two-qubit system. A linear optical network is employed to implement both parameter encoding and deterministic Bell measurements, achieving improved estimation precision compared to any separable measurement strategy. This work proposes a new framework for phase estimation under phase-diffusive noise and underscores the substantial advantages of collective measurements in multi-parameter quantum metrology.

From the formation of social ties to the budding quantum internet, growing networks often exhibit local flexibility upon new nodes attaching to an existing network. In our proposed model, a new node connects uniformly at random to a node within the proximity of the intended target, including, but not restricted to, the target itself. Through numerical simulations and rigorous stochastic analysis, we find this local flexibility to qualitatively change the global network behavior of nonlinear preferential attachment. Depending on whether the preferential attachment is superlinear or (sub)linear, two distinct classes of complex network architectures emerge. The superlinear phase leads to a layered hierarchy, with no stationary degree distribution. Although there is a stationary degree distribution in the linear and sublinear cases, it decays strictly faster than for the Barabási–Albert model. We interpret our results within a two-dimensional phase diagram of network growth models incorporating redirection, with broad implications.

Contrary to the conventional view that noise is detrimental, we show that mixed noise can protect entanglement in a two-atom-cavity system. Specifically, the leakage of the cavity and the stochastic atom-cavity couplings are modeled as two types of noises. From the analytical derivation of the dynamical equations, the mechanism of the entanglement protection is revealed as the high-frequency(HF) noise in the atom-cavity couplings could suppress the decoherence caused by the cavity leakage, thus protect the entanglement. We investigate the entanglement protection induced by mixed noise constructed from diverse noise types, including the Ornstein-Uhlenbeck noise, flicker noise, and telegraph noise. Numerical simulations demonstrate that entanglement protection depends critically on the proportion of HF components in the power spectral density of the mixed noise. Our work establishes that enhanced HF components are essential for effective noise-assisted entanglement protection, offering key insights for noise engineering in practical open quantum systems.

This paper argues that, where deterministic and indeterministic formulations agree on empirically corroborated structure while differing in their completion of structure that remains empirically underdetermined, features invariant across these formulations warrant ontological commitment, whereas any warrant attaching to features that vary across them is categorically more provisional. Because deterministic and indeterministic completions are always formally available, while additional grounds for preferring particular completions are contingent and defeasible, empirically corroborated structure alone cannot determine whether reality is fundamentally deterministic or indeterministic, or whether that very distinction belongs only to specific representations of it. On this basis, I advance a model-invariance criterion according to which structural features are candidates for realist commitment insofar as they are empirically corroborated within a regime and preserved across the admissible formulations of that structure. I show how such invariant content can be characterised in mathematically intelligible ways, yielding a fallibilist form of structural realism grounded in model-invariance rather than in the specific form of any given mathematical representation. Features such as conservation relations, invariant measures, symmetries, and probability or correlation structures over observable histories may satisfy this criterion. By contrast, the localisation of modal selection—whether in fine-grained initial conditions, stochastic outcomes, or state-update and collapse mechanisms—may vary across empirically admissible formulations and therefore constitute a gauge-like representational freedom. This framework offers a realist ontology for modern physics that combines empirical openness with resistance to metaphysical overreach.

Quantum entanglement is commonly assumed to be fragile at ambient temperature and over macroscopic distances, where thermal noise and dissipation are expected to rapidly suppress nonclassical correlations. Here we show that this intuition fails for collective quantum modes whose dynamics is governed by reduced open-system channels rather than by microscopic thermal equilibrium. For two spatially separated collective modes, we derive an exact entanglement boundary based on the positivity of the partial transpose, valid in the symmetric resonant limit. From this result we obtain an explicit minimum collective fluctuation amplitude, expressed entirely in measurable noise, bandwidth, dissipation, and distance-dependent coupling parameters, required to sustain steady-state entanglement at finite temperature. We further show that large collective occupation suppresses but does not eliminate quantum phase diffusion, so the steady state remains phase symmetric and does not collapse to a classical mean-field despite macroscopic signal amplitudes. Stochastic simulations of the reduced open-system dynamics, together with matched classical correlated-noise null models analyzed through an identical pipeline, confirm that entanglement witnesses are violated only in the quantum regime. Our results establish a minimal, platform-independent framework connecting collective-mode dynamics, noise injection, distance, and operational certification of macroscopic entanglement.

The nanoscale charge environment critically influences the performance of semiconductor devices, yet traditional characterization techniques usually lack the spatial resolution to resolve nanoscale charge heterogeneity and identify microscopic noise sources. Here, we address this critical gap by utilizing individual PL5 color centers in commercial silicon carbide as room-temperature, broadband (near-DC to GHz) quantum spectrometers. We report the first real-time, nanoscale observation of single-charge tunneling dynamics at room temperature in 4H-SiC by monitoring the random telegraph noise using optically detected magnetic resonance (ODMR). This capability enables an electrical noise imaging technique that shows distinct noise variations on different wafers. Employing dynamical decoupling and $T_1$ relaxation spectroscopy, we observe correlations of noise spectral density across frequency bands and obtain the nanoscale electron paramagnetic resonance (EPR) fingerprint of spin defects in SiC. Ultimately, through surface chemical engineering, we identify the native oxide layer as the main source of resolved electromagnetic fluctuations. This work establishes a versatile atomic-scale metrology platform bridging quantum sensing and semiconductor engineering, offering critical insights for optimizing third-generation semiconductor interfaces and advancing solid-state quantum technologies.

We present separability criteria based on local symmetric measurements. These experimental plausible criteria are shown to be more efficient in detecting entanglement than the current counterparts by detailed examples. Furthermore, we generalize the separability criteria from bipartite to arbitrary multipartite systems. These criteria establish a richer connection between the quantum entanglement and the probabilities of local measurement outcomes.

We revisit the canonical quantization to assess the spectrum of the modified Emden equation $\ddot{x} + kx\dot{x} + \omega^2 x + \frac{k^2}{9}x^3 = 0$, which is an isochronous case of the Liénard-Kukles equation. While its classical isochronicity and canonical quantization, leading to polynomial solutions with an exactly-equispaced spectrum have been discussed earlier, including in the recent paper [Int. J. Theor. Phys. 64, 212 (2025)], the present study focuses on the quantization of its branched Hamiltonians. For small $k$, we show numerically that the resulting energy spectrum is no longer perfectly harmonic but only approximately equispaced, exhibiting quasi-harmonic behavior characterized by deviations from uniform spacing. Our numerical results are precisely validated by analytical calculations based on perturbation theory.

Two-stage stochastic programming often discretizes uncertainty into scenarios, but scenario enumeration makes expected recourse evaluation scale at least linearly in the scenario count. We propose qGAN-QAOA, a unified quantum-circuit workflow in which a pre-trained quantum generative adversarial network encodes the scenario distribution and QAOA optimizes first-stage decisions by minimizing the full two-stage objective, including expected recourse cost. With the qGAN parameters fixed after training, we evaluate the objective as the expectation value of a problem Hamiltonian and optimize only the QAOA variational parameters. We interpret non-anticipativity as a condition on measurement outcome statistics and prove that the first-stage measurement marginal is independent of the scenario. For uniformly discretized uncertainty, the diagonal operator encoding the uncertainty admits a sparse Pauli-Z expansion via the Walsh–Hadamard transform, yielding polylogarithmic scaling of gate count and circuit depth with the number of scenarios. Numerical experiments on the stochastic unit commitment problem (UCP) with photovoltaic (PV) uncertainty compare the expected cost of the proposed method with classical expected-value and two-stage stochastic programming baselines, demonstrating the effectiveness of qGAN-QAOA as a two-stage decision model.

The Lieb-Robinson correlation function can be used to characterize the propagation of quantum information in Ising chains. Considerable work has been done to establish bounds on this correlation function in various circumstances. To actually calculate the value of the correlation function directly typically requires a state space which grows exponentially with system size, and so is intractable for all but relatively small systems. We employ a recently-developed method that enables direct calculation of the Lieb–Robinson correlation function and which scales linearly with system size. This enables the computation for systems with more than a thousand qubits, revealing the propagation of quantum information down the chain. We extend this technique to the problem of Ising chains with randomly disordered coupling strengths. Increasing disorder causes localization of the quantum correlations and halts propagation of quantum information down the chain. We see light-cone isocontours therefore becoming vertical. The decay of correlations down the chain is characterized by a correlation length which in the paramagnetic phase increases quadratically with mean coupling strength and inverse quadratically with disorder level. The correlation length peaks at the phase transition. We map our general expression for the correlation function in the Ising system onto the probability density in the single particle tight-binding Su-Schrieffer-Heeger model for a specific initial condition.

In quantum information and computation research, symbolic methods have been widely used for human specification and reasoning about quantum states and operations. At the same time, they are essential for ensuring the scalability and efficiency of automated reasoning and verification tools for quantum algorithms and programs. However, a formal theory for symbolic specification and reasoning about quantum data and operations is still lacking, which significantly limits the practical applicability of automated verification techniques in quantum computing. In this paper, we present a general logical framework, called Symbolic Operator Logic $\mathbf{SOL}$, which enables symbolic specification and reasoning about quantum data and operations. Within this framework, a classical first-order logical language is embedded into a language of formal operators used to specify quantum data and operations, including their recursive definitions. This embedding allows reasoning about their properties modulo a chosen theory of the underlying classical data (e.g., Boolean algebra or group theory), thereby leveraging existing automated verification tools developed for classical computing. It should be emphasised that this embedding of classical first-order logic into $\mathbf{SOL}$ is precisely what makes the symbolic method possible. We envision that this framework can provide a conceptual foundation for the formal verification and automated theorem proving of quantum computation and information in proof assistants such as Lean, Coq, and related systems.

We present a method for preparing various exotic modifications of Schrödinger cat states by coupling a semiclassical oscillator to a system of qubits. Varying the number of qubits and parameters of the protocol (involving quantum quench of the coupled system and a subsequent spin measurement), we bring the oscillator into a coherent superposition composed of an arbitrary number of wavepackets in tunable proportions and motion relations. The method can be implemented with the aid of current experimental techniques and may find applications in quantum information and sensing protocols.

A theoretical analysis of the Casimir interaction between an arc and plate is conducted, which remains unexplored despite its relevance to Micro-Electro-Mechanical Systems (MEMS) fabrication. The configuration consists of a rigid finite plate and a flexible curved nanomembrane, with radius 100 micrometers, initially concave toward the rigid plate. The maximum thickness is evaluated for which the nanomembrane undergoes a change in curvature: from concave to convex with respect to the plate, due to the Casimir interaction. The Casimir energy for a curved surface is derived using the Proximity Force Approximation (PFA) with next-to-leading-order (NTLO) corrections. Kirchhoff-Love theory for a thin isotropic plate of constant thickness is used to estimate the bending energy. Material-dependent effects on the Casimir interaction are evaluated by comparing Au and Ag plates. The maximum thickness is derived where U_Casimir > U_bending for distances in the range of 0.1-1 micrometers. Results show curvature reversal occurs for nanomembranes with nanoscale thicknesses at the studied distances. Silver nanomembranes tolerate greater thickness than gold nanomembranes due to material-dependent properties. Comparison between NTLO-corrected PFA and perturbative PFA confirms the accuracy of the NTLO approach. The Casimir arc-to-plate geometry in MEMS enables Casimir-based actuation, enhances devices reliability, and prevents stiction. These findings provide thickness constraints for MEMS design and performance, accounting for the Casimir force.

We demonstrate a three-dimensional magneto-optical trap (MOT) of a metal hydride molecule, CaH. We are able to scatter $\sim$$10^{4}$ photons with vibrational loss covered up to vibrational quantum number $\nu=2$. This allows us to laser slow the molecular beam near zero velocity with a "white-light" technique and subsequently load it into a radio-frequency MOT. The MOT contains $230(40)$ molecules, limited by beam source characteristics and predissociative loss of CaH. The temperature of the MOT is below one millikelvin. The predissociative loss mechanism could, in turn, facilitate controlled dissociation of the molecule, offering a possible route to optical trapping of hydrogen atoms for precision spectroscopy.

We investigate whether a 3-$\delta$ system with positive coupling strengths can approximate the transmission spectrum of a 2-$\delta$ resonance system with opposite-sign couplings for $k <3$. Theoretical analysis establishes exact isospectrality – perfectly matched transmission spectrum – is impossible for physically non-trivial configurations, while numerical experiments identify the minimal constraint set for practicability. These results establish both the practical limits and achievable accuracy of resonance matching under sign constraints, with implications for understanding spectral non-uniqueness in quantum scattering problems.

Standard quantum mechanics relies on two distinct dynamical principles: unitary evolution and collapse. A mathematically self-contained variational framework is presented that replaces this dualism with a single principle, in which nonrelativistic Schrödinger dynamics are not postulated but emerge as an admissible optimality condition of a primal-dual boundary-value problem. By expressing the state in terms of hydrodynamic variables $(\rho,\mathbf{j})$ subject to a continuity constraint, it is shown that Fisher-information regularization yields the linear Schrödinger equation within the admissible single-valued variational class. Rather than evolving an initial state forward in time, the dynamics arise from minimizing a global action that connects the initial and final boundary constraints, with the selected solution corresponding to a specific hydrodynamic flow within an ensemble of admissible histories. A von Neumann pointer model illustrates how Born-rule statistics for recorded outcomes arise without introducing a separate collapse law. Within this formulation, quantum uncertainty is interpreted as effective randomness over boundary-compatible histories rather than as a fundamental stochastic postulate. The resulting framework provides a nonrelativistic proof of concept for how a single time-symmetric variational reformulation can recover key features of quantum theory.

Quantum critical phases are extended regions of phase space characterized by a diverging correlation length. By analogy, we define an information critical phase as an extended region of a mixed state phase diagram where the Markov length, the characteristic length scale governing the decay of the conditional mutual information (CMI), diverges. We demonstrate that such a phase arises in decohered $\mathbb{Z}_{N}$ toric codes by assessing both the CMI and the coherent information, the latter quantifying the robustness of the encoded logical qudits. For $N>4$, we find that the system hosts an information critical phase intervening between the decodable and non-decodable phases where the coherent information saturates to a fractional value in the thermodynamic limit, indicating that a finite fraction of logical information is still preserved. We show that the density matrix in this phase can be decomposed into a convex sum of Coulombic pure states, where gapped anyons reorganize into gapless photons. We further consider the ungauged $\mathbb{Z}_{N}$ toric code and interpret its mixed state phase diagram in the language of strong-to-weak spontaneous symmetry breaking. We argue that in the dual model, the information critical phase arises because the spontaneously broken off-diagonal $\mathbb{Z}_{N}$ symmetry gets enhanced to a $U(1)$ symmetry, resulting in a novel superfluid phase whose gapless modes involve coherent excitations of both the system and the environment. Finally, we propose an optimal decoding protocol for the corrupted $\mathbb{Z}_{N}$ toric code and show that its logical error rate saturates to a fractional value in the information critical phase. Our findings identify a gapless analog for mixed-state phases that still acts as a fractional topological quantum memory, thereby extending the conventional paradigm of quantum memory phases.

We investigate the statistical physics of quantum error correction in ${\rm U}(1)$ symmetry-enriched topological quantum memories. Starting from a phenomenological error model of charge-conserving noise, we study the optimal decoder assuming the local charges of each anyon can be measured. The error threshold of the optimal decoder corresponds to a continuous phase transition in a disordered two-dimensional integer loop model on the Nishimori line. Using an effective replica field theory analysis and Monte Carlo numerics, we show that the optimal decoding transition exhibits Berezinskii-Kosterlitz-Thouless universality with a modified universal jump in winding number variance. We further generalize the model beyond the Nishimori line, which defines a large class of suboptimal decoders. At low nonzero temperatures and strong disorder, we find numerical evidence of a disorder-dominated loop-glass phase which corresponds to a "confidently incorrect" decoder. The zero-temperature limit defines the minimum-cost flow decoder, which serves as the ${\rm U}(1)$ analog of minimum-weight perfect matching in $\mathbb{Z}_2$ topological codes. Both the optimal and minimum-cost flow decoders are shown to dramatically outperform the charge-agnostic optimal decoder in symmetry-enriched topological codes.

The hypergraph product (HGP) construction of quantum error-correcting codes (QECC) offers a general and explicit method for building a QECC from two classical codes, thereby paving the way for the discovery of good quantum low-density parity-check codes. In this letter, we propose a general and explicit construction recipe for QECCs from a total of D classical codes for arbitrary D. Following this recipe guarantees the obtainment of a QECC within the stabilizer formalism and nearly exhausts all possible constructions. As examples, we demonstrate that our construction recovers the HGP construction when D = 2 and leads to four distinct types of constructions for D = 3, including a previously studied case as one of them. When the input classical codes are repetition codes, our D = 3 constructions unify various three-dimensional lattice models into a single framework, encompassing the three-dimensional toric code model, a fracton model, and two other intriguing models not previously investigated. Among these, two types of constructions exhibit a trade-off between code distance and code dimension for a fixed number of qubits by adjusting the lengths of the different classical codes, and the optimal choice can simultaneously achieve relatively large values for both code distance and code dimension. Our general construction protocol provides another perspective for enriching the structure of QECCs and enables the exploration of richer possibilities for good codes.

Informationally complete (IC) measurements are fundamental tools in quantum information processing, yet their physical implementation remains challenging. By the Naimark extension theorem, an IC measurement may be realized by a von Neumann measurement on an extended system after a suitable interaction. In this work, we elaborate on a simple algorithm for realizing Naimark extensions for rank-one Weyl-Heisenberg covariant informationally complete measurements in arbitrary finite dimensions. Exploiting Weyl-Heisenberg covariance, we show that the problem reduces to determining a $d \times d$ unitary from which the full $d^2 \times d^2$ unitary interaction can be constructed. The latter unitary enjoys a block-circulant structure which allows e.g., for an elegant optical implementation. We illustrate the procedure with explicit calculations for qubit, qutrit, and ququart SIC-POVMs. Finally, we show that from another point of view, this method amounts to preparing an ancilla system according to a so-called fiducial state, followed by a generalized Bell-basis measurement on the system and ancilla. These results provide a straightforward framework for implementing informationally complete measurements in the laboratory suitable for both qubit and qudit based systems.

We use dynamical quantum typicality to predict the thermal equilibrium state of ultracold Rydberg atoms exchanging energy via long-range dipole-dipole interactions. We excite atoms to the center of a manifold of nearly-harmonically spaced clusters of Stark energy levels and then allow them to equilibrate. Comparing the equilibrium state to our thermal prediction across a range of Rydberg densities, we find that this system generally fails to thermalize, though it approaches the thermal state at the highest tested density. This is the first direct comparison of a dynamical quantum typicality calculation to experiment.

MaxCut is a canonical NP-hard combinatorial optimization problem in graph theory with broad applications ranging from physics to bioinformatics. Although variational quantum algorithms offer promising new approaches that may eventually outperform classical schemes, they suffer from resource constraints and trainability issues such as barren plateaus, making large-scale instances intractable on noisy intermediate-scale quantum devices. In this paper, we propose an enhanced distributed variational quantum eigensolver for large-scale MaxCut problems, which extends our prior distributed variational quantum eigensolver framework by integrating a novel hybrid classical-quantum perturbation strategy, enhances optimization scalability and efficiency. Our algorithm solves weighted MaxCut instances with up to 1000 vertices using only 10 qubits, and numerical results indicate that it consistently outperforms the Goemans-Williamson algorithm. We further employ a warm-start initialization strategy, seeding the algorithm with high-quality solutions from the Goemans-Williamson algorithm, with results confirming that the optimal classical solution can be effectively further improved. The practical utility of the proposed algorithm is further validated through its application to haplotype phasing on genome sequencing data of the human ABCA1 gene, producing high-quality haplotypes that rival those obtained by the Goemans-Williamson algorithm with $10^6$ projections. These results establish the proposed algorithm as a scalable, NISQ-compatible framework for near-term quantum-enhanced large-scale combinatorial optimization.

This paper studies the capacity limits for quantum secret sharing (QSS). The goal of a QSS scheme is to distribute a quantum secret among multiple participants, such that only authorized parties can recover it through collaboration, while no information can be obtained without such collaboration. We introduce an information-theoretic model for the rate analysis of QSS and its relation to compound quantum channels, following a similar approach as of Zou et al. (2015) on classical secret sharing. We establish a regularized characterization for the QSS capacity, and determine the capacity for QSS with dephasing noise.

We commence our study with review of dispersion interactions in electrolytes. We then reflect on how background media change atom-atom excited-state systems. To highlight the impact of nonlocal media, such as salt solutions, we predict that a new contribution to the resonance interaction energy emerges in a form $\propto e^{-\kappa_{\rm D} \rho}/\rho$. Here $\kappa_{\rm D}$ is the Debye length and $\rho$ is the distance between the atoms. This contribution vanishes at zero temperature, where a new term proportional to $1/\rho^4$ (similar to free space) occurs. This new term is dampened by the electrolyte at large distances, causing it to decrease much faster, proportional to $1/\rho^7$. The long-range electrolyte-induced resonance interaction at finite temperature may, in addition to the dominating van der Waals attraction (which goes as $1/\rho^6$), take part in the molecular formation of biological fluids.

Quantum nonlocality is an essential resource in quantum information and is commonly classified into three distinct forms: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Gisin's theorem shows that pure-state entanglement implies Bell nonlocality, and it motivates the question of how entanglement and EPR steering are related beyond pure states. Here we prove that every entangled rank-2 two-qubit state is EPR steerable, with rank-1 states included as a special case. The proof combines a local-unitary parametrization of rank-2 two-qubit states, a necessary and sufficient separability condition, and a state-dependent nonlinear steering inequality. This gives an analytical characterization of EPR steerability for rank-2 two-qubit entangled states. Thus, rank-2 two-qubit entangled states provide certifiable EPR-steering resources in quantum information.

In the approaches based on matrix-product states (MPSs), such as the density-matrix renormalization group (DMRG) method, the ordering of the sites crucially affects the computational accuracy. We investigate the performance of an algorithm that searches for the optimal site order by iterative local site rearrangement. We improve the algorithm by expanding the range of site rearrangement and apply it to a one-dimensional quantum Heisenberg model with random site permutation. The results indicate that increasing the range of the site rearrangement significantly improves the computational accuracy of the DMRG method. In particular, increasing the rearrangement range from two to three sites reduces the average relative error in the ground-state energy by 65% to 94% in the cases we tested. We also discuss the computational cost of the algorithm and its application as a preprocessing for MPS-based calculations.

This article traces the development of fluctuation theory and its deep connection to irreversibility, from equilibrium to near-equilibrium, and finally to far-from-equilibrium systems. Classical fluctuation theorems, which capture the statistical behaviour of thermodynamic systems far from equilibrium, are now well established. Their quantum counterparts, however, remain an active area of research. In this review, we highlight recent advances by linking quantum fluctuation theorems with linear response theory, offering new insights into the nature of quantum fluctuations and irreversibility in the near-equilibrium regime. Particular emphasis is placed on dissipated work in quantum systems as a pathway to observing non-classical effects in quantum thermodynamics. Understanding quantum fluctuations is not only essential for clarifying the foundations of irreversibility but also crucial for the development of novel quantum technologies, including quantum computers, sensors, and metrological devices.