Papers

Entanglement entropy is a fundamental diagnostic for quantum chaos, typically exhibiting volume-law scaling in highly excited eigenstates of chaotic many-body systems. In this work, we present a striking counterexample: a Floquet-driven quantum many-body system with Rydberg-like blockade that, despite being fully chaotic as indicated by its Wigner-Dyson level statistics and local thermalization, exhibits a strict area-law entanglement entropy. Specifically, the entanglement entropy of every Floquet eigenstate is bounded by $\ln2$, independent of system size. We trace this anomaly to the specific Hilbert space structure imposed by the blockades, which restricts the Schmidt rank across a bipartition. Furthermore, we generalize this discovery by establishing a duality between constrained many-body Hamiltonians and single-particle quantum walks on median graphs, and we outline a general procedure for constructing systems with an entanglement entropy bounded by a predetermined constant. Our results demonstrate that entanglement entropy alone is an insufficient diagnostic of many-body quantum chaos and highlight the profound impact of Hilbert space geometry on quantum dynamics and thermalization.

A promising platform for semi-device-independent quantum information is prepare-and-measure experiments restricted only by a bound on the energy of the communication. Here, we investigate the role of shared entanglement in such scenarios. For classical communication, we derive a general correlation criterion for nonlocal resources and use it to show that entanglement can fail to be a resource in standard tasks. For quantum communication, we consider the basic primitive for energy-constrained communication, namely the probabilistic transmission of a bit, and show that the advantages of entanglement only can be unlocked by non-unitary encoding schemes that purposefully decohere the entangled state. We also find that these advantages can be increased by using entanglement of higher dimension than qubit. We leverage these insights to investigate the impact of entanglement for quantum random number generation, which is a standard application of these systems but whose security so far only has been established against classical side information. In the low-energy regime, our attacks on the protocol indicate that the security remains largely intact, thereby paving the way for strengthened security without more complex setups and with negligible performance reductions.

Extending classical synchronization to the quantum domain is of great interest both from the fundamental physics point of view and with a view toward quantum technology applications. This work characterizes phase synchronization of an effective spin-1 system, which is realized by coupling three quantum states with infinite lifetime to auxiliary excited states that have a finite lifetime. Integrating out the excited states, the effective spin-1 model features coherent and incoherent effective couplings. Our key findings are: (i) Phase synchronization can be controlled by adjusting the phases of the couplings to the excited states. (ii) Unlike in the paradigmatic spin-1 system studied in the literature, where the dissipative couplings describe decay into the limit cycle state, the effective spin-1 model investigated in this work is governed by a competition between dissipative decay into and out of the limit cycle state, with the dissipative decay out of the limit cycle state playing a critical role. (iii) We identify a parameter regime where phase synchronization of the effective spin-1 system is – in the absence of coherent effective couplings – governed entirely by the effective dissipators. The effective spin-1 model is benchmarked through comparisons with master equation calculations for the full Hilbert space. Physical insights are gained through analytical perturbation theory calculations. Our findings, which are expected to hold for a broad class of energy level and coupling schemes, are demonstrated using hyperfine states of $^{87}$Rb.

Stability achieved by large angular momentum is ubiquitous in nature, with examples ranging from classical mechanics, over optics and chemistry, to nuclear physics. In atoms, angular momentum can protect excited electronic orbitals from decay due to selection rules. This manifests spectacularly in highly excited Rydberg states. Low angular momentum Rydberg states are at the heart of recent breakthroughs in quantum computing, simulation and sensing with neutral atoms. For these applications the lifetime of the Rydberg levels sets fundamental limits for gate fidelities, coherence times, or spectroscopic precision. The quest for longer Rydberg state lifetimes has motivated the generation, coherent control and trapping of circular Rydberg atoms, which are characterized by the maximally allowed electron orbital momentum and were key to seminal experiments with single atoms and photons. Here, we report the observation of individually trapped circular Rydberg atoms with lifetimes of more than 10 milliseconds, two orders of magnitude longer-lived than the established low angular momentum orbitals. This is achieved via Purcell suppression of blackbody modes at room temperature. We coherently control individual circular Rydberg levels at so far elusive principal quantum numbers of up to $n=103$, and observe tweezer trapping of the Rydberg atoms on the hundred millisecond scale. Our results pave the way for quantum information processing and sensing utilizing the combination of extreme lifetimes and giant Rydberg blockade.

This paper investigates the construction of efficient quantum secret sharing schemes for quantum access structures based on hypergraphs with three hyperedges. We prove that hypercycles with three hyperedges are quantum access structures if and only if they can be classified into 12 non-isomorphic types under hypergraph isomorphism, and these hypercyclic quantum access structures encompass all four hyperstars with three hyperedges.In prior work, efficient and perfect quantum secret sharing schemes were constructed for hyperstar access structures with three hyperedges using single photons in d -dimensional quantum systems. These schemes correspond to classical perfect secret sharing schemes with optimal information rates. However, for hypercyclic access structures with three hyperedges, the method described above fails to yield classical perfect secret sharing schemes with optimal information rates. In this work, we explicitly construct classical perfect secret sharing schemes with optimal information rates for these access structures by combining Simmons' geometric method with Shamir's threshold scheme. Subsequently, we employ single photons in d-dimensional quantum systems to build perfect QSS schemes upon these classical constructions.We introduce the concept of idealized information rate for minimal access structures in perfect QSS schemes. By extending the notion of efficiency proposed by Cabello [Phys. Rev. Lett., vol. 85, no. 26, p. 5635, 2000] for quantum key distribution protocols to QSS, we define the efficiency of minimally authorized subsets. Furthermore, we establish the relationship between the efficiency of minimally authorized subsets and the idealized information rate of minimal access structures. Finally, we rigorously prove that the QSS schemes constructed in this work achieve the highest efficiency among existing solutions.

We develop a wave packet molecular dynamics framework for modeling the structural properties of partially-ionized dense plasmas, based on a chemical model that explicitly includes bound state wavefunctions. Using hydrogen as a representative system, we compute self-consistent charge state distributions through free energy minimization, following the approach of Plummer et al. [Phys. Rev. E 111, 015204 (2025)]. This enables a direct comparison of static equilibrium properties with path integral Monte Carlo data, facilitating an evaluation of the model's underlying approximations and its ability to capture the complex interplay between ionization and structure in dense plasma environments.

The precise measurement of spatial attitude parameters is critical for applications in inertial navigation, industrial monitoring, instrument calibration, quantum metrology, etc. In this work, we theoretically investigate and experimentally realize the simultaneous measurement of the yaw and pitch angles using a Hermite-Gaussian-postselected double weak value system integrated with two sets of high-order-mode balanced homodyne detections, thereby achieving a complete characterization of the beam deflection. Signals of the yaw and pitch angles that are involved in TEM$_{10}$ and TEM$_{01}$ modes output from two dark ports of the system can be measured independently. As a result, the obtained minimum measurable yaw and pitch angles of beam deflection are 83 prad and 89 prad, respectively. Meanwhile, the corresponding displacements are 0.79 pm and 0.85 pm, respectively. This work expands the beam deflection measurement to two dimensions, which provides a new insight for future high-precision multi-parameter spatial precise detection.

The mean squared displacement has been widely used as the primary metric for comparing quantum and classical random walks, with quantum walks showing quadratic scaling versus linear scaling for classical walks. However, this comparison may not capture the full picture: while the mean squared displacement is well-suited for Gaussian distributions, quantum walk distributions exhibit distinctly non-Gaussian features. We propose that the mean hitting time offers a complementary perspective with clear operational meaning for search algorithms. Through analytical calculations, we show that quantum and classical walks yield identical MHT for symmetric initial conditions with two detectors, suggesting that the apparent quantum advantage seen in MSD comparisons may be context-dependent. Interestingly, introducing stochastic resetting reveals new dynamics. We demonstrate analytically that quantum walks can achieve reduced MHT under stochastic reset through quasi-momentum redistribution, while classical walks see no benefit. This quantum advantage naturally degrades with noise, the quantum walk converges to classical behavior. We suggest that MHT reduction under stochastic reset can serve as an additional signature of quantum behavior, particularly useful for characterizing quantum walk implementations on noisy quantum devices. Our results indicate that different metrics can reveal different aspects of quantum-classical comparisons in walk-based algorithms.

Quantum simulation aims to recreate complex many-body phenomena in controlled environments, offering insights into dynamics that are otherwise difficult to model. Existing platforms, however, are often complex and costly to scale, typically requiring ultra pure vacuum or low temperatures. Here, we introduce a platform based on a thin, strongly interacting ${}^{13}\text{C}$ nuclear spin layer in diamond that allows controlled exploration of many-body dynamics at room temperature. Nearby nitrogen-vacancy centers enable polarization, readout, and, combined with radio-frequency fields, coherent control of the nuclear spins. We demonstrate strong, tunable interactions among the nuclear spins and use the system to probe discrete time-crystalline order across varying interaction ranges. By combining ease of use with operation at ambient temperatures, our work opens new opportunities for investigating strongly correlated many-body effects.

Waveguide quantum electrodynamics (wQED) has become a central platform for studying collective light-matter interactions in low-dimensional photonic environments. While conventional wQED systems rely on uniform chirality or reciprocal emitter-waveguide coupling, we propose a structured wQED framework, where the coupling directionality of each emitter can be engineered locally to control excitation transport in an atom-nanophotonic interface. For different combinations of patterned coupling directionalities of the emitters, we identify four representative configurations that exhibit distinct dynamical behaviors: centering, wave-like, leap-frog, and dispersion excitations. Spectral analysis of the effective non-Hermitian Hamiltonian reveals that these dynamics originate from interferences among subradiant eigenmodes. Variance analysis further quantifies the spreading of excitation as functions of interatomic spacing and global chirality, showing tunable localization-delocalization transitions. Including nonguided losses, we find that the transport characteristics remain robust for realistic coupling efficiencies (beta >= 0.99). These results establish structured wQED as a practical route to manipulate excitation localization, coherence, and transport through programmable directionality patterns, paving the way for controllable subradiant transport and chiral quantum information routing.

Scalable quantum computing requires modular multi-chip architectures integrating multiple quantum cores interconnected through quantum-coherent and classical links. The classical communication subsystem is critical for coordinating distributed control operations and supporting quantum protocols such as teleportation. In this work, we consider a realization based on a wireless network-on-chip for implementing classical communication within cryogenic environments. Traditional token-based medium access control (MAC) protocols, however, incur latency penalties due to inefficient token circulation among inactive nodes. We propose the instruction-directed token MAC (ID-MAC), a protocol that leverages the deterministic nature of quantum circuit execution to predefine transmission schedules at compile time. By embedding instruction-level information into the MAC layer, ID-MAC restricts token circulation to active transmitters, thereby improving channel utilization and reducing communication latency. Simulations show that ID-MAC reduces classical communication time by up to 70% and total execution time by up to 30-70%, while also extending effective system coherence. These results highlight ID-MAC as a scalable and efficient MAC solution for future multi-chip quantum architectures.

Unlike classical correlations, entanglement cannot be freely shared among multiple parties. This unique feature of quantum systems is known as the monogamy of entanglement. While it holds for all multipartite pure states, its converse – weak entanglement between two parties enforces strong entanglement with a third party – occurs only under specific conditions. In particular, Hayashi and Chen [Phys. Rev. A 84, 012325 (2011)] demonstrated a qualitative version of the converse monogamy of entanglement (CMoE) for tripartite pure states by employing a hierarchy of bipartite entanglement defined through the relations among various separability criteria, and Singh and Datta [IEEE Trans. Inf. Theory 69, 6564 (2023)] later extended this notion of the CMoE from the viewpoint of distillability under one-way or two-way classical communication. In this work, we extend their results to the CMoE with broader conditions, and furthermore show that our extensions are maximal with respect to the hierarchies they considered.

We explicitly show how to derive the $(D+1)$-dimensional Einstein equation from the entanglement entropy between codimension-one disjoint regions in $D$-dimensional conformal field theory.

In this work, we analytically derive a semi-classical equation of motion describing the zitterbewegung effects arising in the dynamics of wavepackets in non-Hermitian systems. In Hermitian non-relativistic quantum systems, the zitterbewegung effects can arise due to the spin precession and spin-orbit coupling. Interestingly, the spin dynamics in non-Hermitian systems are qualitatively different because of the effective nonlinear terms induced by the non-Hermitian part of the Hamiltonian. In this work, we show the effects from the non-Hermitian spin dynamics by generalising the description of zitterbewegung effects to non-Hermitian systems. We also uncover novel non-Hermitian correction to the group velocity, which can be expressed in terms of the non-Hermitian quantum metric tensor in the absence of out-of-plane effective field.

Geometry can fundamentally govern the propagation of light, independent of material constraints. Here, we demonstrate that a fractal phase space, endowed with a non-Euclidean, scale-dependent geometry, can intrinsically induce resonance quantization, spatial confinement, and tunable damping without the need for material boundaries or external potentials. Employing a fractional formalism with a fixed scaling exponent, we reveal how closed-loop geodesics enforce constructive interference, leading to discrete resonance modes that arise purely from geometric considerations. This mechanism enables light to localize and dissipate in a controllable fashion within free space, with geometry acting as an effective quantizing and confining agent. Numerical simulations confirm these predictions, establishing geometry itself as a powerful architect of wave dynamics. Our findings open a conceptually new and experimentally accessible paradigm for material-free control in photonic systems, highlighting the profound role of geometry in shaping fundamental aspects of light propagation.

Light is the fundamental medium through which we perceive the world around us. In the modern era, light can not only be used in its raw form but can also be used as a versatile tool. Generally, light fields carry energy and momentum (both linear and angular). Due to the transfer of linear momentum from light to matter, the radiation pressure is exerted, whereas, the intrinsic spin angular momentum (SAM) is associated with the polarization states of light. Light fields embedded with optical orbital angular momentum (OAM) – also known as optical vortices or phase singular beams – have truly revolutionized the field of optics and extended our basic understanding of the light-matter interaction process across various scales. Optical vortices – spatially characterized by the presence of twisted phase fronts and a central intensity null – have found a myriad of applications starting from microparticle trapping and manipulation to microscopy, optical communication, and quantum information science, among others. Here, we revisit some of the fundamental concepts on optical vortices and discuss extensively on how this new dimension of light i.e., the OAM, has been exploited in both linear and nonlinear optical regimes. We discuss the different types of vortex beams, the techniques used to generate and detect their OAM, and their propagation. Particularly, we put a special emphasis on the utilization of vortex beams in nonlinear regimes to explain different optical phenomena such as the second harmonic generation, parametric down-conversion, and high-order harmonic generation. The generation of vortex beams in the UV to XUV regimes, encoded with higher OAM values, could potentially extend their application range to areas such as high-capacity data transmission, stimulated emission depletion microscopy, phase-contrast imaging, and particle trapping in optical tweezers, among others.

Nelson's stochastic mechanics links quantum mechanics to an underlying Brownian motion with the identification $\hbar = m\sigma$. Ghose's interpolating equation introduces a continuous parameter $\lambda$ that suppresses the quantum potential $Q[\psi]$ and yields a smooth transition between quantum ($\lambda=0$) and classical ($\lambda=1$) regimes. In this short note, we show that the Koopman–von Neumann (KvN) Hilbert-space formulation of classical mechanics emerges naturally as the $\lambda \to 1$ limit of this stochastic $\sigma$–$\lambda$ hierarchy. The KvN phase-space amplitude provides an operator representation of the classical Liouville equation, while the $\lambda$ parameter acts as a projection flow from the complex projective Hilbert manifold $\mathbb{C}P^n$ to its classical quotient $\mathbb{C}P^*/U(1)$, implementing phase superselection. This unified picture links quantum, stochastic, and classical dynamics within a single continuous framework.

We theoretically investigate reflection and transmission measurements of two-photon and four-photon Kerr parametric oscillators (KPOs), introducing interference effects between inter-level transitions. Due to the level degeneracy of a KPO, a probe field can be resonant with multiple inter-level transitions. We extend the previous theory of reflection measurements by incorporating the interaction between inter-level transitions and off-diagonal elements of the density matrix which had previously been neglected. We demonstrate that interference among these transitions substantially modifies the spectrum. We identify the conditions for the interference, as well as those under which the off-diagonal elements of the density matrix affect the spectrum. The theory is also generalized to transmission measurements, and is applicable to a broad class of systems beyond KPOs.

Quantum theory provides non-classical principles, such as superposition and entanglement, that inspires promising paradigms in machine learning. However, most existing quantum-inspired fusion models rely solely on unitary or unitary-like transformations to generate quantum entanglement. While theoretically expressive, such approaches often suffer from training instability and limited generalizability. In this work, we propose a Quantum-inspired Neural Network with Quantum Jump (QiNN-QJ) for multimodal entanglement modelling. Each modality is firstly encoded as a quantum pure state, after which a differentiable module simulating the QJ operator transforms the separable product state into the entangled representation. By jointly learning Hamiltonian and Lindblad operators, QiNN-QJ generates controllable cross-modal entanglement among modalities with dissipative dynamics, where structured stochasticity and steady-state attractor properties serve to stabilize training and constrain entanglement shaping. The resulting entangled states are projected onto trainable measurement vectors to produce predictions. In addition to achieving superior performance over the state-of-the-art models on benchmark datasets, including CMU-MOSI, CMU-MOSEI, and CH-SIMS, QiNN-QJ facilitates enhanced post-hoc interpretability through von-Neumann entanglement entropy. This work establishes a principled framework for entangled multimodal fusion and paves the way for quantum-inspired approaches in modelling complex cross-modal correlations.

Quantum communication is a growing area of research, with quantum internet being one of the most promising applications. Studying the statistical properties of this network is essential to understanding its connectivity and the efficiency of the entanglement distribution. However, the models proposed in the literature often assume homogeneous distributions in the connections of the optical fiber infrastructure, without considering the heterogeneity of the network. In this work, we propose new models for the quantum internet that incorporate this heterogeneity of node connections in the optical fiber network, analyzing how this characteristic influences fundamental metrics such as the degree distribution, the average clustering coefficient, the average shortest path and assortativity. Our results indicate that, compared to homogeneous models, heterogeneous networks efficiently reproduce key structural properties of real optical fiber networks, including degree distribution, assortativity, and hierarchical behavior. These findings highlight the impact of network structure on quantum communication and can contribute to more realistic modeling of quantum internet infrastructure.

We recast the well-known axiom system of quantum mechanics used by physicists (the Dirac calculus) in the language of Continuous Logic. For the basic version of the axiomatic system we prove that along with the canonical continuous model the axioms have approximate finite models of large sizes, in fact the continuous model is isomorphic to an ultraproduct of finite models. We analyse the continuous logic quantifier corresponding to Dirac integration and show that in finite context it has two versions, local and global, which coincide on Gaussian wave-functions.

Large language models are now integrated into many scientific workflows, accelerating data analysis, hypothesis generation, and design space exploration. In parallel with this growth, there is a growing need to carefully evaluate whether models accurately capture domain-specific knowledge and notation, since general-purpose benchmarks rarely reflect these requirements. This gap is especially clear in quantum science, which features non-intuitive phenomena and requires advanced mathematics. In this study, we introduce QuantumBench, a benchmark for the quantum domain that systematically examine how well LLMs understand and can be applied to this non-intuitive field. Using publicly available materials, we compiled approximately 800 questions with their answers spanning nine areas related to quantum science and organized them into an eight-option multiple-choice dataset. With this benchmark, we evaluate several existing LLMs and analyze their performance in the quantum domain, including sensitivity to changes in question format. QuantumBench is the first LLM evaluation dataset built for the quantum domain, and it is intended to guide the effective use of LLMs in quantum research.

We study the problem of $n$-fold rotationally symmetric bosonic state preparation, which is of great importance to bosonic quantum error correction, using a multiphoton interaction between an oscillator and an auxiliary qubit. We present an $n$-photon Law-Eberly ($n$LE) protocol that serves as an analytic baseline, alongside numerical optimal control calculations that further reduce state preparation time. We find that multiphoton control protocols substantially reduce preparation times for binomial, cat, and Gottesman-Kitaev-Preskill codewords compared to schemes relying on standard linear interactions. Further, we achieve arbitrary control over the oscillator's Hilbert space by combining different multiphoton interaction orders. We also extend these control improvements to the preparation of rotationally symmetric multi-oscillator states. Lastly, numerical simulations using realistic planar superconducting circuit parameters validate the robustness of our scheme against qubit and oscillator decoherence. Our findings can significantly enhance the performance of bosonic codes on planar superconducting hardware, an important ingredient for scalable fault-tolerant quantum computers.

Classical linear optics posits that at sufficiently low intensities, light propagation in dielectric media is governed solely by their linear susceptibilities. Here, we demonstrate a departure from this paradigm in high-Q microresonators, where prolonged photon confinement enables rare quantum electrodynamical (QED) events, mediated by the quantum vacuum, to embed distinctive Raman signatures of the coupled analyte into the resonator's linear transmission spectrum despite their absence from the linear susceptibility. We further show that increasing the amount of adsorbed analyte amplifies these Raman fingerprints well above typical noise floors, rendering them experimentally accessible with state-of-the-art photonic architectures and detection schemes. This novel weak-coupling cavity-QED effect offers unique routes to harness extended photon lifetimes and constrained geometries for leveraging vacuum fluctuations in next-generation photonic technologies for chemical and biological sensing and high-precision optical spectroscopy.

Photonic interconnects are a key technology for scaling up atomic based quantum computers. By facilitating the connection of multiple systems, high-performance modular quantum processing units may be constructed to perform deeper and more useful algorithms. Most previous implementations of photonic interconnects in trapped ions utilize the scheme of preparing a state, exciting it, and collecting single photons from decays of the excited state. State preparation is responsible for the vast majority of the total attempt time, often taking hundreds of nanoseconds to several microseconds. Here, we describe and analyze a novel technique called “electron juggling" to speed up photonic interconnects by reducing the state preparation step substantially. Using a theoretical framework, we illustrate how this scheme can significantly increase remote entanglement generation rates, approaching the atomic physics limit of the attempt rate in trapped-ion photonic interconnects. Our results indicate that this scheme holds the possibility of achieving remote entanglement generation rates of over 1,000 Bell pairs per second.

We apply the recently proposed Sample-based Krylov Quantum Diagonalization (SKQD) method to lattice gauge theories, using the Schwinger model with a $\theta$-term as a benchmark. SKQD approximates the ground state of a Hamiltonian, employing a hybrid quantum-classical approach: (i) constructing a Krylov space from bitstrings sampled from time-evolved quantum states, and (ii) classically diagonalizing the Hamiltonian within this subspace. We study the dependence of the ground-state energy and particle number on the value of the $\theta$-term, accurately capturing the model's phase structure. The algorithm is implemented on trapped-ion and superconducting quantum processors, demonstrating consistent performance across platforms. We show that SKQD substantially reduces the effective Hilbert space, and although the Krylov space dimension still scales exponentially, the slower growth underscores its promise for simulating lattice gauge theories in larger volumes.

Periodically driven quantum systems can function as highly selective parameter filters. We demonstrate this capability in a finite-size, three-qubit system described by the transverse-field Floquet Ising model. In this system, we identify a period-doubling (PD) dynamical phase that exhibits a stark asymmetry in metrological sensitivity to the magnetic field applied on the qubits and to the coupling strength between the qubits. The PD phase originates from $\pi$-pairing, where the initial state exhibits strong overlap with $\pi$-paired Floquet eigenstates, leading to robust period-doubled dynamics and enhanced metrological sensitivity. The analysis of quantum Fisher information reveals that the PD regime significantly enhances precision for estimating the Ising interaction strength while simultaneously suppressing sensitivity to the transverse magnetic field. Conversely, non-PD regimes are optimal for sensing the transverse field. This filtering effect is robust for larger system sizes and is quantifiable using experimentally accessible observables, such as magnetization and two-qubit correlations, via the classical Fisher information. Our work shows that distinct dynamical regimes in finite-size Floquet systems can be harnessed for targeted quantum sensing.

The Krylov subspace expansion is a workhorse method for sparse numerics that has been increasingly explored as source of physical insight into many-body dynamics in recent years. In this work we revisit the venerable Anderson model of localization in dimensions $d=1, 2, 3, 4$ to construct local integrals of motion (LIOM) in Krylov space. These appear as zero eigenvalue edge states of an effective hopping problem in the Krylov superoperator subspace and can be analytically constructed given the Lanczos coefficients. We exploit this idea, focusing on $d=3$, to study the manifestation of the disorder driven Anderson transition in the anatomy of LIOMs. We find that the increasing complexity of the Krylov operators results in a suppression of the fluctuations of the Lanczos coefficients. As such, one can study the phenomenology of the integrals of motion in the disorder averaged Krylov chain. We find edge states localized on vanishing fraction of Krylov space (of dimension $D_K=V^2$ for cubes of volume $V$), both in localized and extended phases. Importantly, in the localized phase, disorder induces powerlaw decaying dimerization in the (Krylov) hopping problem, producing stretched exponential decay of the LIOMs in Krylov space with a stretching exponent $1/2d$. Metallic LIOMs are completely delocalized albeit across only $\propto \sqrt{D_K}$ states. Critical LIOMs exhibit powerlaw decay with an exponent matching the expected value of $0.29$.

Symmetries strongly influence transport properties of quantum many-body systems, and can lead to deviations from the generic case of diffusion. In this work, we study the impact of time-reversal symmetry breaking on the transport and its universal aspects in integrable chiral spin ladders. We observe that the infinite-temperature spin transport is superdiffusive with a dynamical critical exponent z = 3/2 matching the one of the Kardar-Parisi-Zhang (KPZ) universality class, which also lacks the time reversal symmetry. However, we find that fluctuations of the net magnetization transfer deviate from the KPZ predictions. Moreover, the full probability distribution of the associated spin current obeys fluctuation symmetry despite broken time-reversal and space-reflection symmetries. To further investigate the role of conserved quantities, we introduce an integrable quantum circuit that shares the essential symmetries with the chiral ladder, and which exhibits analogous dynamical behaviour in the absence of energy conservation. Our work shows that time-reversal symmetry breaking is compatible with superdiffusion, but insufficient to stabilize the KPZ universality in integrable systems. This suggests that additional fundamental features are missing in order to identify the emergence of such dynamics in quantum matter.

Channels $\mathcal{N}$ that describe open quantum dynamics are inherently irreversible: it is impossible to undo their effect completely, but one can study partial recovery of the information. The Petz recovery map $\hat{\mathcal{N}}_{\gamma}^{(\texttt{P})}$ is a systematic construction that depends only on $\mathcal{N}$ and on a reference state $\gamma$, which will be recovered exactly. If the real input state was different from $\gamma$, the recovery is partial, with a guarantee of near-optimality. Generically, an implementation of the Petz recovery map would look very different from the implementation of the channel. It is natural to study under which conditions the two maps require similar or even identical resources. The noisy forward channel $\mathcal{N}$ is called “tabletop time-reversible” for a given $\gamma$ when the corresponding Petz recovery map is realizable in such a way. First, we study the exact tabletop reversibility (TTR) conditions. We show in particular that a time-sensitive control of an ancilla system is needed. Second, we present the approximate TTR conditions, which do not require such a time-sensitive control. Third, we derive Lindbladian TTR conditions under a random-time collision model.