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Long-range nonstabilizerness can be defined as the amount of nonstabilizerness which cannot be removed by shallow local quantum circuits. In this work, we study long-range nonstabilizerness in the context of many-body quantum physics, a task with possible implications for quantum-state preparation protocols and implementation of quantum-error correcting codes. After presenting a simple argument showing that long-range nonstabilizerness is a generic property of many-body states, we restrict to the class of ground states of gapped local Hamiltonians. We focus on one-dimensional systems and present rigorous results in the context of translation-invariant matrix product states (MPSs). By analyzing the fixed points of the MPS renormalization-group flow, we provide a sufficient condition for long-range nonstabilizerness, which depends entirely on the local MPS tensors. Physically, our condition captures the fact that the mutual information between distant regions of stabilizer fixed points is quantized, and this fact is not changed after applying shallow quantum circuits. We also discuss possible ramifications in the classification of phases of matter and quantum error correction., Comment: 7 pages + 8 pages, 3 figures

We study the dynamics of entanglement asymmetry in random unitary circuits (RUCs). Focusing on a local $U(1)$ charge, we consider symmetric initial states evolved by both local one-dimensional circuits and geometrically non-local RUCs made of two-qudit gates. We compute the entanglement asymmetry of subsystems of arbitrary size, analyzing the relaxation time scales. We show that the entanglement asymmetry of the whole system approaches its stationary value in a time independent of the system size for both local and non-local circuits. For subsystems, we find qualitative differences depending on their size. When the subsystem is larger than half of the full system, the equilibration time scales are again independent of the system size for both local and non-local circuits and the entanglement asymmetry grows monotonically in time. Conversely, when the subsystems are smaller than half of the full system, we show that the entanglement asymmetry is non-monotonic in time and that it equilibrates in a time proportional to the quantum-information scrambling time, providing a physical intuition. As a consequence, the subsystem-equilibration time depends on the locality of interactions, scaling linearly and logarithmically in the system size, respectively, for local and non-local RUCs. Our work confirms the entanglement asymmetry as a versatile and computable probe of symmetry in many-body physics and yields a phenomenological overview of entanglement-asymmetry evolution in typical non-integrable dynamics., Comment: 25 pages, 10 figures

We introduce a nonstabilizerness monotone which we name basis-minimised stabilizerness asymmetry (BMSA). It is based on the notion of $G$-asymmetry, a measure of how much a certain state deviates from being symmetric with respect to a symmetry group $G$. For pure states, we show that the BMSA is a strong monotone for magic-state resource theory, while it can be extended to mixed states via the convex roof construction. We discuss its relation with other magic monotones, first showing that the BMSA coincides with the recently introduced basis-minimized measurement entropy, thereby establishing the strong monotonicity of the latter. Next, we provide inequalities between the BMSA and other nonstabilizerness measures known in the literature. Finally, we present numerical methods to compute the BMSA, highlighting its advantages and drawbacks compared to other nonstabilizerness measures in the context of pure many-body quantum states. We also discuss the importance of additivity and strong monotonicity for measures of nonstabilizerness in many-body physics, motivating the search for additional computable nonstabilizerness monotones., Comment: 19 pages, 3 figures

Quantum circuits make it possible to simulate the continuous-time dynamics of a many-body Hamiltonian by implementing discrete Trotter steps of duration $\tau$. However, when $\tau$ is sufficiently large, the discrete dynamics exhibit qualitative differences compared to the original evolution, potentially displaying novel features and many-body effects. We study an interesting example of this phenomenon, by considering the integrable Trotterization of a prototypical integrable model, the XXZ Heisenberg spin chain. We focus on the well-known bipartition protocol, where two halves of a large system are prepared in different macrostates and suddenly joined together, yielding non-trivial nonequilibrium dynamics. Building upon recent results and adapting the generalized hydrodynamics (GHD) of integrable models, we develop an exact large-scale description of an explicit one-dimensional quantum-circuit setting, where the input left and right qubits are initialized in two distinct product states. We explore the phenomenology predicted by the GHD equations, which depend on the Trotter step and the gate parameters. In some phases of the parameter space, we show that the quantum-circuit large-scale dynamics is qualitatively different compared to the continuous-time evolution. In particular, we find that a single microscopic defect at the junction, such as the addition of a single qubit, may change the nonequilibrium macrostate appearing at late time., Comment: 31 pages, 5 figures; v4: minor revision

Classical shadows are a versatile tool to probe many-body quantum systems, consisting of a combination of randomised measurements and classical post-processing computations. In a recently introduced version of the protocol, the randomization step is performed via unitary circuits of variable depth $t$, defining the so-called shallow shadows. For sufficiently large $t$, this approach allows one to get around the use of non-local unitaries to probe global properties such as the fidelity with respect to a target state or the purity. Still, shallow shadows involve the inversion of a many-body map, the measurement channel, which requires non-trivial computations in the post-processing step, thus limiting its applicability when the number of qubits $N$ is large. In this work, we put forward a simple approximate post-processing scheme where the infinite-depth inverse channel is applied to the finite-depth classical shadows and study its performance for fidelity and purity estimation. The scheme allows for different circuit connectivity, as we illustrate for geometrically local circuits in one and two spatial dimensions and geometrically non-local circuits made of two-qubit gates. For the fidelity, we find that the resulting estimator coincides with a known linear cross-entropy, achieving an arbitrary small approximation error $\delta$ at depth $t=O(\log (N/\delta))$ (independent of the circuit connectivity). For the purity, we show that the estimator becomes accurate at a depth $O(N)$. In addition, at those depths, the variances of both the fidelity and purity estimators display the same scaling with $N$ as in the case of global random unitaries. We establish these bounds by analytic arguments and extensive numerical computations in several cases of interest. Our work extends the applicability of shallow shadows to large system sizes and general circuit connectivity., Comment: 21 pages, 8 figures; v2: minor revision and references added

We study measurement-induced phases of free fermion systems with U(1) symmetry. Following a recent approach developed for Majorana chains, we derive a field theory description for the purity and bipartite entanglement at large space and time scales. We focus on a multi-flavor one-dimensional chain with random complex hoppings and continuous monitoring of the local fermion density. By means of the replica trick, and using the number of flavors as a large parameter controlling our approximations, we derive an effective field theory made up of a SU(N) non-linear sigma model (NL$\sigma$M) coupled to fluctuating hydrodynamics. Contrary to the case of non-interacting Majorana fermions, displaying no U(1) symmetry, we find that the bipartite entanglement entropy satisfies an area law for all monitoring rates, but with a nontrivial scaling of entanglement when the correlation length is large. We provide numerical evidence supporting our claims. We briefly show how imposing a reality condition on the hoppings can change the NL$\sigma$M and also discuss higher dimensional generalizations., Comment: 23 pages, 3 figures; v3: minor revision

Autonomous vehicles rely on camera, LiDAR, and radar sensors to navigate the environment. Adverse weather conditions like snow, rain, and fog are known to be problematic for both camera and LiDAR-based perception systems. Currently, it is difficult to evaluate the performance of these methods due to the lack of publicly available datasets containing multimodal labeled data. To address this limitation, we propose the SemanticSpray++ dataset, which provides labels for camera, LiDAR, and radar data of highway-like scenarios in wet surface conditions. In particular, we provide 2D bounding boxes for the camera image, 3D bounding boxes for the LiDAR point cloud, and semantic labels for the radar targets. By labeling all three sensor modalities, the SemanticSpray++ dataset offers a comprehensive test bed for analyzing the performance of different perception methods when vehicles travel on wet surface conditions. Together with comprehensive label statistics, we also evaluate multiple baseline methods across different tasks and analyze their performances. The dataset will be available at https://semantic-spray-dataset.github.io ., Comment: Accepted at IEEE Intelligent Vehicles Symposium (IV 2024)

Adverse weather conditions can severely affect the performance of LiDAR sensors by introducing unwanted noise in the measurements. Therefore, differentiating between noise and valid points is crucial for the reliable use of these sensors. Current approaches for detecting adverse weather points require large amounts of labeled data, which can be difficult and expensive to obtain. This paper proposes a label-efficient approach to segment LiDAR point clouds in adverse weather. We develop a framework that uses few-shot semantic segmentation to learn to segment adverse weather points from only a few labeled examples. Then, we use a semi-supervised learning approach to generate pseudo-labels for unlabelled point clouds, significantly increasing the amount of training data without requiring any additional labeling. We also integrate good weather data in our training pipeline, allowing for high performance in both good and adverse weather conditions. Results on real and synthetic datasets show that our method performs well in detecting snow, fog, and spray. Furthermore, we achieve competitive performance against fully supervised methods while using only a fraction of labeled data., Comment: Accepted for publication in IEEE Robotics and Automation Letters (RA-L)

Goldilocks quantum cellular automata (QCA) have been simulated on quantum hardware and produce emergent small-world correlation networks. In Goldilocks QCA, a single-qubit unitary is applied to each qubit in a one-dimensional chain subject to a balance constraint: a qubit is updated if its neighbors are in opposite basis states. Here, we prove that a subclass of Goldilocks QCA -- including the one implemented experimentally -- map onto free fermions and therefore can be classically simulated efficiently. We support this claim with two independent proofs, one involving a Jordan--Wigner transformation and one mapping the integrable six-vertex model to QCA. We compute local conserved quantities of these QCA and predict experimentally measurable expectation values. These calculations can be applied to test large digital quantum computers against known solutions. In contrast, typical Goldilocks QCA have equilibration properties and quasienergy-level statistics that suggest nonintegrability. Still, the latter QCA conserve one quantity useful for error mitigation. Our work provides a parametric quantum circuit with tunable integrability properties with which to test quantum hardware., Comment: 7 pages (3 figures) + appendices (8 pages)

We introduce protocols to prepare many-body quantum states with quantum circuits assisted by local operations and classical communication. We show that by lifting the requirement of exact preparation, one can substantially save resources. In particular, the so-called $W$ and, more generally, Dicke states require a circuit depth and number of ancillas per site that are independent of the system size. As a byproduct of our work, we introduce an efficient scheme to implement certain non-local, non-Clifford unitary operators. We also discuss how similar ideas may be applied in the preparation of eigenstates of well-known spin models, both free and interacting., Comment: Published version

It is a classic result that certain interacting integrable spin chains host robust edge modes known as strong zero modes (SZMs). In this work, we extend this result to the Floquet setting of local quantum circuits, focusing on a prototypical model providing an integrable Trotterization for the evolution of the XXZ Heisenberg spin chain. By exploiting the algebraic structures of integrability, we show that an exact SZM operator can be constructed for these integrable quantum circuits in certain regions of parameter space. Our construction, which recovers a well-known result by Paul Fendley in the continuous-time limit, relies on a set of commuting transfer matrices known from integrability, and allows us to easily prove important properties of the SZM, including normalizabilty. Our approach is different from previous methods and could be of independent interest even in the Hamiltonian setting. Our predictions, which are corroborated by numerical simulations of infinite-temperature autocorrelation functions, are potentially interesting for implementations of the XXZ quantum circuit on available quantum platforms., Comment: 7 pages + 11 pages of Supplementary Material

Hawking's discovery that black holes can evaporate through radiation emission has posed a number of questions that with time became fundamental hallmarks for a quantum theory of gravity. The most famous one is likely the information paradox, which finds an elegant explanation in the Page argument suggesting that a black hole and its radiation can be effectively represented by a random state of qubits. Leveraging the same assumption, we ponder the extent to which a black hole may display emergent symmetries, employing the entanglement asymmetry as a modern, information-based indicator of symmetry breaking. We find that for a random state devoid of any symmetry, a $U(1)$ symmetry emerges and it is exact in the thermodynamic limit before the Page time. At the Page time, the entanglement asymmetry shows a finite jump to a large value. Our findings imply that the emitted radiation is symmetric up to the Page time and then undergoes a sharp transition. Conversely the black hole is symmetric only after the Page time., Comment: 6 pages, 3 figures. Comments added. Final version published in Phys. Rev. D

Estimating global properties of many-body quantum systems such as entropy or bipartite entanglement is a notoriously difficult task, typically requiring a number of measurements or classical post-processing resources growing exponentially in the system size. In this work, we address the problem of estimating global entropies and mixed-state entanglement via partial-transposed (PT) moments, and show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite. Focusing on one-dimensional systems, we identify a set of approximate factorization conditions (AFCs) on the system density matrix which allow us to reconstruct entropies and PT moments from information on local subsystems. This yields a simple and efficient strategy for entropy and entanglement estimation. Our method could be implemented in different ways, depending on how information on local subsystems is extracted. Focusing on randomized measurements (RMs), providing a practical and common measurement scheme, we prove that our protocol only requires polynomially-many measurements and post-processing operations, assuming that the state to be measured satisfies the AFCs. We prove that the AFCs hold for finite-depth quantum-circuit states and translation-invariant matrix-product density operators, and provide numerical evidence that they are satisfied in more general, physically-interesting cases, including thermal states of local Hamiltonians. We argue that our method could be practically useful to detect bipartite mixed-state entanglement for large numbers of qubits available in today's quantum platforms., Comment: 30 pages, 10 figures; v2: references added and general revision

The unique properties of radar sensors, such as their robustness to adverse weather conditions, make them an important part of the environment perception system of autonomous vehicles. One of the first steps during the processing of radar point clouds is often the detection of clutter, i.e. erroneous points that do not correspond to real objects. Another common objective is the semantic segmentation of moving road users. These two problems are handled strictly separate from each other in literature. The employed neural networks are always focused entirely on only one of the tasks. In contrast to this, we examine ways to solve both tasks at the same time with a single jointly used model. In addition to a new augmented multi-head architecture, we also devise a method to represent a network's predictions for the two tasks with only one output value. This novel approach allows us to solve the tasks simultaneously with the same inference time as a conventional task-specific model. In an extensive evaluation, we show that our setup is highly effective and outperforms every existing network for semantic segmentation on the RadarScenes dataset., Comment: Published at IEEE International Conference on Intelligent Transportation Systems (ITSC), Bilbao, ESP, 2023

LiDAR-based 3D object detectors have achieved unprecedented speed and accuracy in autonomous driving applications. However, similar to other neural networks, they are often biased toward high-confidence predictions or return detections where no real object is present. These types of detections can lead to a less reliable environment perception, severely affecting the functionality and safety of autonomous vehicles. We address this problem by proposing LS-VOS, a framework for identifying outliers in 3D object detections. Our approach builds on the idea of Virtual Outlier Synthesis (VOS), which incorporates outlier knowledge during training, enabling the model to learn more compact decision boundaries. In particular, we propose a new synthesis approach that relies on the latent space of an auto-encoder network to generate outlier features with a parametrizable degree of similarity to in-distribution features. In extensive experiments, we show that our approach improves the outlier detection capabilities of a state-of-the-art object detector while maintaining high 3D object detection performance., Comment: Published at IEEE International Conference on Intelligent Transportation Systems ITSC 2023

LiDAR sensors are used in autonomous driving applications to accurately perceive the environment. However, they are affected by adverse weather conditions such as snow, fog, and rain. These everyday phenomena introduce unwanted noise into the measurements, severely degrading the performance of LiDAR-based perception systems. In this work, we propose a framework for improving the robustness of LiDAR-based 3D object detectors against road spray. Our approach uses a state-of-the-art adverse weather detection network to filter out spray from the LiDAR point cloud, which is then used as input for the object detector. In this way, the detected objects are less affected by the adverse weather in the scene, resulting in a more accurate perception of the environment. In addition to adverse weather filtering, we explore the use of radar targets to further filter false positive detections. Tests on real-world data show that our approach improves the robustness to road spray of several popular 3D object detectors., Comment: Published at IEEE International Conference on Intelligent Transportation Systems ITSC 2023

We consider a one-dimensional system of non-interacting fermions featuring both boundary driving and continuous monitoring of the bulk particle density. Due to the measurements, the expectation values of the local density and current operators are random variables whose average behavior is described by a well studied Lindblad master equation. By means of exact numerical computations, we go beyond the averaged dynamics and study their full probability distribution functions, focusing on the late-time stationary regime. We find that, contrary to the averaged values, the spatial profiles of the median density and current are non-trivial, exhibiting qualitative differences as a function of the monitoring strength. At weak monitoring, the medians are close to the means, displaying diffusive spatial profiles. At strong monitoring, we find that the median density and current develop a domain-wall and single-peak profile, respectively, which are suggestive of a Zeno-like localization in typical quantum trajectories. While we are not able to identify a sharp phase transition as a function of the monitoring rate, our work highlights the usefulness of characterizing typical behavior beyond the averaged values in the context of monitored many-body quantum dynamics., Comment: 10 pages, 6 figures; v3: minor revision

Autonomous vehicles rely on LiDAR sensors to perceive the environment. Adverse weather conditions like rain, snow, and fog negatively affect these sensors, reducing their reliability by introducing unwanted noise in the measurements. In this work, we tackle this problem by proposing a novel approach for detecting adverse weather effects in LiDAR data. We reformulate this problem as an outlier detection task and use an energy-based framework to detect outliers in point clouds. More specifically, our method learns to associate low energy scores with inlier points and high energy scores with outliers allowing for robust detection of adverse weather effects. In extensive experiments, we show that our method performs better in adverse weather detection and has higher robustness to unseen weather effects than previous state-of-the-art methods. Furthermore, we show how our method can be used to perform simultaneous outlier detection and semantic segmentation. Finally, to help expand the research field of LiDAR perception in adverse weather, we release the SemanticSpray dataset, which contains labeled vehicle spray data in highway-like scenarios. The dataset is available at https://semantic-spray-dataset.github.io ., Comment: Accepted for publication in IEEE Robotics and Automation Letters (RA-L)

We study different aspects of the stabilizer entropies (SEs) and compare them against known nonstabilizerness monotones such as the min-relative entropy and the robustness of magic. First, by means of explicit examples, we show that, for R\'enyi index $0\leq n<2$, the SEs are not monotones with respect to stabilizer protocols which include computational-basis measurements, not even when restricting to pure states (while the question remains open for $n\geq 2$). Next, we show that, for any R\'enyi index, the SEs do not satisfy a strong monotonicity condition with respect to computational-basis measurements. We further study SEs in different classes of many-body states. We compare the SEs with other measures, either proving or providing numerical evidence for inequalities between them. Finally, we discuss exact or efficient tensor-network numerical methods to compute SEs of matrix-product states (MPSs) for large numbers of qubits. In addition to previously developed exact methods to compute the R\'enyi SEs, we also put forward a scheme based on perfect MPS sampling, allowing us to compute efficiently the von Neumann SE for large bond dimensions., Comment: 14 pages, 5 figures

Radar sensors employed for environment perception, e.g. in autonomous vehicles, output a lot of unwanted clutter. These points, for which no corresponding real objects exist, are a major source of errors in following processing steps like object detection or tracking. We therefore present two novel neural network setups for identifying clutter. The input data, network architectures and training configuration are adjusted specifically for this task. Special attention is paid to the downsampling of point clouds composed of multiple sensor scans. In an extensive evaluation, the new setups display substantially better performance than existing approaches. Because there is no suitable public data set in which clutter is annotated, we design a method to automatically generate the respective labels. By applying it to existing data with object annotations and releasing its code, we effectively create the first freely available radar clutter data set representing real-world driving scenarios. Code and instructions are accessible at www.github.com/kopp-j/clutter-ds., Comment: To be published in IEEE International Conference on Robotics and Automation (ICRA), London, UK, 2023

We derive field theory descriptions for measurement-induced phase transitions in free fermion systems. We focus on a multi-flavor Majorana chain, undergoing Hamiltonian evolution with continuous monitoring of local fermion parity operators. Using the replica trick, we map the dynamics to the imaginary time evolution of an effective spin chain, and use the number of flavors as a large parameter for a controlled derivation of the effective field theory. This is a nonlinear sigma model for an orthogonal $N\times N$ matrix, in the replica limit $N\to 1$. (On a boundary of the phase diagram, another sigma model with higher symmetry applies.) Together with known results for the renormalization-group beta function, this derivation establishes the existence of stable phases -- nontrivially entangled and disentangled respectively -- in the physically-relevant replica limit $N\to 1$. In the nontrivial phase, an asymptotically exact calculation shows that the bipartite entanglement entropy for a system of size $L$ scales as $(\log L)^2$, in contrast to findings in previously-studied models. Varying the relative strength of Hamiltonian evolution and monitoring, as well as a dimerization parameter, the model's phase diagram contains transitions out of the nontrivial phase, which we map to vortex-unbinding transitions in the sigma model, and also contains separate critical points on the measurement-only axis. We highlight the close analogies as well as the differences with the replica approach to Anderson transitions in disordered systems., Comment: Version accepted for publication; added discussion of the phase diagram for more than one flavor. 33 pages, 9 figures

We study quantum circuits consisting of unitary gates, projective measurements, and control operations that steer the system towards a pure absorbing state. Two types of phase transition occur as the rate of these control operations is increased: a measurement-induced entanglement transition, and a directed percolation transition into the absorbing state (taken here to be a product state). In this work we show analytically that these transitions are generically distinct, with the quantum trajectories becoming disentangled before the absorbing state transition is reached, and we analyze their critical properties. We introduce a simple class of models where the measurements in each quantum trajectory define an Effective Tensor Network (ETN) -- a subgraph of the initial spacetime graph where nontrivial time evolution takes place. By analyzing the entanglement properties of the ETN, we show that the entanglement and absorbing-state transitions coincide only in the limit of infinite local Hilbert-space dimension. Focusing on a Clifford model which allows numerical simulations for large system sizes, we verify our predictions and study the finite-size crossover between the two transitions at large local Hilbert space dimension. We give evidence that the entanglement transition is governed by the same fixed point as in hybrid circuits without feedback., Comment: 18 pages, 9 figures; v2: Appendix added, minor revision

The Trotter-Suzuki decomposition is a promising avenue for digital quantum simulation (DQS), approximating continuous-time dynamics by discrete Trotter steps of duration $\tau$. Recent work suggested that DQS is typically characterized by a sharp Trotter transition: when $\tau$ is increased beyond a threshold value, approximation errors become uncontrolled at large times due to the onset of quantum chaos. Here we contrast this picture with the case of \emph{integrable} DQS. We focus on a simple quench from a spin-wave state in the prototypical XXZ Heisenberg spin chain, and study its integrable Trotterized evolution as a function of $\tau$. Due to its exact local conservation laws, the system does not heat up to infinite temperature and the late-time properties of the dynamics are captured by a discrete Generalized Gibbs Ensemble (dGGE). By means of exact calculations we find that, for small $\tau$, the dGGE depends analytically on the Trotter step, implying that discretization errors remain bounded even at infinite times. Conversely, the dGGE changes abruptly at a threshold value $\tau_{\rm th}$, signaling a novel type of Trotter transition. We show that the latter can be detected locally, as it is associated with the appearance of a non-zero staggered magnetization with a subtle dependence on $\tau$. We highlight the differences between continuous and discrete GGEs, suggesting the latter as novel interesting nonequilibrium states exclusive to digital platforms., Comment: 7+14 pages, 3+5 figures; v2: minor revision, appendix added

We study non-homogeneous quantum quenches in a one-dimensional gas of repulsive spin-$1/2$ fermions, as described by the integrable Yang-Gaudin model. By means of generalized hydrodynamics (GHD), we analyze in detail the real-time evolution following a sudden change of the confining potential. We consider in particular release protocols and trap quenches, including a version of the quantum Newton's cradle. At zero temperature, we employ a simplified phase-space hydrodynamic picture to characterize the dynamics of the particle- and spin-density profiles. Away from zero temperatures, we perform a thorough numerical study of the GHD equations, and provide quantitative predictions for different values of the temperature, external magnetic field, and chemical potential. We highlight the qualitative features arising due to the multi-component nature of the elementary excitations, discussing in particular effects of spin-charge separation and dynamical polarization., Comment: 13 pages, 13 figures; v2:minor changes

In non-interacting isolated quantum systems out of equilibrium, local subsystems typically relax to non-thermal stationary states. In the standard framework, information on the rest of the system is discarded, and such states are described by a Generalized Gibbs Ensemble (GGE), maximizing the entropy while respecting the constraints imposed by the local conservation laws. Here we show that the latter also completely characterize a recently introduced projected ensemble (PE), constructed by performing projective measurements on the rest of the system and recording the outcomes. By focusing on the time evolution of fermionic Gaussian states in a tight-binding chain, we put forward a random ensemble constructed out of the local conservation laws, which we call deep GGE (dGGE). For infinite-temperature initial states, we show that the dGGE coincides with a universal Haar random ensemble on the manifold of Gaussian states. For both infinite and finite temperatures, we use a Monte Carlo approach to test numerically the predictions of the dGGE against the PE. We study in particular the $k$-moments of the state covariance matrix and the entanglement entropy, finding excellent agreement. Our work provides a first step towards a systematic characterization of projected ensembles beyond the case of chaotic systems and infinite temperatures., Comment: 13 pages, 4 figures; v2: minor revision

Nonstabilizerness, also known as magic, quantifies the number of non-Clifford operations needed in order to prepare a quantum state. As typical measures either involve minimization procedures or a computational cost exponential in the number of qubits $N$, it is notoriously hard to characterize for many-body states. In this work, we show that nonstabilizerness, as quantified by the recently introduced Stabilizer R\'enyi Entropies (SREs), can be computed efficiently for matrix product states (MPSs). Specifically, given an MPS of bond dimension $\chi$ and integer R\'enyi index $n>1$, we show that the SRE can be expressed in terms of the norm of an MPS with bond dimension $\chi^{2n}$. For translation-invariant states, this allows us to extract it from a single tensor, the transfer matrix, while for generic MPSs this construction yields a computational cost linear in $N$ and polynomial in $\chi$. We exploit this observation to revisit the study of ground-state nonstabilizerness in the quantum Ising chain, providing accurate numerical results up to large system sizes. We analyze the SRE near criticality and investigate its dependence on the local computational basis, showing that it is in general not maximal at the critical point., Comment: 11 pages, 7 figures

LiDAR sensors used in autonomous driving applications are negatively affected by adverse weather conditions. One common, but understudied effect, is the condensation of vehicle gas exhaust in cold weather. This everyday phenomenon can severely impact the quality of LiDAR measurements, resulting in a less accurate environment perception by creating artifacts like ghost object detections. In the literature, the semantic segmentation of adverse weather effects like rain and fog is achieved using learning-based approaches. However, such methods require large sets of labeled data, which can be extremely expensive and laborious to get. We address this problem by presenting a two-step approach for the detection of condensed vehicle gas exhaust. First, we identify for each vehicle in a scene its emission area and detect gas exhaust if present. Then, isolated clouds are detected by modeling through time the regions of space where gas exhaust is likely to be present. We test our method on real urban data, showing that our approach can reliably detect gas exhaust in different scenarios, making it appealing for offline pre-labeling and online applications such as ghost object detection., Comment: Accepted for ITSC2022

Given a statistical ensemble of quantum states, the corresponding Page curve quantifies the average entanglement entropy associated with each possible spatial bipartition of the system. In this work, we study a natural extension in the presence of a conservation law and introduce the symmetry-resolved Page curves, characterizing average bipartite symmetry-resolved entanglement entropies. We derive explicit analytic formulae for two important statistical ensembles with a $U(1)$-symmetry: Haar-random pure states and random fermionic Gaussian states. In the former case, the symmetry-resolved Page curves can be obtained in an elementary way from the knowledge of the standard one. This is not true for random fermionic Gaussian states. In this case, we derive an analytic result in the thermodynamic limit based on a combination of techniques from random-matrix and large-deviation theories. We test our predictions against numerical calculations and discuss the sub-leading finite-size corrections., Comment: 13 pages, 4 Figures

Adverse weather conditions can negatively affect LiDAR-based object detectors. In this work, we focus on the phenomenon of vehicle gas exhaust condensation in cold weather conditions. This everyday effect can influence the estimation of object sizes, orientations and introduce ghost object detections, compromising the reliability of the state of the art object detectors. We propose to solve this problem by using data augmentation and a novel training loss term. To effectively train deep neural networks, a large set of labeled data is needed. In case of adverse weather conditions, this process can be extremely laborious and expensive. We address this issue in two steps: First, we present a gas exhaust data generation method based on 3D surface reconstruction and sampling which allows us to generate large sets of gas exhaust clouds from a small pool of labeled data. Second, we introduce a point cloud augmentation process that can be used to add gas exhaust to datasets recorded in good weather conditions. Finally, we formulate a new training loss term that leverages the augmented point cloud to increase object detection robustness by penalizing predictions that include noise. In contrast to other works, our method can be used with both grid-based and point-based detectors. Moreover, since our approach does not require any network architecture changes, inference times remain unchanged. Experimental results on real data show that our proposed method greatly increases robustness to gas exhaust and noisy data., Comment: Oral

We investigate entanglement dynamics in continuously monitored open quantum systems featuring current-carrying non-equilibrium states. We focus on a prototypical one-dimensional model of boundary-driven non-interacting fermions with monitoring of the local density, whose average Lindblad dynamics features a well-studied ballistic to diffusive crossover in transport. Here we analyze the dynamics of the fermionic negativity, mutual information, and purity along different quantum trajectories. We show that monitoring this boundary-driven system enhances its entanglement negativity at long times, which otherwise decays to zero in absence of measurements. This result is in contrast with the case of unitary evolution where monitoring suppresses entanglement production. For small values of $\gamma$, the stationary-state negativity shows a logarithmic scaling with system size, transitioning to an area-law scaling as $\gamma$ is increased beyond a critical value. Similar critical behavior is found in the mutual information, while the late-time purity shows no apparent signature of a transition, being $O(1)$ for all values of $\gamma$. Our work unveils the double role of weak monitoring in current-driven open quantum systems, simultaneously damping transport and enhancing entanglement., Comment: 10 pages, comments are welcome

We develop a general approach to compute the symmetry-resolved R\'enyi and von Neumann entanglement entropies (SREE) of thermodynamic macrostates in interacting integrable systems. Our method is based on a combination of the thermodynamic Bethe ansatz and the G\"artner-Ellis theorem from large deviation theory. We derive an explicit simple formula for the von Neumann SREE, which we show to coincide with the thermodynamic Yang-Yang entropy of an effective macrostate determined by the charge sector. Focusing on the XXZ Heisenberg spin chain, we test our result against iTEBD calculations for thermal states, finding good agreement. As an application, we provide analytic predictions for the asymptotic value of the SREE following a quantum quench., Comment: 12 pages, 2 figures; v2: minor revision

In quantum many-body dynamics admitting a description in terms of non-interacting quasiparticles, the Feynman-Vernon influence matrix (IM), encoding the effect of the system on the evolution of its local subsystems, can be analyzed exactly. For discrete dynamics, the temporal entanglement (TE) of the corresponding IM satisfies an area law, suggesting the possibility of an efficient representation of the IM in terms of matrix-product states. A natural question is whether and how integrable interactions, which preserve stable quasiparticles, affect the behavior of the TE. While a simple semiclassical picture suggests a sublinear growth in time, one can wonder whether interactions may lead to violations of the area law. We address this problem by analyzing quantum quenches in a family of discrete integrable dynamics corresponding to the real-time Trotterization of the interacting XXZ Heisenberg model. By means of an analytical solution at the dual-unitary point and numerical calculations for generic values of the system parameters, we provide evidence that, away from the non-interacting limit, the TE displays a logarithmic growth in time, thus violating the area law. Our findings highlight the non-trivial role of interactions, and raise interesting questions on the possibility to efficiently simulate the local dynamics of interacting integrable systems.

We study the entanglement dynamics of thermofield double (TFD) states in integrable spin chains and quantum field theories. We show that, for a natural choice of the Hamiltonian eigenbasis, the TFD evolution may be interpreted as a quantum quench from an initial state which is low-entangled in the real-space representation and displays a simple quasiparticle structure. Based on a semiclassical picture analogous to the one developed for standard quantum quenches, we conjecture a formula for the entanglement dynamics, which is valid for both discrete and continuous integrable field theories, and expected to be exact in the scaling limit of large space and time scales. We test our conjecture in two prototypical examples of integrable spin chains, where numerical tests are possible. First, in the XY-model, we compare our predictions with exact results obtained by mapping the system to free fermions, finding excellent agreement. Second, we test our conjecture in the interacting XXZ Heisenberg model, against numerical iTEBD calculations. For the latter, we generally find good agreement, although, for some range of the system parameters and within the accessible simulation times, some small discrepancies are visible, which we attribute to finite-time effects., Comment: 19 pages, 6 figures; v2: minor revision

In two-dimensional Floquet systems, many-body localized dynamics in the bulk may give rise to a chaotic evolution at the one-dimensional edges that is characterized by a nonzero chiral topological index. Such anomalous dynamics is qualitatively different from local-Hamiltonian evolution. Here we show how the presence of a nonzero index affects entanglement generation and the spreading of local operators, focusing on the coarse-grained description of generic systems. We tackle this problem by analyzing exactly solvable models of random quantum cellular automata (QCA) which generalize random circuits. We find that a nonzero index leads to asymmetric butterfly velocities with different diffusive broadening of the light cones, and to a modification of the order relations between the butterfly and entanglement velocities. We propose that these results can be understood via a generalization of the recently-introduced entanglement membrane theory, by allowing for a spacetime entropy current, which in the case of a generic QCA is fixed by the index. We work out the implications of this current on the entanglement "membrane tension" and show that the results for random QCA are recovered by identifying the topological index with a background velocity for the coarse-grained entanglement dynamics., Comment: 6 + 11 pages, 4 + 6 figures, published version

Automotive radar sensors output a lot of unwanted clutter or ghost detections, whose position and velocity do not correspond to any real object in the sensor's field of view. This poses a substantial challenge for environment perception methods like object detection or tracking. Especially problematic are clutter detections that occur in groups or at similar locations in multiple consecutive measurements. In this paper, a new algorithm for identifying such erroneous detections is presented. It is mainly based on the modeling of specific commonly occurring wave propagation paths that lead to clutter. In particular, the three effects explicitly covered are reflections at the underbody of a car or truck, signals traveling back and forth between the vehicle on which the sensor is mounted and another object, and multipath propagation via specular reflection. The latter often occurs near guardrails, concrete walls or similar reflective surfaces. Each of these effects is described both theoretically and regarding a method for identifying the corresponding clutter detections. Identification is done by analyzing detections generated from a single sensor measurement only. The final algorithm is evaluated on recordings of real extra-urban traffic. For labeling, a semi-automatic process is employed. The results are promising, both in terms of performance and regarding the very low execution time. Typically, a large part of clutter is found, while only a small ratio of detections corresponding to real objects are falsely classified by the algorithm., Comment: To be published in IEEE 24th International Conference on Intelligent Transportation Systems (ITSC), Indianapolis, USA, 2021

We revisit early suggestions to observe spin-charge separation (SCS) in cold-atom settings {in the time domain} by studying one-dimensional repulsive Fermi gases in a harmonic potential, where pulse perturbations are initially created at the center of the trap. We analyze the subsequent evolution using generalized hydrodynamics (GHD), which provides an exact description, at large space-time scales, for arbitrary temperature $T$, particle density, and interactions. At $T=0$ and vanishing magnetic field, we find that, after a nontrivial transient regime, spin and charge dynamically decouple up to perturbatively small corrections which we quantify. In this limit, our results can be understood based on a simple phase-space hydrodynamic picture. At finite temperature, we solve numerically the GHD equations, showing that for low $T>0$ effects of SCS survive and {characterize} explicitly the value of $T$ for which the two distinguishable excitations melt., Comment: 12 pages, 7 figures; v2: modified layout; corrected some typos

We give a pedagogical introduction to the Generalized Hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for generic time-dependent correlation functions and entanglement evolution, and discuss in detail the range of applicability of the theory. Finally, we present some open questions and suggest perspectives on possible future directions., Comment: 46 pages, 13 figures. To appear in JSTAT special issue "Emergent Hydrodynamics in Integrable Many-body Systems"; v2 minor revision. As appears in JSTAT special issue "Emergent Hydrodynamics in Integrable Many-body Systems"

We introduce deterministic state-transformation protocols between many-body quantum states which can be implemented by low-depth Quantum Circuits (QC) followed by Local Operations and Classical Communication (LOCC). We show that this gives rise to a classification of phases in which topologically-ordered states or other paradigmatic entangled states become trivial. We also investigate how the set of unitary operations is enhanced by LOCC in this scenario, allowing one to perform certain large-depth QC in terms of low-depth ones., Comment: 6+5 pages, no figures; v4: minor revision, references added

We study the probability distribution of entanglement in the Quantum Symmetric Simple Exclusion Process, a model of fermions hopping with random Brownian amplitudes between neighboring sites. We consider a protocol where the system is initialized in a pure product state of $M$ particles, and focus on the late-time distribution of R\'enyi-$q$ entropies for a subsystem of size $\ell$. By means of a Coulomb gas approach from Random Matrix Theory, we compute analytically the large-deviation function of the entropy in the thermodynamic limit. For $q>1$, we show that, depending on the value of the ratio $\ell/M$, the entropy distribution displays either two or three distinct regimes, ranging from low- to high-entanglement. These are connected by points where the probability density features singularities in its third derivative, which can be understood in terms of a transition in the corresponding charge density of the Coulomb gas. Our analytic results are supported by numerical Monte Carlo simulations., Comment: 6 pages, 3 figures; v2: minor revision

We study the out-of-equilibrium dynamics of the quantum cellular automaton known as "Rule 54". For a class of low-entangled initial states, we provide an analytic description of the effect of the global evolution on finite subsystems in terms of simple quantum channels, which gives access to the full thermalization dynamics at the microscopic level. As an example, we provide analytic formulae for the evolution of local observables and R\'enyi entropies. We show that, in contrast to other known examples of exactly solvable quantum circuits, Rule 54 does not behave as a simple Markovian bath on its own parts, and displays typical non-equilibrium features of interacting integrable many-body quantum systems such as finite relaxation rate and interaction-induced dressing effects. Our study provides a rare example where the full thermalization dynamics can be solved exactly at the microscopic level., Comment: 9 (6+3) pages; v2 as appears in Phys. Rev. Lett

A fundamental result in modern quantum chaos theory is the Maldacena-Shenker-Stanford upper bound on the growth of out-of-time-order correlators, whose infinite-temperature limit is related to the operator-space entanglement entropy of the evolution operator. Here we show that, for one-dimensional quantum cellular automata (QCA), there exists a lower bound on quantum chaos quantified by such entanglement entropy. This lower bound is equal to twice the index of the QCA, which is a topological invariant that measures the chirality of information flow, and holds for all the R\'enyi entropies, with its strongest R\'enyi-$\infty$ version being tight. The rigorous bound rules out the possibility of any sublinear entanglement growth behavior, showing in particular that many-body localization is forbidden for unitary evolutions displaying nonzero index. Since the R\'enyi entropy is measurable, our findings have direct experimental relevance. Our result is robust against exponential tails which naturally appear in quantum dynamics generated by local Hamiltonians., Comment: 6 + 6 pages, 3 + 4 figures

Autonomous vehicles need precise knowledge on dynamic objects in their surroundings. Especially in urban areas with many objects and possible occlusions, an infrastructure system based on a multi-sensor setup can provide the required environment model for the vehicles. Previously, we have published a concept of object reference points (e.g. the corners of an object), which allows for generic sensor "plug and play" interfaces and relatively cheap sensors. This paper describes a novel method to additionally incorporate multiple hypotheses for fusing the measurements of the object reference points using an extension to the previously presented Labeled Multi-Bernoulli (LMB) filter. In contrast to the previous work, this approach improves the tracking quality in the cases where the correct association of the measurement and the object reference point is unknown. Furthermore, this paper identifies options based on physical models to sort out inconsistent and unfeasible associations at an early stage in order to keep the method computationally tractable for real-time applications. The method is evaluated on simulations as well as on real scenarios. In comparison to comparable methods, the proposed approach shows a considerable performance increase, especially the number of non-continuous tracks is decreased significantly.