We consider the distribution of secret keys, both in a bipartite and a multipartite (conference) setting, via a quantum network and establish a framework to obtain bounds on the achievable rates. We show that any multipartite private state—the output of a protocol distilling secret key among the trusted parties—has to be genuinely multipartite entangled. In order to describe general network settings, we introduce a multiplex quantum channel, which links an arbitrary number of parties where each party can take the role of sender only, receiver only, or both sender and receiver. We define asymptotic and nonasymptotic local quantum operations and classical communication-assisted secret-key-agreement (SKA) capacities for multiplex quantum channels and provide strong and weak converse bounds. The structure of the protocols we consider, manifested by an adaptive strategy of secret-key and entanglement [Greenberger–Horne–Zeilinger (GHZ) state] distillation over an arbitrary multiplex quantum channel, is generic. As a result, our approach also allows us to study the performance of quantum key repeaters and measurement-device-independent quantum key distribution (MDI-QKD) setups. For teleportation-covariant multiplex quantum channels, we get upper bounds on the SKA capacities in terms of the entanglement measures of their Choi states. We also obtain bounds on the rates at which secret key and GHZ states can be distilled from a finite number of copies of an arbitrary multipartite quantum state. We are able to determine the capacities for MDI-QKD setups and rates of GHZ-state distillation for some cases of interest.

The Fermi-polaron problem of a mobile impurity interacting with fermionic medium emerges in various contexts, ranging from the foundations of Landau’s Fermi-liquid theory to electron-exciton interaction in semiconductors, to unusual properties of high-temperature superconductors. While classically the medium provides only a dissipative environment to the impurity, the quantum picture of polaronic dressing is more intricate and arises from the interplay of few- and many-body aspects of the problem. The conventional expectation for the dynamics of Fermi polarons is that it is dissipative in character, and any excess energy is rapidly emitted away from the impurity as particle-hole excitations. Here we report a strikingly different type of polaron dynamics in a one-dimensional system of the impurity interacting repulsively with the fermions. When the total momentum of the system equals the Fermi momentum, there emerges a sharp collective mode corresponding to long-lived oscillations of the polaronic cloud surrounding the impurity. This mode can be observed experimentally with ultracold atoms using Ramsey interferometry and radio-frequency spectroscopy.

Order parameters are key to our understanding of phases of matter. Not only do they allow one to classify phases, but they also enable the study of phase transitions through their critical exponents which identify the universal long-range physics underlying the transition. Topological phases are exotic quantum phases which are lacking the characterization in terms of order parameters. While probes have been developed to identify such phases, those probes are only qualitative, in that they take discrete values, and, thus, provide no means to study the scaling behavior in the vicinity of phase transitions. In this paper, we develop a unified framework based on variational tensor networks (infinite projected entangled pair states) for the quantitative study of both topological and conventional phase transitions through entanglement order parameters. To this end, we employ tensor networks with suitable physical and/or entanglement symmetries encoded and allow for order parameters detecting the behavior of any of those symmetries, both physical and entanglement ones. On the one hand, this gives rise to entanglement-based order parameters for topologically ordered phases. These topological order parameters allow one to quantitatively probe the behavior when going through topological phase transitions and, thus, to identify universal signatures of such transitions. We apply our framework to the study of the toric code model in different magnetic fields, which along some special lines maps to the $(2+1)\mathrm{D}$ Ising model. Our method identifies 3D Ising critical exponents for the entire transition, consistent with those special cases and general belief. However, we, in addition, also find an unknown critical exponent ${\beta }^{*}\approx 0.021$ for one of our topological order parameters. We take this—together with known dualities between the toric code and the Ising model—as a motivation to also apply our framework of entanglement order parameters to conventional phase transitions. There, it enables us to construct a novel type of disorder operator (or disorder parameter), which is nonzero in the disordered phase and measures the response of the wave function to a symmetry twist in the entanglement. We numerically evaluate this disorder operator for the $(2+1)\mathrm{D}$ transverse field Ising model, where we again recover a critical exponent hitherto unknown in the $(2+1)\mathrm{D}$ Ising model, ${\beta }^{*}\approx 0.024$, consistent with the findings for the toric code. This shows that entanglement order parameters can provide additional means of characterizing the universal data both at topological and conventional phase transitions and altogether demonstrates the power of this framework to identify the universal data underlying the transition.

The physics of the triangular lattice Hubbard model exhibits a rich phenomenology, ranging from a metal-insulator transition, intriguing thermodynamic behavior, and a putative spin liquid phase at intermediate coupling, ultimately becoming a magnetic insulator at strong coupling. In this multimethod study, we combine a finite-temperature tensor network method, minimally entangled thermal typical states (METTS), with two Green-function-based methods, connected-determinant diagrammatic Monte Carlo and cellular dynamical mean-field theory, to establish several aspects of this model. We elucidate the evolution from the metallic to the insulating regime from the complementary perspectives brought by these different methods. We compute the full thermodynamics of the model on a width-four cylinder using METTS in the intermediate to strong coupling regime. We find that the insulating state hosts a large entropy at intermediate temperatures, which increases with the strength of the coupling. Correspondingly, and consistently with a thermodynamic Maxwell relation, the double occupancy has a minimum as a function of temperature which is the manifestation of the Pomeranchuk effect of increased localization upon heating. The intermediate coupling regime is found to exhibit both pronounced chiral as well as stripy antiferromagnetic spin correlations. We propose a scenario in which time-reversal symmetry-broken states compete with stripy-spin states at lowest temperatures.

Unraveling ultrafast molecular processes initiated by energetic radiation provides direct information on the chemical evolution under extreme conditions. A prominent example is interstellar media where complex molecules such as polycyclic aromatic hydrocarbons (PAHs) are excited by energetic photons. Until recently, ultrafast dynamics following such excitations remained largely unexplored due to the lack of relevant technologies. Here, we use time-resolved mass spectrometry combining ultrashort femtosecond XUV and IR pulses, to investigate the dynamics induced by high-energy photon excitation in PAHs. We demonstrate that excited cations relax through a progressive loss of vibrational selectivity, created at the early-stage dynamics, and which represents the first steps of a complete intramolecular vibrational energy redistribution. This process is in competition with the recently revealed correlation-band dynamics. These results might have direct consequences for the development of XUV molecular physics and other fields such as astrochemistry.

Quantum neural networks (QNNs) have generated excitement around the possibility of efficiently analyzing quantum data. But this excitement has been tempered by the existence of exponentially vanishing gradients, known as barren plateau landscapes, for many QNN architectures. Recently, quantum convolutional neural networks (QCNNs) have been proposed, involving a sequence of convolutional and pooling layers that reduce the number of qubits while preserving information about relevant data features. In this work, we rigorously analyze the gradient scaling for the parameters in the QCNN architecture. We find that the variance of the gradient vanishes no faster than polynomially, implying that QCNNs do not exhibit barren plateaus. This result provides an analytical guarantee for the trainability of randomly initialized QCNNs, which highlights QCNNs as being trainable under random initialization unlike many other QNN architectures. To derive our results, we introduce a novel graph-based method to analyze expectation values over Haar-distributed unitaries, which will likely be useful in other contexts. Finally, we perform numerical simulations to verify our analytical results.

Recently discovered $Z_2$ topological kagome metals $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, and Cs) exhibit charge-density-wave (CDW) phases and novel superconducting paring states providing a versatile platform for studying the interplay between electron correlation and quantum orders. Here we directly visualize CDW-induced bands renormalization and energy gaps in ${\mathrm{RbV}}_3{\mathrm{Sb}}_5$ using angle-resolved photoemission spectroscopy pointing to the key role of tuning van Hove singularities to the Fermi energy in mechanisms of ordering phases. Near the CDW transition temperature, the bands around the Brillouin zone (BZ) boundary are shifted to high-binding energy, forming an $\mathsf{M}$-shaped band with singularities near the Fermi energy. The Fermi surfaces are partially gapped, and the electronic states on the residual ones should be possibly dedicated to the superconductivity. Our findings are significant in understanding CDW formation and its associated superconductivity.

Motivated by recent core-level x-ray photoemission spectroscopy, x-ray absorption spectroscopy (XAS), and resonant inelastic x-ray scattering (RIXS) experiments for the newly discovered superconducting infinite-layer nickelate, we investigate the core-level spectra of the parent compounds ${\mathrm{NdNiO}}_2$ and ${\mathrm{LaNiO}}_2$ using the combination of local density approximation and dynamical mean-field theory ($\mathrm{LDA}+\mathrm{DMFT}$). Adjusting a charge-transfer energy to match the experimental spectra, we determine the optimal model parameters and discuss the nature of the ${\mathrm{NdNiO}}_2$ ground state. We find that self-doping from the Nd $5d$ states in the vicinity of the Fermi energy prohibits opening of a Mott-Hubbard gap in ${\mathrm{NdNiO}}_2$. The present Ni $L_3$ XAS and RIXS calculation for ${\mathrm{LaNiO}}_2$ cannot explain the difference from ${\mathrm{NdNiO}}_2$ spectra.

The simplest topologically ordered phase in $2+1\mathrm{D}$ is the deconfined phase of ${\mathbb{Z}}_2$ gauge theory (realized in the toric code, for example). This phase permits a duality that exchanges electric and magnetic excitations (“$e$” and “$m$” particles). The phase transition where one of these particles condenses, while the other remains gapped, has 3D Ising exponents. But the transition out of the deconfined phase when self-duality symmetry is preserved is more mysterious. It has so far been unclear whether this transition is continuous, but if continuous, it may be the simplest critical point for which a useful continuum Lagrangian is still lacking. These questions are relevant to soft matter, too, since the gauge theory also describes classical membranes in 3D. Here, we study the self-dual transition with Monte Carlo simulations of the ${\mathbb{Z}}_2$ gauge-Higgs model on cubic lattices of linear size $L\le 96$. Our results indicate a continuous transition, for example via a striking parameter-free scaling collapse. We use duality symmetry to distinguish the leading duality-odd and duality-even scaling operators $A$ and $S$. We explain why standard techniques for locating the critical point are ineffective, and we develop an alternative using “renormalization group trajectories” of cumulants. We check that two- and three-point functions are scale invariant, with scaling dimensions $x_A$ and $x_S$ (autocorrelations in the Monte Carlo dynamics also yield a dynamical exponent $z$). Separately, we propose a general picture for emergent 1-form symmetries, in terms of “patching” of membranes or world surfaces. We relate this to the percolation of anyon worldlines in spacetime. The latter yields a fourth exponent for the self-dual transition. We propose variations of the model for further investigation.

Local three- and four-point correlators yield important insight into strongly correlated systems and have many applications. However, the nonperturbative, accurate computation of multipoint correlators is challenging, particularly in the real-frequency domain for systems at low temperatures. In the accompanying paper, we introduce generalized spectral representations for multipoint correlators. Here, we develop a numerical renormalization group approach, capable of efficiently evaluating these spectral representations, to compute local three- and four-point correlators of quantum impurity models. The key objects in our scheme are partial spectral functions, encoding the system’s dynamical information. Their computation via numerical renormalization group allows us to simultaneously resolve various multiparticle excitations down to the lowest energies. By subsequently convolving the partial spectral functions with appropriate kernels, we obtain multipoint correlators in the imaginary-frequency Matsubara, the real-frequency zero-temperature, and the real-frequency Keldysh formalisms. We present exemplary results for the connected four-point correlators of the Anderson impurity model, and for resonant inelastic x-ray scattering spectra of related impurity models. Our method can treat temperatures and frequencies—imaginary or real—of all magnitudes, from large to arbitrarily small ones.

The many-body problem is usually approached from one of two perspectives: the first originates from an action and is based on Feynman diagrams, the second is centered around a Hamiltonian and deals with quantum states and operators. The connection between results obtained in either way is made through spectral (or Lehmann) representations, well known for two-point correlation functions. Here, we complete this picture by deriving generalized spectral representations for multipoint correlation functions that apply in all of the commonly used many-body frameworks: the imaginary-frequency Matsubara and the real-frequency zero-temperature and Keldysh formalisms. Our approach separates spectral from time-ordering properties and thereby elucidates the relation between the three formalisms. The spectral representations of multipoint correlation functions consist of partial spectral functions and convolution kernels. The former are formalism independent but system specific; the latter are system independent but formalism specific. Using a numerical renormalization group method described in the accompanying paper, we present numerical results for selected quantum impurity models. We focus on the four-point vertex (effective interaction) obtained for the single-impurity Anderson model and for the dynamical mean-field theory solution of the one-band Hubbard model. In the Matsubara formalism, we analyze the evolution of the vertex down to very low temperatures and describe the crossover from strongly interacting particles to weakly interacting quasiparticles. In the Keldysh formalism, we first benchmark our results at weak and infinitely strong interaction and then reveal the rich real-frequency structure of the dynamical mean-field theory vertex in the coexistence regime of a metallic and insulating solution.

We present a new theoretical picture of magnetically dominated, decaying turbulence in the absence of a mean magnetic field. With direct numerical simulations, we demonstrate that the rate of turbulent decay is governed by the reconnection of magnetic structures, and not necessarily by ideal dynamics, as has previously been assumed. We obtain predictions for the magnetic-energy-decay laws by proposing that turbulence decays on reconnection timescales while respecting the conservation of certain integral invariants representing topological constraints satisfied by the reconnecting magnetic field. As is well known, the magnetic helicity is such an invariant for initially helical field configurations, but it does not constrain nonhelical decay, where the volume-averaged magnetic-helicity density vanishes. For such a decay, we propose a new integral invariant, analogous to the Loitsyansky and Saffman invariants of hydrodynamic turbulence, that expresses the conservation of the random (scaling as ${\text{volume}}^{1/2}$) magnetic helicity contained in any sufficiently large volume. We verify that this invariant is indeed well conserved in our numerical simulations. Our treatment leads to novel predictions for the magnetic-energy-decay laws: In particular, while we expect the canonical $t^{-2/3}$ power law for helical turbulence when reconnection is fast (i.e., plasmoid-dominated or stochastic), we find a shallower $t^{-4/7}$ decay in the slow “Sweet-Parker” reconnection regime, in better agreement with existing numerical simulations. For nonhelical fields, for which there currently exists no definitive theory, we predict power laws of $t^{-10/9}$ and $t^{-20/17}$ in the fast- and slow-reconnection regimes, respectively. We formulate a general principle of decay of turbulent systems subject to conservation of Saffman-like invariants and propose how it may be applied to MHD turbulence with a strong mean magnetic field and to isotropic MHD turbulence with initial equipartition between the magnetic and kinetic energies.

A wave function subject to unitary time evolution and exposed to measurements undergoes pure state dynamics, with deterministic unitary and probabilistic measurement-induced state updates, defining a quantum trajectory. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions. To access this competition despite the randomness of single quantum trajectories, we construct an $n$-replica Keldysh field theory for the ensemble average of the $n$th moment of the trajectory projector. A key finding is that this field theory decouples into one set of degrees of freedom that heats up indefinitely, while $n-1$ others can be cast into the form of pure state evolutions generated by an effective non-Hermitian Hamiltonian. This decoupling is exact for free theories, and useful for interacting ones. In particular, we study locally measured Dirac fermions in ($1+1$) dimensions, which can be bosonized to a monitored interacting Luttinger liquid at long wavelengths. For this model, the non-Hermitian Hamiltonian corresponds to a quantum sine-Gordon model with complex coefficients. A renormalization group analysis reveals a gapless critical phase with logarithmic entanglement entropy growth, and a gapped area law phase, separated by a Berezinskii-Kosterlitz-Thouless transition. The physical picture emerging here is a measurement-induced pinning of the trajectory wave function into eigenstates of the measurement operators, which succeeds upon increasing the monitoring rate across a critical threshold.

Under physiological conditions, ballistic long-range transfer of electronic excitations in molecular aggregates is generally expected to be suppressed by noise and dissipative processes. Hence, quantum phenomena are not considered to be relevant for the design of efficient and controllable energy transfer over significant length scales and timescales. Contrary to this conventional wisdom, here we show that the robust quantum properties of small configurations of repeating clusters of molecules can be used to tune energy-transfer mechanisms that take place on much larger scales. With the support of an exactly solvable model, we demonstrate that coherent exciton delocalization and dark states within unit cells can be used to harness dissipative phenomena of varying nature (thermalization, fluorescence, nonradiative decay, and weak intersite correlations) to support classical propagation over macroscopic distances. In particular, we argue that coherent delocalization of electronic excitations over just a few pigments can drastically alter the relevant dissipation pathways that influence the energy-transfer mechanism and thus serve as a molecular control tool for large-scale properties of molecular materials. Building on these principles, we use extensive numerical simulations to demonstrate that they can explain currently not-understood measurements of micron-scale exciton diffusion in nanofabricated arrays of bacterial photosynthetic complexes. Based on these results, we provide quantum design guidelines at the molecular scale to optimize both energy-transfer speed and range over macroscopic distances in artificial light-harvesting architectures.

Intense laser-plasma ion sources are characterized by an unsurpassed acceleration gradient and exceptional beam emittance. They are promising candidates for next-generation accelerators towards a broad range of potential applications. However, the laser-accelerated ion beams available currently have limitations in energy spread and peak energy. Here, we propose and demonstrate an all-optical single laser scheme to generate proton beams with low spread at about 1% level and hundred MeV energy by irradiating the edge of a microtape with a readily available femtosecond petawatt laser. Three-dimensional particle-in-cell simulations show that when the electron beam extracted from both sides of the tape is injected into vacuum, a longitudinal bunching and transverse focusing field is self-established because of its huge charge (about 100 nC) and small divergence. Protons are accelerated and bunched simultaneously, leading to a monoenergetic high-energy proton beam. The proposed scheme opens a new route for the development of future compact ion sources.

The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary correlations and non-negligible decoherence. Ergodicity includes and vastly generalizes random independence. We obtain a theorem which shows that the composition of such a sequence of channels converges exponentially fast to a replacement (rank-one) channel. Using this theorem, we derive the limiting behavior of translation-invariant channels and stochastically independent random channels. We then use our formalism to describe the thermodynamic limit of ergodic matrix product states. We derive formulas for the expectation value of a local observable and prove that the two-point correlations of local observables decay exponentially. We then analytically compute the entanglement spectrum across any cut, by which the bipartite entanglement entropy (i.e., Rényi or von Neumann) across an arbitrary cut can be computed exactly. Other physical implications of our results are that most Floquet phases of matter are metastable and that noisy random circuits in the large depth limit will be trivial as far as their quantum entanglement is concerned. To obtain these results, we bridge quantum information theory to dynamical systems and random matrix theory.

The quantum alternating operator ansatz (QAOA) is a prominent example of variational quantum algorithms. We propose a generalized QAOA called CD-QAOA, which is inspired by the counterdiabatic driving procedure, designed for quantum many-body systems and optimized using a reinforcement learning (RL) approach. The resulting hybrid control algorithm proves versatile in preparing the ground state of quantum-chaotic many-body spin chains by minimizing the energy. We show that using terms occurring in the adiabatic gauge potential as generators of additional control unitaries, it is possible to achieve fast high-fidelity many-body control away from the adiabatic regime. While each unitary retains the conventional QAOA-intrinsic continuous control degree of freedom such as the time duration, we consider the order of the multiple available unitaries appearing in the control sequence as an additional discrete optimization problem. Endowing the policy gradient algorithm with an autoregressive deep learning architecture to capture causality, we train the RL agent to construct optimal sequences of unitaries. The algorithm has no access to the quantum state, and we find that the protocol learned on small systems may generalize to larger systems. By scanning a range of protocol durations, we present numerical evidence for a finite quantum speed limit in the nonintegrable mixed-field spin-$1/2$ Ising and Lipkin-Meshkov-Glick models, and for the suitability to prepare ground states of the spin-1 Heisenberg chain in the long-range and topologically ordered parameter regimes. This work paves the way to incorporate recent success from deep learning for the purpose of quantum many-body control.

When interacting motile units self-organize into flocks, they realize one of the most robust ordered states found in nature. However, after 25 years of intense research, the very mechanism controlling the ordering dynamics of both living and artificial flocks has remained unsettled. Here, combining active-colloid experiments, numerical simulations, and analytical work, we explain how flocking liquids heal their spontaneous flows initially plagued by collections of topological defects to achieve long-ranged polar order even in two dimensions. We demonstrate that the self-similar ordering of flocking matter is ruled by a living network of domain walls linking all $\pm 1$ vortices and guiding their annihilation dynamics. Crucially, this singular orientational structure echoes the formation of extended density patterns in the shape of interconnected bow ties. We establish that this double structure emerges from the interplay between self-advection and density gradients dressing each $-1$ topological charge with four orientation walls. We then explain how active Magnus forces link all topological charges with extended domain walls, while elastic interactions drive their attraction along the resulting filamentous network of polarization singularities. Taken together, our experimental, numerical, and analytical results illuminate the suppression of all flow singularities and the emergence of pristine unidirectional order in flocking matter.

Fluctuating superconductivity—vestigial Cooper pairing in the resistive state of a material—is usually associated with low dimensionality, strong disorder, or low carrier density. Here, we report single-particle spectroscopic, thermodynamic and magnetic evidence for persistent superconducting fluctuations in the heavily hole-doped cuprate superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ ($T_c=66\mathrm{K}$) despite the high carrier density. With a sign-problem-free quantum Monte Carlo calculation, we show how a partially flat band at $(\pi ,0)$ can help enhance superconducting phase fluctuations. Finally, we discuss the implications of an anisotropic band structure on the phase-coherence-limited superconductivity in overdoped cuprates and other superconductors.

We illuminate the many-body effects underlying the structure, formation, and dissolution of cellular adhesion domains in the presence and absence of forces. We consider mixed Glauber-Kawasaki dynamics of a two-dimensional model of nearest-neighbor-interacting adhesion bonds with intrinsic binding affinity under the action of a shared pulling or pushing force. We consider adhesion bonds that are immobile due to being anchored to the underlying cytoskeleton, as well as adhesion molecules that are transiently diffusing. Highly accurate analytical results are obtained on the pair-correlation level of the Bethe-Guggenheim approximation for the complete thermodynamics and kinetics of adhesion clusters of any size, including the thermodynamic limit. A new kind of dynamical phase transition is uncovered—the mean formation and dissolution times per adhesion bond change discontinuously with respect to the bond-coupling parameter. At the respective critical points, cluster formation and dissolution are the fastest, while the statistically dominant transition path undergoes a qualitative change—the entropic barrier to a completely bound or unbound state is rate-limiting below, and the phase transition between dense and dilute phases above the dynamical critical point. In the context of the Ising model, the dynamical phase transition reflects a first-order discontinuity in the magnetization-reversal time. Our results provide a potential explanation for the mechanical regulation of cell adhesion and suggest that the quasistatic and kinetic responses to changes in the membrane stiffness or applied forces is largest near the statical and dynamical critical points, respectively.