All phase-encoded BB84 implementations have signal states with unbalanced amplitudes in practice. Thus the original security analyses a priori do not apply to them. Previous security proofs use signal tagging of multiphoton pulses to recover the behavior of regular BB84. This is overly conservative as for unbalanced signals the photon number splitting attack does not leak full information to Eve. In this work we exploit the flag-state squashing model to preserve some parts of the multiphoton-generated private information in our analysis. Using a numerical proof technique we obtain significantly higher key rates compared with previously published results in the low-loss regime. It turns out that the usual scenario of untrusted dark counts runs into conceptual difficulties in some parameter regimes. Thus we discuss the trusted dark-count scenario in this paper as well. We also report a gain in key rates when part of the total loss is known to be induced by a trusted device. We highlight that all these key rate improvements can be achieved without modification of the experimental setup.

A topological mechanism is a zero-elastic-energy deformation of a mechanical structure that is robust against smooth changes in system parameters. Here, we map the nonlinear elasticity of a paradigmatic class of topological mechanisms onto a supersymmetric field theory introduced by Witten and Olive. Heuristically, this approach entails taking the square root of a nonlinear Hamiltonian. It generalizes the standard procedure of obtaining two copies of the Dirac equation by taking the square root of the linear Klein-Gordon equation. Our real-space formalism goes beyond topological band theory by incorporating nonlinearities and spatial inhomogeneities, such as domain walls (i.e., kinks), where topological states are typically localized. We interpret the two components of the real fermionic field as site and bond displacements, respectively. The constraint of zero elastic energy insures that kinks in the mechanical system saturate the Bogomolny-Prasad-Sommerfield bound, while forbidding antikinks. This mechanism can be viewed as a manifestation of the underlying supersymmetry being half broken.

Recent work has shown that coupling two identical Sachdev-Ye-Kitaev (SYK) models can realize a phase of matter that is holographically dual to an eternal traversable wormhole. This phase supports revival oscillations between two quantum chaotic systems that can be interpreted as information traversing the wormhole. Here we generalize these ideas to a pair of coupled SYK models with complex fermions that respect a global U(1) charge symmetry. Such models show richer behavior than conventional SYK models with Majorana fermions and may be easier to realize experimentally. We consider two different couplings, namely, tunneling and charge-conserving two-body interactions, and obtain the corresponding phase diagram using a combination of numerical and analytical techniques. At low temperature, we find a charge-neutral gapped phase that supports revival oscillations, with a ground state close to the thermofield double, which we argue is dual to a traversable wormhole. We also find two different gapless non-Fermi liquid phases with tunable charge density which we interpret as dual to a “large” and “small” charged black hole. The gapped and gapless phases are separated by a first-order phase transition of the Hawking-Page type. Finally, we discuss an SU(2)-symmetric limit of our model that is closely related to proposed realizations of SYK physics with spinful fermions in graphene, and explain its relevance for future experiments on this system.

We explore the nonlinear dynamics of a cavity optomechanical system. Our realization consisting of a drumhead nanoelectromechanical resonator (NEMS) coupled to a microwave cavity allows for a nearly ideal platform to study the nonlinearities arising purely due to radiation-pressure physics. Experiments are performed under a strong microwave Stokes pumping which triggers mechanical self-sustained oscillations. We analyze the results in the framework of an extended nonlinear optomechanical theory and demonstrate that quadratic and cubic coupling terms in the opto-mechanical Hamiltonian have to be considered. Quantitative agreement with the measurements is obtained considering only genuine geometrical nonlinearities: no thermo-optical instabilities are observed, in contrast with laser-driven systems. Based on these results, we describe a method to quantify nonlinear properties of microwave optomechanical devices. Such a technique, now available in the quantum electromechanics toolbox, but completely generic, is mandatory for the development of schemes where higher-order coupling terms are proposed as a resource, like quantum nondemolition measurements or in the search for new fundamental quantum signatures, like quantum gravity. We also find that the motion imprints a wide comb of extremely narrow peaks in the microwave output field, which could also be exploited in specific microwave-based measurements, potentially limited only by the quantum noise of the optical and the mechanical fields for a ground-state-cooled NEMS device.

We report the observation of strongly ferromagnetic $F=1$ spinor Bose-Einstein condensates of ${}^7\mathrm{Li}$ atoms. The condensates are generated in an optical dipole trap without using magnetic Feshbach resonances, so that the condensates have internal spin degrees of freedom. Studying the nonequilibrium spin dynamics, we have measured the ferromagnetic spin interaction energy and determined the $s$-wave scattering length difference among total spin $f$ channels to be $a_{f=2}-a_{f=0}=-18\left(3\right)$ Bohr radius. This strong collision-channel dependence leads to a large variation in the condensate size with different spin composition. We were able to excite a radial monopole mode after a spin-flip transition between the $|m_F=0\rangle$ and $|m_F=1\rangle$ spin states. From the experiments, we estimated the scattering length ratio $a_{f=2}/a_{f=0}=0.27\left(6\right)$, and determined $a_{f=2}=7\left(2\right)$ and $a_{f=0}=25\left(5\right)$ Bohr radii, respectively. The results indicate the spin-dependent interaction energy of our system is as large as $46\%$ of the condensate chemical potential.

Recent years have seen strong progress in quantum simulation of gauge-theory dynamics using ultracold-atom experiments. A principal challenge in these efforts is the certification of gauge invariance, which has recently been realized [Yang et al., arXiv:2003.08945]. One major but poorly investigated experimental source of gauge-invariance violation is an imperfect preparation of the initial state. Using the time-dependent density-matrix renormalization group, we analyze the robustness of gauge-invariant dynamics against potential preparation defects in the above ultracold-atom implementation of a $\mathrm{U}\left(1\right)$ gauge theory. We find defects related to an erroneous initialization of matter fields to be innocuous, as the associated gauge-invariance violation remains strongly localized throughout the time evolution. A defect due to faulty initialization of the gauge field leads to a mild proliferation of the associated violation. Furthermore, we characterize the influence of immobile and mobile defects by monitoring the spread of entanglement entropy. Overall, our results indicate that the aforementioned experimental realization exhibits a high level of fidelity in the gauge invariance of its dynamics at all evolution times. Our work provides strong evidence that ultracold-atom setups can serve as an extremely reliable framework for the quantum simulation of gauge-theory dynamics.

We discuss the possibility of torsional Nieh-Yan anomaly of the type ${\partial }_{\mu }\left(e{j}_5^{\mu }\right)=\gamma T^2({\mathcal{T}}^a\wedge {\mathcal{T}}_a)$ in Weyl superfluids, where $T$ is the infrared (IR) temperature scale and ${\mathcal{T}}^a$ is the effective or emergent torsion from the superfluid order parameter. As distinct from the dimensionful ultraviolet (UV) parameter ${\mathrm{\Lambda }}^2$ in the conventional torsional Nieh-Yan anomaly, the parameter $\gamma$ is dimensionless in canonical units. This suggests that such dimensionless parameter may be fundamental, being determined by the geometry, topology, and number of chiral quantum fields in the system. By comparing this to a Weyl superfluid with low-temperature corrections, $T\ll {\mathrm{\Delta }}_0$, we show that such a term does exist in the hydrodynamics of a chiral $p$-wave superfluid, such as ${}^3\mathrm{He}$-A, or a chiral superconductor. We also discuss and show how other $T^2$ terms of similar form and of the same order in gradients, coming from, e.g., Fermi-liquid corrections, effective curvature, and the chiral chemical potential, can also be expressed in terms of dimensionless fundamental parameters with emergent low-energy relativistic fields. Lastly, we discuss our results in comparison to relativistic Weyl fermions and the connection of the torsional gravitational anomalies to thermal transport in Weyl systems.

We show that the combination of two achiral components—an atomic or molecular target plus a circularly polarized photon—can yield chirally structured photoelectron angular distributions. For photoionization of CO, the angular distribution of carbon $K$-shell photoelectrons is chiral when the molecular axis is neither perpendicular nor (anti)parallel to the light propagation axis. In photo-double-ionization of He, the distribution of one electron is chiral if the other electron is oriented like the molecular axis in the former case and if the electrons are distinguishable by their energy. In both scenarios, the circularly polarized photon defines a plane with a sense of rotation and an additional axis is defined by the CO molecule or one electron. This is sufficient to establish an unambiguous coordinate frame of well-defined handedness. To produce a chirally structured electron angular distribution, such a coordinate frame is necessary but not sufficient. We show that additional electron-electron interaction or scattering processes are needed to create the chiral angular distribution.

The swimming of cells, far from any boundary, can arise in the absence of long-range liquid-crystalline order within the cytoplasm, but simple models of this effect are lacking. Here, we present a two-dimensional model of droplet self-propulsion involving two scalar fields, representing the cytoplasm and a contractile cortex. An active stress results from coupling between these fields; self-propulsion results when rotational symmetry is spontaneously broken. The swimming speed is predicted, and shown numerically, to vary linearly with the activity parameter and with the droplet area fraction. The model exhibits a Crowley-like instability for an array of active droplets.

The anomalous Hall effect is commonly considered a signature of ferromagnetism. However, recently, an enormous anomalous Hall conductivity was measured in the compensated kagome magnets ${\mathrm{Mn}}_3\mathrm{Sn}$ and ${\mathrm{Mn}}_3\mathrm{Ge}$. The occurrence of this effect is allowed by the magnetic point group of these materials; however, its emergence is still lacking a microscopic explanation. Herein we show that the spin-orbit coupling and an out-of-plane tilting of the texture are equivalent for several kagome magnets. Consequently, a coplanar system with spin-orbit coupling behaves as if it were virtually noncoplanar. We show via tight-binding model calculations that the Hall effect can mainly be interpreted as a topological Hall effect generated by the opening angle of the virtually tilted texture. Furthermore, upon tilting the fixed texture out of the kagome plane, we find a critical tilting angle for which the Hall conductivity vanishes for all energies. In this case, the Hamiltonian is invariant under a combined time-reversal and mirror symmetry, because the virtual texture is coplanar.

Classic measures of graph centrality capture distinct aspects of node importance, from the local (e.g., degree) to the global (e.g., closeness). Here we exploit the connection between diffusion and geometry to introduce a multiscale centrality measure. A node is defined to be central if it breaks the metricity of the diffusion as a consequence of the effective boundaries and inhomogeneities in the graph. Our measure is naturally multiscale, as it is computed relative to graph neighborhoods within the varying time horizon of the diffusion. We find that the centrality of nodes can differ widely at different scales. In particular, our measure correlates with degree (i.e., hubs) at small scales and with closeness (i.e., bridges) at large scales, and also reveals the existence of multicentric structures in complex networks. By examining centrality across scales, our measure thus provides an evaluation of node importance relative to local and global processes on the network.

Recent studies found that the diffusive transport of conserved quantities in nonintegrable many-body systems has an imprint on quantum entanglement: while the von Neumann entropy of a state grows linearly in time $t$ under a global quench, all $n\mathrm{th}$ Rényi entropies with $n>1$ grow with a diffusive scaling $\sqrt{t}$. To understand this phenomenon, we introduce an amplitude $A\left(t\right)$, which is the overlap of the time evolution operator $U\left(t\right)$ of the entire system with the tensor product of the two evolution operators of the subsystems of a spatial bipartition. As long as $\left|A\left(t\right)\right|\ge e^{-\sqrt{Dt}}$, which we argue holds true for generic diffusive nonintegrable systems, all $n\mathrm{th}$ Rényi entropies with $n>1$ (annealed averaged over initial product states) are bounded from above by $\sqrt{t}$. We prove the following inequality for the disorder average of the amplitude, $\overline{\left|A\right(t\left)\right|}\ge e^{-\sqrt{Dt}}$, in a local spin-$\frac{1}{2}$ random circuit with a $\text{U}\left(1\right)$ conservation law by mapping to the survival probability of a symmetric exclusion process. Furthermore, we numerically show that the typical decay behaves asymptotically, for long times, as $\left|A\left(t\right)\right|\sim e^{-\sqrt{Dt}}$ in the same random circuit as well as in a prototypical nonintegrable model with diffusive energy transport but no disorder.

We present random quantum circuit models for nonunitary quantum dynamics of free fermions in one spatial dimension. Numerical simulations reveal that the dynamics tends toward steady states with logarithmic violations of the entanglement area law and power law correlation functions. Moreover, starting with a short-range entangled many-body state, the dynamical evolution of entanglement and correlations quantitatively agrees with the predictions of two-dimensional conformal field theory with a spacelike time direction. We argue that this behavior is generic in nonunitary free quantum dynamics with time-dependent randomness, and we show that the emergent conformal dynamics of two-point functions arises out of a simple “nonlinear master equation.”

This paper focuses on two aspects of the statistics of cosmological observables that are important for the next stages of precision cosmology. First, we note that the theory of reduced angular $N$-point spectra has only been developed in detail up to the trispectrum case and in a fashion that makes it difficult to go beyond. To fill this gap, here we present a constructive approach that provides a systematic description of reduced angular $N$-point spectra and their covariance matrices, for arbitrary $N$. Second, we focus on the common practice in the literature on cosmological observables, which consists in simply discarding a part of the expression, namely, the terms containing fields evaluated at the observer position. We point out that this is not justified beyond linear order in perturbation theory, as these terms contribute to all the multipoles of the corresponding spectra and with a magnitude that is of the same order as the rest of the nonlinear corrections. We consider the possibility that the reason for neglecting these terms is a conceptual discomfort when using ensemble averages, which originates in an apparent tension between the ergodic hypothesis and the privileged position of the observer on the light-cone. We clarify this subtle issue by performing a careful derivation of the relation between the theoretical statistical predictions and the observational estimators for all $N$. We conclude that there is no inconsistency whatsoever in ensemble-averaging fields at and near the observer position, thus clearing the way for consistent and robust high-precision calculations.

The discovery of intrinsic two-dimensional magnetism has ignited intense research interest due to the several and attractive applications in spintronics. ${\mathrm{Nb}}_3{\mathrm{I}}_8$ is a recently investigated van der Waals material, exhibiting ferromagnetism and extraordinary visible light-harvesting ability in monolayer form, besides useful remarkable features for the realization of future high-performance nanodevices. Here we use density functional theory and classical Monte Carlo simulations to investigate the electronic and magnetic properties of ${\mathrm{Nb}}_3{\mathrm{I}}_8$ in bulk, monolayer, and some multilayer (bilayer and trilayer) forms. Two suitable vdW exchange-correlation functionals, $\mathsf{vdW-DF2-C09}$ and $\mathsf{rev-vdW-DF2}$, have been chosen to compare the first-principles calculation predictions. The layer number directly influences the ground-state magnetism, indicating the possibility of using the thickness as a parameter to control the magnetic response of the material. In particular, it is possible to switch on the antiferromagnetism by adding one or two layers to the ferromagnetic monolayer. This makes ${\mathrm{Nb}}_3{\mathrm{I}}_8$ an excellent platform for spintronics applications. Monte Carlo simulations based on a third-nearest-neighbor Ising model provide a Curie temperature close to room temperature ($\sim 307$ K) for the monolayer. The results on the electronic and magnetic properties render the two-dimensional ${\mathrm{Nb}}_3{\mathrm{I}}_8$ an ideal and promising candidate for future research and applications.

We revisit the long-standing question of the relation between image appreciation and its statistical properties. We generate two different sets of random images well distributed along three measures of entropic complexity. We run a large-scale survey in which people are asked to sort the images by preference, which reveals maximum appreciation at intermediate entropic complexity. We show that the algorithmic complexity of the coarse-grained images, expected to capture structural complexity while abstracting from high frequency noise, is a good predictor of preferences. Our analysis suggests that there might exist some universal quantitative criteria for aesthetic judgment.

A spin current—a flow of spin angular momentum—can be carried either by spin-polarized free electrons or by magnons, the quanta of a moving collective oscillation of localized electron spins, i.e., a spin wave. Traditionally, it was assumed that a spin wave in a magnetic film with spin-sink-free surfaces can transfer energy and angular momentum only along its propagation direction. In this work, using Brillouin light-scattering spectroscopy in combination with a theory of dipole-exchange spin-wave spectra, we show that in obliquely magnetized free magnetic films, the in-plane propagation of spin waves is accompanied by a transverse spin current along the film normal without any corresponding transverse transport of energy.

A system is non-Hermitian when it exchanges energy with its environment and nonreciprocal when it behaves differently upon the interchange of input and response. Within the field of metamaterial research on synthetic topological matter, the skin effect describes the conspiracy of non-Hermiticity and nonreciprocity to yield extensive anomalous localization of all eigenmodes in a (quasi) one-dimensional geometry. Here, we introduce the reciprocal skin effect, which occurs in non-Hermitian but reciprocal systems in two or more dimensions: Eigenmodes with opposite longitudinal momentum exhibit opposite transverse anomalous localization. We experimentally demonstrate the reciprocal skin effect in a passive RLC circuit, suggesting convenient alternative implementations in optical, acoustic, mechanical, and related platforms. Skin mode localization brings forth potential applications in directional and polarization detectors for electromagnetic waves.

We study the quantum dynamics of many-body systems, in the presence of dissipation due to the interaction with the environment, under Kibble-Zurek (KZ) protocols in which one Hamiltonian parameter is slowly, and linearly in time, driven across the critical value of a zero-temperature quantum transition. In particular we address whether, and under which conditions, open quantum systems can develop a universal dynamic scaling regime similar to that emerging in closed systems. We focus on a class of dissipative mechanisms the dynamics of which can be reliably described through a Lindblad master equation governing the time evolution of the system's density matrix. We argue that a dynamic scaling limit exists even in the presence of dissipation, the main features of which are controlled by the universality class of the quantum transition. This requires a particular tuning of the dissipative interactions, the decay rate $u$ of which should scale as $u\sim t_s^{-\kappa }$ with increasing the time scale $t_s$ of the KZ protocol, where the exponent $\kappa =z/(y_{\mu }+z)$ depends on the dynamic exponent $z$ and the renormalization-group dimension $y_{\mu }$ of the driving Hamiltonian parameter. Our dynamic scaling arguments are supported by numerical results for KZ protocols applied to a one-dimensional fermionic wire undergoing a quantum transition in the same universality class of the quantum Ising chain, in the presence of dissipative mechanisms which include local pumping, decay, and dephasing.

We propose a new parton theory of the hole-doped cuprates, describing the evolution from the pseudogap metal with small Fermi surfaces to the conventional Fermi liquid with a large Fermi surface. We introduce two ancilla qubits per square lattice site, and employ them to obtain a variational wave function of a fractionalized Fermi liquid for the pseudogap metal state. We propose a multilayer Hamiltonian for the cuprates, with the electrons residing in the physical layer, and the ancilla qubits in two hidden layers: the hidden layers can be decoupled from the physical layer by a canonical transformation, which leaves the hidden layers in a trivial gapped state. This Hamiltonian yields an emergent gauge theory, which describes not only the fractionalized Fermi liquid, but also the conventional Fermi liquid, and possible exotic intermediate phases and critical points. The fractionalized Fermi liquid has hole pockets with quasiparticle weight which is large only on Fermi arcs, and fermionic spinon excitations, which carry charges of the emergent gauge fields.