Rydberg-cavity systems are emerging as promising platforms for quantum simulation and quantum information processing. These hybrid architectures combine two complementary interaction mechanisms: cavity photons mediate collective long-range couplings, while Rydberg excitations generate strong short-range interactions. Together, they offer a setting for engineering many-body phases characterized by a hierarchy of interactions across widely different length scales. In this work, we introduce a minimal and scalable model for such systems. Focusing on the strong Rydberg blockade regime, we restrict the Hilbert space to the subspace enforced by the blockade, yielding a kinetically constrained long-range model in one spatial dimension. This approach both captures the physics of Rydberg-cavity experiments in the regime of strong Rydberg interactions and provides a conceptually transparent framework for studying the interplay of long-range and short-range interactions. At equilibrium, in addition to paramagnetic and Néel-ordered phases, the system supports a blockaded ferromagnetic/superradiant phase, distinct from the conventional superradiant phase. Out of equilibrium, we identify long-range quantum many-body scars, which are atypical nonthermal eigenstates that evade the eigenstate thermalization hypothesis, and giving rise to slow entanglement growth. In contrast to the linear-in-time entanglement growth characteristic of short-range scarred models, these long-range scars exhibit logarithmic entanglement dynamics. Our results establish a minimal yet versatile framework for Rydberg-cavity systems, and provide a stepping stone for future theoretical and experimental studies of this frontier platform in quantum many-body physics.

Controlling and measuring the temperature in different devices and platforms that operate in the quantum regime is, without any doubt, essential for any potential application. In this review, we report the most recent theoretical developments dealing with accurate estimation of very low temperatures in quantum systems. Together with the emerging experimental techniques and developments of measurement protocols, the theory of quantum thermometry will decisively impinge and shape the forthcoming quantum technologies. While current quantum thermometric methods differ greatly depending on the experimental platform, the achievable precision, and the temperature range of interest, the theory of quantum thermometry is built under a unifying framework at the crossroads of quantum metrology, open quantum systems, and quantum many-body physics. At a fundamental level, theoretical quantum thermometry is concerned with finding the ultimate bounds and scaling laws that limit the precision of temperature estimation for systems in and out-of-thermal equilibrium. At a more practical level, it provides tools to formulate precise, yet feasible, thermometric protocols for relevant experimental architectures. Last but not least, the theory of quantum thermometry examines genuine quantum features, like entanglement and coherence, for their exploitation in enhanced-resolution thermometry.

Cavity quantum electrodynamics with atomic ensembles is typically associated with collective spin phenomena, such as superradiance and spin squeezing, in which the atoms evolve collectively as a macroscopic spin ($S\sim N/2$) on the Bloch sphere. Surprisingly, we show that the tendency toward a collective spin description need not imply collective spin phenomena; rather, it can be exploited to generate new forms of strongly correlated quantum matter. The key idea is to use uniform cavity-mediated interactions to energetically project the system into the total-spin singlet sector ($S=0$) - a highly entangled subspace where the physics is governed entirely by cavity fluctuations. Focusing on Rydberg atom arrays coupled to a single-mode cavity, we show that global cavity fluctuations can effectively squeeze classical antiferromagnets into quantum spin liquids, characterized by non-local entanglement, fractionalized excitations, and emergent gauge fields. This work suggests that cavity QED can be a surprising resource for inducing strongly correlated phenomena, which could be explored in the new generation of hybrid tweezer-cavity platforms.

We establish several relations between quantum error correction (QEC) and tensor network (TN) methods of quantum many-body physics. We exhibit correspondences between well-known families of QEC codes and TNs, and demonstrate a formal equivalence between decoding a QEC code and contracting a TN. We build on this equivalence to propose a new family of quantum codes and decoding algorithms that generalize and improve upon quantum polar codes and successive cancellation decoding in a natural way.

We propose a four-stroke quantum thermal machine based on the 1D anyon Hubbard model, which is capable of extracting the excess energy arising from anyon exclusion statistics at low temperature into finite work. Defining a hybrid anyon-Otto (HAO) cycle, we find that the low temperature work, in the absence of any interactions, is maximised in the pseudo fermionic limit, where the anyons most closely resemble free fermions. However, when weak interactions are introduced, the work output is no longer maximized at the bosonic or pseudo-fermionic extremes, but instead peaks at intermediate statistical angles. This clearly demonstrates that interactions and anyonic statistics conspire non-trivially to enhance performance, with interacting anyons offering greater quantum thermodynamic advantage than either bosons or pseudo-fermions, in this regime. Furthermore, we also identify different modes of operation of the HAO cycle, one of which emerges as a direct consequence of the finite anyon energy at low temperature.

Device-independent quantum key distribution aims to provide key distribution schemes whose security is based on the laws of quantum physics but which does not require any assumptions about the internal working of the quantum devices used in the protocol. This strong form of security, unattainable with standard schemes, is possible only when using correlations that violate a Bell inequality. We provide a general security proof valid for a large class of device-independent quantum key distribution protocols in a model in which the raw key elements are generated by causally independent measurement processes. The validity of this independence condition may be justifiable in a variety of implementations and is necessarily satisfied in a physical realization where the raw key is generated by N separate pairs of devices. Our work shows that device-independent quantum key distribution is possible with key rates comparable to those of standard schemes.

Photonic technologies continue to drive the quest for new optical materials with unprecedented responses. A major frontier in this field is the exploration of nonlocal (spatially dispersive) materials, going beyond the local, wavevector-independent assumption traditionally made in optical material modeling. On one end, the growing interest in plasmonic, polaritonic and quantum materials has revealed naturally occurring nonlocalities, emphasizing the need for more accurate models to predict and design their optical responses. This has major implications also for topological, nonreciprocal, and time-varying systems based on these material platforms. Beyond natural materials, artificially structured materials--metamaterials and metasurfaces--can provide even stronger and engineered nonlocal effects, emerging from long-range interactions or multipolar effects. This is a rapidly expanding area in the field of photonic metamaterials, with open frontiers yet to be explored. In the case of metasurfaces, in particular, nonlocality engineering has become a powerful tool for designing strongly wavevector-dependent responses, enabling enhanced wavefront control, spatial compression, multifunctional devices, and wave-based computing. Furthermore, nonlocality and related concepts play a critical role in defining the ultimate limits of what is possible in optics, photonics, and wave physics. This Roadmap aims to survey the most exciting developments in nonlocal photonic materials, highlight new opportunities and open challenges, and chart new pathways that will drive this emerging field forward--toward new scientific discoveries and technological advancements.

Bell inequalities define experimentally observable quantities to detect non-locality. In general, they involve correlation functions of all the parties. Unfortunately, these measurements are hard to implement for systems consisting of many constituents, where only few-body correlation functions are accessible. Here we demonstrate that higher-order correlation functions are not necessary to certify nonlocality in multipartite quantum states by constructing Bell inequalities from one- and two-body correlation functions for an arbitrary number of parties. The obtained inequalities are violated by some of the Dicke states, which arise naturally in many-body physics as the ground states of the two-body Lipkin-Meshkov-Glick Hamiltonian.

A new unbiased Monte Carlo technique called Tensor Network Monte Carlo (TNMC) is introduced based on sampling all possible renormalizations (or course-grainings) of tensor networks, in this case matrix-product states. Tensor networks are a natural language for expressing a wide range of discrete physical and statistical problems, such as classical and quantum systems on a lattice at thermal equilibrium. By simultaneously sampling multiple degrees of freedom associated with each bond of the tensor network (and its renormalized form), we can achieve unprecedented low levels of statistical fluctuations which simultaneously parallel the impressive accuracy scaling of tensor networks while avoiding completely the variational bias inherent to those techniques, even with small bond dimensions. The resulting technique is essentially an aggressive multi-sampling technique that can account for the great majority of the partition function in a single sample. The method is quite general and can be combined with a variety of tensor renormalization techniques appropriate to different geometries and dimensionalities.

By solving the quench dynamics of a frustrated many-body spin-boson problem, we investigate the role of spin size on the dynamical formation of spin glass order. In particular, we observe that quantum and classical spin glasses exhibit markedly different evolution. The former displays a quick relaxation of magnetization together with an exponential dependence of the spin glass order parameter on spin size, while the latter has long-lasting prethermal magnetization and a spin glass order parameter independent of spin size. The quantum-to-classical crossover is sharp and occurs for relatively small spins, highlighting the fragility of the quantum regime. Furthermore, we show that spin glass order is resonantly enhanced when the frequency of the bosonic mediators of the interactions approaches the value of the transverse field. Our predictions are relevant for all spin glass systems with $SU(2)$ degrees of freedom away from equilibrium, and can be examined in recently developed multi-mode cavity QED experiments.

Advancements in quantum optics and squeezed light generation have revolutionized various fields of quantum science over the past three decades, with notable applications such as gravitational wave detection. Here, we extend the use of squeezed light to the realm of ultrafast quantum science. We demonstrate the generation of ultrafast, broadband quantum light pulses spanning 0.33 to 0.73 PHz using light field synthesizer and a four-wave mixing nonlinear process. Experimental results confirm that these pulses exhibit amplitude squeezing, which is consistent with theoretical predictions. This work lays the groundwork for a new field of ultrafast quantum science, enabling real-time studies of quantum light-matter interaction dynamics, which expect to reveal new physics. We also demonstrate the encoding of binary digital data onto these quantum light waveforms, synthesized with attosecond resolution, showcasing potential applications in secure quantum communication. This work paves the way for ultrafast quantum optoelectronics, quantum computing, and next-generation encrypted quantum communication networks, capable of achieving petahertz-scale data transmission speeds.

Practical implementations of Quantum Key Distribution (QKD) often deviate from the theoretical protocols, exposing the implementations to various attacks even when the underlying (ideal) protocol is proven secure. We present new analysis tools and methodologies for quantum cybersecurity, adapting the concepts of vulnerabilities, attack surfaces, and exploits from classical cybersecurity to QKD implementation attacks. We also present three additional concepts, derived from the connection between classical and quantum cybersecurity: "Quantum Fuzzing", which is the first tool for black-box vulnerability research on QKD implementations; "Reversed-Space Attacks", which are a generic exploit method using the attack surface of imperfect receivers; and concrete quantum-mechanical definitions of "Quantum Side-Channel Attacks" and "Quantum State-Channel Attacks", meaningfully distinguishing them from each other and from other attacks. Using our tools, we analyze multiple existing QKD attacks and show that the "Bright Illumination" attack could have been found even with minimal knowledge of the device implementation. This work begins to bridge the gap between current analysis methods for experimental attacks on QKD implementations and the decades-long research in the field of classical cybersecurity, improving the practical security of QKD products and enhancing their usefulness in real-world systems.

We study extremality in various sets of states that have positive partial transposes. One of the tools we use for this purpose is the recently formulated criterion allowing to judge if a given state is extremal in the set of PPT states. First we investigate qubit--ququart states and show that the only candidates for extremal PPT entangled states (PPTES) have ranks of the state and its partial transposition (5,5) or (5,6) (equivalently (6,5)). Then, examples of extremal states of (5,5) type and the so--called edge states of type (5,6) are provided. We also make an attempt to explore the set of PPT states with ranks (5,6). Finally, we discuss what are the possible configurations of ranks of density matrices and their respective partial transposition in general three-qubit and four-qubit symmetric states for which there may exist extremal entangled PPT states. For instance in the first case we show that the only possibilities are (4,4,4) and (4,4,5).

Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law. Translationally invariant systems of free fermions in arbitrary dimensions as well as 1D systems solved by the Jordan-Wigner transformation are shown to be exactly represented in this class. Further, it is proposed that these tensor networks be used as generic structures to variationally describe more complicated systems, such as interacting fermions. This class shares some similarities with Evenbly & Vidal's branching MERA, but with some important differences and greatly reduced computational demands.

Optical microcavities supporting exciton-polariton quasi-particles offer one of the most powerful platforms for investigation of rapidly developing area of topological photonics in general, and of photonic topological insulators in particular. Energy bands of the microcavity polariton graphene are readily controlled by magnetic field and influenced by the spin-orbit coupling effects, a combination leading to formation of linear unidirectional edge states in polariton topological insulators as predicted very recently. In this work we depart from the linear limit of non-interacting polaritons and predict instabilities of the nonlinear topological edge states resulting in formation of the localized topological quasi-solitons, which are exceptionally robust and immune to backscattering wavepackets propagating along the graphene lattice edge. Our results provide a background for experimental studies of nonlinear polariton topological insulators and can influence other subareas of photonics and condensed matter physics, where nonlinearities and spin-orbit effects are often important and utilized for applications.

We provide a unified framework for nonsignalling quantum and classical multipartite correlations, allowing all to be written as the trace of some local (quantum) measurements multiplied by an operator. The properties of this operator define the corresponding set of this http URL then show that if the theory is such that all local quantum measurements are possible, one obtains the correlations corresponding to the extension of Gleason's Theorem to multipartite systems. Such correlations coincide with the quantum ones for one and two parties, but we prove the existence of a gap for three or more parties.

Nonlinear optical phenomena such as parametric amplification and frequency conversion are typically driven by external optical fields. Free electrons can also act as electromagnetic sources, offering unmatched spatial precision. Combining optical and electron-induced fields via the nonlinear response of material structures therefore holds potential for revealing new physical phenomena and enabling disruptive applications. Here, we theoretically investigate wave mixing between external light and the evanescent fields of free electrons, giving rise to inelastic photon scattering mediated by the second-order nonlinear response of a specimen. Specifically, an incident photon may be blue- or red-shifted, while the passing electron correspondingly loses or gains energy. These processes are strongly enhanced when the frequency shift matches an optical resonance of the specimen. We present a general theoretical framework to quantify the photon conversion probability and demonstrate its application by revealing far-infrared vibrational fingerprints of retinal using only visible light. Beyond its fundamental interest, this phenomenon offers a practical approach for spatially mapping low-frequency excitations with nanometer resolution using visible photon energies and existing electron microscopes.

We derive, and experimentally demonstrate, an interferometric scheme for unambiguous phase estimation with precision scaling at the Heisenberg limit that does not require adaptive measurements. That is, with no prior knowledge of the phase, we can obtain an estimate of the phase with a standard deviation that is only a small constant factor larger than the minimum physically allowed value. Our scheme resolves the phase ambiguity that exists when multiple passes through a phase shift, or NOON states, are used to obtain improved phase resolution. Like a recently introduced adaptive technique [Higgins et al 2007 Nature 450 393], our experiment uses multiple applications of the phase shift on single photons. By not requiring adaptive measurements, but rather using a predetermined measurement sequence, the present scheme is both conceptually simpler and significantly easier to implement. Additionally, we demonstrate a simplified adaptive scheme that also surpasses the standard quantum limit for single passes.

It is virtually impossible to directly solve the Schrödinger equation for a many-electron wave function due to the exponential growth in degrees of freedom with increasing particle number. The two-body reduced density matrix (2-RDM) formalism reduces this coordinate dependence to that of four particles irrespective of the wave function's dimensionality, providing a promising path to solve the many-body problem. Unfortunately, errors arise in this approach because the 2-RDM cannot practically be constrained to guarantee that it corresponds to a valid wave function. Here we approach this so-called $N$-representability problem by expanding the 2-RDM in a complete basis of two-electron wave functions and studying the matrix formed by the expansion coefficients. This quantity, which we call the geminal density matrix (GDM), is found to evolve in time by a unitary transformation that preserves $N$-representability. This evolution law enables us to calculate eigenstates of strongly correlated systems by a fictitious adiabatic evolution in which the electron-electron interaction is slowly switched on. We show how this technique is used to diagonalize atomic Hamiltonians, finding that the problem reduces to the solution of $\sim N(N-1)/2$ two-electron eigenstates of the Helium atom on a grid of electron-electron interaction scaling factors.