We propose an operational definition of complementarity, pinning down the concept originally introduced by Bohr. Two properties of a system are considered complementary if they cannot be simultaneously well defined. We further show that, within quantum theory, this notion is equivalent to the incompatibility of operations -- that is, their inability to be performed simultaneously.

Quarks and gluon, as quantum particles, are subjects to various effects that go beyond the naive parton picture and are not captured by ordinary parton densities. In this work, we investigate the twist-three parton distribution functions, which encode quantum interference between quark-gluon-quark states, and for the first time, determine them directly from experimental data. The analysis combines observables described by collinear and transverse-momentum-dependent factorization theorems within a unified global fit, incorporating a complete leading-order QCD evolution at the twist-three level. The extracted distributions reveal a clear flavor-dependent patterns and distinct from zero at a statistically significant level ($2-3\sigma$). These findings provide the first quantitative evidence for quark-gluon-quark correlations within the proton, revealing its genuinely quantum nature and opening a new direction for precision studies of partonic correlations.

Quantum thermometry aims at determining temperature with ultimate precision in the quantum regime. Standard equilibrium approaches, limited by the Quantum Fisher Information given by static energy fluctuations, lose sensitivity outside a fixed temperature window. Non-equilibrium strategies have therefore been recently proposed to overcome these limits, but their advantages are typically model-dependent or tailored for a specific purpose. This Letter establishes a general, model-independent result showing that any temperature-dependent unitary driving applied to a thermalized probe enhances its quantum Fisher information with respect to its equilibrium value. Such information gain is expressed analytically through a positive semi-definite kernel of information currents that quantify the flow of statistical distinguishability. Our results are benchmarked on a driven spin-$1/2$ thermometer, furthermore showing that resonant modulations remarkably restore the quadratic-in-time scaling of the Fisher information and allow to shift the sensitivity peak across arbitrary temperature ranges. Our findings identify external unitary control as a universal resource for precision metrology and pave the way for future implementations in quantum sensing.

We address the problem of constructing fundamental solutions and Hadamard states for a Klein-Gordon field in half-Minkowski spacetime with Robin boundary conditions in $d \geq 2$ spacetime dimensions. First, using a generalisation of the Robin-to-Dirichlet map exploited by Bondurant and Fulling [J. Phys. A: Math. Theor. {\bf 38} 7 (2005)] in dimension $2$, we obtain a representation for the advanced and retarded Green operators in terms of a convolution with the kernel of the inverse Robin-to-Dirichlet map. This allows us to prove the uniqueness and support properties of the Green operators. Second, we obtain a local representation for the Hadamard parametrix that provides the correct local definition of Hadamard states in $d \geq 2$ dimensions, capturing `reflected' singularities from the spacetime boundary. We show that our fundamental solutions abide by this local parametrix representation. Finally, we prove the equivalence of our local Hadamard condition and the global Hadamard condition with a wave-front set described in terms of generalized broken bi-characteristics, obtaining a Radzikowski-like theorem in half-Minkowski spacetime.

After proving a general no-cloning theorem for black boxes, we derive the optimal universal cloning of unitary transformations, from one to two copies. The optimal cloner is realized by quantum channels with memory, and greately outperforms the optimal measure-and-reprepare cloning strategy. Applications are outlined, including two-way quantum cryptographic protocols.

We review and examine in detail recent developments regarding the question of the nucleon mass decomposition. We discuss in particular the virial theorem in quantum field theory and its implications for the nucleon mass decomposition and mechanical equilibrium. We reconsider the renormalization of the QCD energy-momentum tensor in minimal-subtraction-type schemes and the physical interpretation of its components, as well as the role played by the trace anomaly and Poincar\'e symmetry. We also study the concept of "quantum anomalous energy" proposed in some works as a new contribution to the nucleon mass. Examining the various arguments, we conclude that the quantum anomalous energy is not a genuine contribution to the mass sum rule, as a consequence of translation symmetry.

The certification of randomness is essential for both fundamental science and information technologies. Unlike traditional random number generators, randomness obtained from nonlocal correlations is fundamentally guaranteed to be unpredictable. However, it is also highly susceptible to noise. Here, we show that extending the conventional bipartite Bell scenario to hybrid quantum networks -- which incorporate both quantum channels and entanglement sources -- enhances the robustness of certifiable randomness. Our protocol even enables randomness to be certified from Bell-local states, broadening the range of quantum states useful for this task. Through both theoretical analysis and experimental validation in a photonic network, we demonstrate enhanced performance and improved noise resilience.

The dSphs around the Milky Way are commonly considered as systems that are supported by velocity dispersion against self-gravitation. They have been long accounted among the best targets to search for indirect DM signatures in the GeV-to-TeV gamma-rays due to absence of astrophysical gamma-ray foreground or background emission. We present forecasts on the sensitivity of the future CTAO for the search for annihilating or decaying DM in such targets. We perform an original selection of candidates out of the current catalog of known objects, including both classical and ultra-faint targets. For each of them, we calculate the expected amount of DM using the most updated and complete available samples of photometric and spectroscopic data of member stars, adopting a common framework of data treatment for both classes of objects. In this way, we are able to generate novel astrophysical factor profiles for general indirect DM searches that we compare with the current literature. Out of a starting sample of 64 dSphs, we highlight the 8 most promising targets - DraI, CBe, UMaII, UMi and Wil1 in the Northern hemisphere; RetII, Scl and SgrII in the Southern hemisphere - for which different DM density models (either cored or cuspy) lead to similar expectations, at variance with what happens for other DM targets - thus resulting in more robust predictions. We find that CTAO will provide the strongest limits above ~10 TeV, down to values of velocity-averaged annihilation cross section of ~5$\times 10^{-25}$ cm$^3$ s$^{-1}$ and up to decay lifetimes of ~10$^{26}$ s for combined limits on the best targets. We argue that the largest source of inaccuracy is due to the still imprecise determination of the DM content, especially for ultra-faint dSphs. We propose possible strategies of observation for CTAO, either optimized on a deep focus on the best known candidates, or on the diversification of targets.

Randomness certification is a foundational and practical aspect of quantum information science, essential for securing quantum communication protocols. Traditionally, these protocols have been implemented and validated with a single entanglement source, as in the paradigmatic Bell scenario. However, advancing these protocols to support more complex configurations involving multiple entanglement sources is key to building robust architectures and realizing large-scale quantum networks. In this work, we show how to certify randomness in an entanglement-teleportation experiment, the building block of a quantum repeater displaying two independent sources of entanglement. Utilizing the scalar extension method, we address the challenge posed by the non-convexity of the correlation set, providing effective bounds on an eavesdropper's knowledge of the shared secret bits. Our theoretical model characterizes the certifiable randomness within the network and is validated through the analysis of experimental data from a photonic quantum network.

We present an experimental scheme that achieves ideal phase detection on a two-mode field. The two modes $a$ and $b$ are the signal and image band modes of an heterodyne detector, with the field approaching an eigenstate of the photocurrent $\hat{Z}=a+b^†$. The field is obtained by means of a high-gain phase-insensitive amplifier followed by a high-transmissivity beam-splitter with a strong local oscillator at the frequency of one of the two modes.

This White Paper is exploring the potential of intense secondary muon, neutrino, and (hypothetical) light dark matter beams produced in interactions of high-intensity electron beams with beam dumps. Light dark matter searches with the approved Beam Dump eXperiment (BDX) are driving the realization of a new underground vault at Jefferson Lab that could be extended to a Beamdump Facility with minimal additional installations. The paper summarizes contributions and discussions from the International Workshop on Secondary Beams at Jefferson Lab (BDX & Beyond). Several possible muon physics applications and neutrino detector technologies for Jefferson Lab are highlighted. The potential of a secondary neutron beam will be addressed in a future edition.

We describe an algorithm that constructs a list of all topological types of holomorphic actions of a finite group on a compact Riemann surface $C$ of genus at least $g \geq 2$ with $C/G \cong \mathbb{P}^1$.

JUNO is a massive liquid scintillator detector with a primary scientific goal of determining the neutrino mass ordering by studying the oscillated anti-neutrino flux coming from two nuclear power plants at 53 km distance. The expected signal anti-neutrino interaction rate is only 60 counts per day, therefore a careful control of the background sources due to radioactivity is critical. In particular, natural radioactivity present in all materials and in the environment represents a serious issue that could impair the sensitivity of the experiment if appropriate countermeasures were not foreseen. In this paper we discuss the background reduction strategies undertaken by the JUNO collaboration to reduce at minimum the impact of natural radioactivity. We describe our efforts for an optimized experimental design, a careful material screening and accurate detector production handling, and a constant control of the expected results through a meticulous Monte Carlo simulation program. We show that all these actions should allow us to keep the background count rate safely below the target value of 10 Hz in the default fiducial volume, above an energy threshold of 0.7 MeV.

Resistive Plate Chambers detectors are extensively used in several domains of Physics. In High Energy Physics, they are typically operated in avalanche mode with a high-performance gas mixture based on Tetrafluoroethane (C2H2F4), a fluorinated high Global Warming Potential greenhouse gas. The RPC EcoGas@GIF++ Collaboration has pursued an intensive R\&D activity to search for new gas mixtures with low environmental impact, fulfilling the performance expected for the LHC operations as well as for future and different applications. Here, results obtained with new eco-friendly gas mixtures based on Tetrafluoropropene and carbon dioxide, even under high-irradiation conditions, will be presented. Long-term aging tests carried out at the CERN Gamma Irradiation Facility will be discussed along with their possible limits and future perspectives.

We consider a four-dimensional globally hyperbolic spacetime $(M,g)$ conformal to Minkowski spacetime, together with a massless, conformally coupled scalar field. Using a bulk-to-boundary correspondence, one can establish the existence of an injective $*$-homomorphism $\Upsilon_M$ between $\mathcal{W}(M)$, the Weyl algebra of observables on $M$ and a counterpart which is defined intrinsically on future null infinity $\Im^+\simeq\mathbb{R}\times\mathbb{S}^2$, a component of the conformal boundary of $(M,g)$. Using invariance under the asymptotic symmetry group of $\Im^+$, we can individuate thereon a distinguished two-point correlation function whose pull-back to $M$ via $\Upsilon_M$ identifies a quasi-free Hadamard state for the bulk algebra of observables. In this setting, if we consider $\mathsf{V}^+_x$, a future light cone stemming from $x\in M$ as well as $\mathcal{W}(\mathsf{V}^+_x)=\mathcal{W}(M)|_{\mathsf{V}^+_x}$, its counterpart at the boundary is the Weyl subalgebra generated by suitable functions localized in $\mathsf{K}_x$, a positive half strip on $\Im^+$. To each such cone, we associate a standard subspace of the boundary one-particle Hilbert space, which coincides with the one associated naturally to $\mathsf{K}_x$. We extend such correspondence replacing $\mathsf{K}_x$ and $\mathsf{V}^+_x$ with deformed counterparts, denoted by $\mathsf{S}_C$ and $\mathsf{V}_C$. In addition, since the one particle Hilbert space at the boundary decomposes as a direct integral on the sphere of $U(1)$-currents defined on the real line, we prove that also the generator of the modular group associated to the standard subspace of $\mathsf{V}_C$ decomposes as a suitable direct integral. This result allows us to study the relative entropy between coherent states of the algebras associated to the deformed cones $\mathsf{V}_C$ establishing the quantum null energy condition.

Finding the solution to linear systems is at the heart of many applications in science and technology. Over the years a number of algorithms have been proposed to solve this problem on a digital quantum device, yet most of these are too demanding to be applied to the current noisy hardware. In this work, an original algorithmic procedure to solve the Quantum Linear System Problem (QLSP) is presented, which combines ideas from Variational Quantum Algorithms (VQA) and the framework of classical shadows. The result is the Shadow Quantum Linear Solver (SQLS), a quantum algorithm solving the QLSP avoiding the need for large controlled unitaries, requiring a number of qubits that is logarithmic in the system size. In particular, our heuristics show an exponential advantage of the SQLS in circuit execution per cost function evaluation when compared to other notorious variational approaches to solving linear systems of equations. We test the convergence of the SQLS on a number of linear systems, and results highlight how the theoretical bounds on the number of resources used by the SQLS are conservative. Finally, we apply this algorithm to a physical problem of practical relevance, by leveraging decomposition theorems from linear algebra to solve the discretized Laplace Equation in a 2D grid for the first time using a hybrid quantum algorithm.

Efficient ways to prepare fermionic ground states on quantum computers are in high demand and different techniques have been developed over the last years. Despite having a vast set of methods, it is still unclear which method performs well for which system. In this work, we combine interpretable circuit designs with an effective basis approach in order to optimize a multiconfigurational valence bond wavefunction. Based on selected model systems, we show how this leads to explainable performance. We demonstrate that the developed methodology outperforms related methods in terms of the size of the effective basis as well as individual quantum resources for the involved circuits.

Quantum metrology, a cornerstone of quantum technologies, exploits entanglement and superposition to achieve higher precision than classical protocols in parameter estimation tasks. When combined with critical phenomena such as phase transitions, the divergence of quantum fluctuations is predicted to enhance the performance of quantum sensors. Here, we implement a critical quantum sensor using a superconducting parametric (i.e., two-photon driven) Kerr resonator. The sensor, a linear resonator terminated by a supercondicting quantum interference device, operates near the critical point of a finite-component second-order dissipative phase transition obtained by scaling the system parameters. We analyze the performance of a frequency-estimation protocol and show that quadratic precision scaling with respect to the system size can be achieved with finite values of the Kerr nonlinearity. Since each photon emitted from the cavity carries more information about the parameter to be estimated compared to its classical counterpart, our protocol opens perspectives for faster or more precise metrological protocols. Our results demonstrate that quantum advantage in a sensing protocol can be achieved by exploiting a finite-component phase transition.

We present a tomographic protocol for the characterization of multiqubit quantum channels. We discuss a specific class of input states, for which the set of Pauli measurements at the output of the channel directly relates to its Pauli transfer matrix components. We compare our results to those of standard quantum process tomography, showing an exponential reduction in the number of different experimental configurations required by a single matrix element extraction, while keeping the same number of shots. This paves the way for more efficient experimental implementations, whenever a selective knowledge of the Pauli transfer matrix is needed. We provide several examples and simulations.

Owing to their exceptional chemical and electronic tunability, metal-organic frameworks can be designed to develop magnetic ground states making a range of applications feasible, from magnetic gas separation to the implementation of lightweight, rare-earth free permanent magnets. However, the typically weak exchange interactions mediated by the diamagnetic organic ligands result in ordering temperatures confined to the cryogenic limit. The itinerant magnetic ground state realized in the chromium-based framework Cr(tri)$_{2}$(CF$_{3}$SO$_{3}$)$_{0.33}$ (Htri, $1H$-$1$,$2$,$3$-triazole) is a remarkable exception to this trend, showing a robust ferromagnetic behavior almost at ambient conditions. Here, we use dc SQUID magnetometry, nuclear magnetic resonance, and ferromagnetic resonance to study the magnetic state realized in this material. We highlight several thermally-activated relaxation mechanisms for the nuclear magnetization due to the tendency of electrons towards localization at low temperatures as well as the rotational dynamics of the charge-balancing triflate ions confined within the pores. Most interestingly, we report the development within the paramagnetic regime of mesoscopic magnetic correlated clusters whose slow dynamics in the MHz range are tracked by the nuclear moments, in agreement with the highly unconventional nature of the magnetic transition detected by dc SQUID magnetometry. We discuss the similarity between the clustered phase in the paramagnetic phase and the magnetoelectronic phase segregation leading to colossal magnetoresistance in manganites and cobaltites. These results demonstrate that high-temperature magnetic metal-organic frameworks can serve as a versatile platform for exploring correlated electron phenomena in low-density, chemically tunable materials.