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Uhlmann’s theorem states that, for any two quantum states $rho_{AB}$ and $sigma_A$, there exists an extension $sigma_{AB}$ of $sigma_A$ such that the fidelity between $rho_{AB}$ and $sigma_{AB}$ equals the fidelity between their reduced states $rho_A$ and $sigma_A$. In this work, we generalize Uhlmann’s theorem to $alpha$-R’enyi relative entropies for $alpha in [frac{1}{2},infty]$, a family of divergences that encompasses fidelity, relative entropy, and max-relative entropy corresponding to $alpha=frac{1}{2}$, $alpha=1$, and $alpha=infty$, respectively.

Optomechanical systems subjected to environmental noise give rise to rich physical phenomena. We investigate entanglement between a mechanical oscillator and the reflected coherent optical field in a general, not necessarily Markovian environment. For the input optical field, we consider stationary Gaussian states and frequency dependent squeezing. We demonstrate that for a coherent laser drive, either unsqueezed or squeezed in a frequency-independent manner, optomechanical entanglement is destroyed after a threshold that depends only on the environmental noises — independent of the coherent coupling between the oscillator and the optical field, or the squeeze factor. In this way, we have found a universal entangling-disentangling transition. We also show that for a configuration in which the oscillator and the reflected field are separable, entanglement cannot be generated by incorporating frequency-dependent squeezing in the optical field.

We study an optomechanical system, where a mechanical oscillator interacts with a Gaussian input optical field. In the linearized picture, we analytically prove that if the input light field is the vacuum state, or is frequency-independently squeezed, the stationary entanglement between the oscillator and the output optical field is independent of the coherent coupling between them, which we refer to as the universality of entanglement. Furthermore, we demonstrate that entanglement cannot be generated by performing arbitrary frequency-dependent squeezing on the input optical field. Our results hold in the presence of general, Gaussian environmental noise sources, including non-Markovian noise.

Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories (SMCs). However, various generalizations, including time-neutral, higher-order, and enriched process theories, do not naturally conform to this structure. In this work, we propose an alternative formalization using operad algebras, motivated by recent results connecting SMCs to operadic structures, which captures a broader class of process theories. By leveraging the string-diagrammatic language, we provide an accessible yet rigorous formulation that unifies and extends traditional process-theoretic approaches. Our operadic framework not only recovers standard process theories as a special case but also enables new insights into quantum foundations and compositional structures. This work paves the way for further investigations into the algebraic and operational properties of generalised process theories within an operadic setting.

We address the classical limit of quantum mechanics, focusing on its emergence through coarse-grained measurements when multiple outcomes are conflated into slots. We rigorously derive effective classical kinematics under such measurements, demonstrating that when the volume of the coarse-grained slot in phase space significantly exceeds Planck’s constant, quantum states can be effectively described by classical probability distributions. Furthermore, we show that the dynamics, derived under coarse-grained observations and the linear approximation of the quantum Hamiltonian around its classical values within the slots, is effectively described by a classical Hamiltonian following Liouville dynamics. The classical Hamiltonian obtained through this process is equivalent to the one from which the underlying quantum Hamiltonian is derived via the (Dirac) quantization procedure, completing the quantization-classical limit loop. The Ehrenfest time, marking the duration within which classical behavior remains valid, is analyzed for various physical systems. The implications of these findings are discussed in the context of both macroscopic and microscopic systems, revealing the mechanisms behind their observed classicality. This work provides a comprehensive framework for understanding the quantum-to-classical transition and addresses foundational questions about the consistency of the quantization-classical limit cycle.

In standard quantum theory, the causal relations between operations are fixed. One can relax this notion by allowing for dynamical arrangements, where operations may influence the causal relations of future operations, as certified by violation of fixed-order inequalities, e.g., the k-cycle inequalities. Another, non-causal, departure further relaxes these limitations, and is certified by violations of causal inequalities. In this paper, we explore the interplay between dynamic and indefinite causality. We study the k-cycle inequalities and show that the quantum switch violates these inequalities without exploiting its indefinite nature. We further introduce non-adaptive strategies, which effectively remove the dynamical aspect of any process, and show that the k-cycle inequalities become ovel causal inequalities; violating k-cycle inequalities under the restriction of non-adaptive strategies requires non-causal setups. The quantum switch is known to be incapable of violating causal inequalities, and it is believed that a device-independent certification of its causal indefiniteness requires extended setups incorporating spacelike separation. This work reopens the possibility for a device-independent certification of the quantum switch in isolation via fixed-order inequalities instead of causal inequalities. The inequalities we study here, however, turn out to be unsuitable for such a device-independent certification.

Boundaries in gauge theory and gravity give rise to symmetries and charges at both finite and asymptotic distance. Due to their structural similarities, it is often held that soft modes are some kind of asymptotic limit of edge modes. Here, we show in Maxwell theory that there is an arguably more interesting relationship between the emph{asymptotic} symmetries and their charges, on one hand, and their emph{finite-distance} counterparts, on the other, without the need of a limit. Key to this observation is to embed the finite region in the global spacetime and identify edge modes as dynamical $rm{U}(1)$-reference frames for dressing subregion variables. Distinguishing emph{intrinsic} and emph{extrinsic} frames, according to whether they are built from field content in- or outside the region, we find that non-trivial corner symmetries arise only for extrinsic frames. Further, the asymptotic-to-finite relation requires asymptotically charged ones (like Wilson lines). Such frames, called emph{soft edges}, extend to asymptotia and realize the corner charge algebra by “pulling in” the asymptotic one from infinity. Realizing an infinite-dimensional algebra requires a new set of emph{soft boundary conditions}, relying on the distinction between extrinsic and intrinsic data. We identify the subregion Goldstone mode as the relational observable between extrinsic and intrinsic frames and clarify the meaning of vacuum degeneracy. We also connect the asymptotic memory effect with a more operational emph{quasi-local} one. A main conclusion is that the relationship between asymptotia and finite distance is emph{frame-dependent}; each choice of soft edge mode probes distinct cross-boundary data of the global theory. Our work combines the study of boundary symmetries with the program of dynamical reference frames and we anticipate that core insights extend to Yang-Mills theory and gravity.

Multipartite entanglement is a valuable resource for quantum technologies. However, detecting this resource can be challenging: for genuine multipartite entanglement, the detection may require global measurements that are hard to implement experimentally. Here we introduce the concept of entanglement detection length, defined as the minimum number of particles that have to be jointly measured in order to detect genuine multipartite entanglement. For symmetric states, we show that the entanglement detection length can be determined by testing separability of the marginal states. For general states, we provide an upper bound on the entanglement detection length based on semidefinite programming. We show that the entanglement detection length is generally smaller than the minimum observable length needed to uniquely determine a multipartite state, and we provide examples achieving the maximum gap between these two quantities.

We revisit the formalism of $text{T}overline{text{T}}$ deformations for quantum theories that are holographically dual to two-dimensional dilaton-gravity theories with Dirichlet boundary conditions. To better understand the microscopics of de Sitter space, we focus on deformations for which the dual bulk geometry flows from Anti-de Sitter to de Sitter space. We explore two distinct ways to achieve this: either through so-called centaur geometries that interpolate between AdS$_2$ and dS$_2$, or by a spherical dimensional reduction of $text{T}overline{text{T}} + Lambda_2$ theories that were proposed to give a microscopic interpretation of three-dimensional de Sitter entropy. We derive the microscopic energy spectrum, heat capacities, and deformed Cardy expressions for the thermodynamic entropy in the canonical and microcanonical ensembles for these two setups. In both setups a signature of the change from AdS to dS is that the heat capacity at a fixed deformation parameter of the boundary system changes sign, indicating the existence of a thermodynamically unstable de Sitter patch. Our findings provide important consistency conditions for holographic models of the dS$_2$ static patch.

Einstein’s general theory of relativity is based on the principle of equivalence – in essence, dating back to Galileo – which asserts that, locally, the effect of a gravitational field is equivalent to that of an accelerating reference frame, so that the local gravitational field is eliminated in a freely-falling frame. Einstein’s theory enables this principle to extend to a global description of relativistic space-time, at the expense of allowing space-time to become curved, realising a consistent frame-independent description of nature at the classical level. Einstein’s theory has been confirmed to great accuracy for astrophysical bodies. However, in the quantum domain the equivalence principle has been predicted to take a unique form involving a gauge phase that is observable if the wavefunction – fundamental to quantum descriptions – allows an object to interfere with itself after being simultaneously at rest in two differently accelerating frames, one being the laboratory (Newtonian) frame and the other in the freely-falling (Einsteinian) frame. To measure this gauge phase we realise a novel cold-atom interferometer in which one wave packet stays static in the laboratory frame while the other is in free fall. We follow the relative-phase evolution of the wave packets in the two frames, confirming the equivalence principle in the quantum domain. Our observation is yet another fundamental test of the interface between quantum theory and gravity. The new interferometer also opens the door for further probing of the latter interface, as well as to searches for new physics.