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In this paper, we present a comprehensive toolbox for studying Carrollian stretched horizons, encompassing their geometry, dynamics, symplectic geometry, symmetries, and corresponding Noether charges. We introduce a precise definition of ruled stretched Carrollian structures (sCarrollian structures) on any surface, generalizing the conventional Carrollian structures of null surfaces, along with the notions of sCarrollian connection and sCarrollian stress tensor. Our approach unifies the sCarrollian (intrinsic) and stretched horizon (embedding) perspectives, providing a universal framework for any causal surface, whether timelike or null. We express the Einstein equations in sCarrollian variables and discuss the phase space symplectic structure of the sCarrollian geometry. Through Noether’s theorem, we derive the Einstein equation and canonical charge and compute the evolution of the canonical charge along the transverse (radial) direction. The latter can be interpreted as a spin-2 symmetry charge. Our framework establishes a novel link between gravity on stretched horizons and Carrollian fluid dynamics and unifies various causal surfaces studied in the literature, including non-expanding and isolated horizons. We expect this work to provide insights into the hydrodynamical description of black holes and the quantization of null surfaces.

A catalysis state is a quantum state that is used to make some desired operation possible or more efficient, while not being consumed in the process. Recent years have seen catalysis used in state-of-the-art protocols for implementing magic state distillation or small angle phase rotations. In this paper we will see that we can also use catalysis to prove that certain gate sets are computationally universal, and to extend completeness results of graphical languages to larger fragments. In particular, we give a simple proof of the computational universality of the CS+Hadamard gate set using the catalysis of a $T$ gate using a CS gate, which sidesteps the more complicated analytic arguments of the original proof by Kitaev. This then also gives us a simple self-contained proof of the computational universality of Toffoli+Hadamard. Additionally, we show that the phase-free ZH-calculus can be extended to a larger complete fragment, just by using a single catalysis rule (and one scalar rule).

We study extensions of the mappings arising in usual Channel-State duality to the case of Hilbert spaces with a direct sum structure. This setting arises in representations of algebras with centers, which are commonly associated with constraints, and it has many physical applications from quantum many-body theory to holography and quantum gravity. We establish that there is a general relationship between non-separability of the state and the isometric properties of the induced channel. We also provide a generalisation of our approach to algebras of trace-class operators on infinite dimensional Hilbert spaces.

Trends of genuine entanglement in Haar uniformly generated multimode pure Gaussian states with fixed average energy per mode are explored. A distance-based metric known as the generalized geometric measure (GGM) is used to quantify genuine entanglement. The GGM of a state is defined as its minimum distance from the set of all non-genuinely entangled states. To begin with, we derive an expression for the Haar averaged value of any function defined on the set of energy-constrained states. Subsequently, we investigate states with a large number of modes and provide a closed-form expression for the Haar averaged GGM in terms of the average energy per mode. Furthermore, we demonstrate that typical states closely approximate their Haar averaged GGM value, with deviation probabilities bounded by an exponentially suppressed limit. We then analyze the GGM content of typical states with a finite number of modes and present the distribution of GGM. Our findings indicate that as the number of modes increases, the distribution shifts towards higher entanglement values and becomes more concentrated. We quantify these features by computing the Haar averaged GGM and the standard deviation of the GGM distribution, revealing that the former increases while the latter decreases with the number of modes.

The $mathrm{Caus}[-]$ construction takes a base category of “raw materials” and builds a category of higher order causal processes, that is a category whose types encode causal (a.k.a. signalling) constraints between collections of systems. Notable examples are categories of higher-order stochastic maps and higher-order quantum channels. Well-typedness in $mathrm{Caus}[-]$ corresponds to a composition of processes being causally consistent, in the sense that any choice of local processes of the prescribed types yields an overall process respecting causality constraints. It follows that closed processes always occur with probability 1, ruling out e.g. causal paradoxes arising from time loops. It has previously been shown that $mathrm{Caus}[mathcal{C}]$ gives a model of MLL+MIX and BV logic, hence these logics give sufficient conditions for causal consistency, but they fail to provide a complete characterisation. In this follow-on work, we introduce graph types as a tool to examine causal structures over graphs in this model. We explore their properties, standard forms, and equivalent definitions; in particular, a process obeys all signalling constraints of the graph iff it is expressible as an affine combination of factorisations into local causal processes connected according to the edges of the graph. The properties of graph types are then used to prove completeness for causal consistency of a new causal logic that conservatively extends pomset logic. The crucial extra ingredient is a notion of distinguished atoms that correspond to first-order states, which only admit a flow of information in one direction. Using the fact that causal logic conservatively extends pomset logic, we finish by giving a physically-meaningful interpretation to a separating statement between pomset and BV.

What does it mean for a causal structure to be `unknown’? Can we even talk about `repetitions’ of an experiment without prior knowledge of causal relations? And under what conditions can we say that a set of processes with arbitrary, possibly indefinite, causal structure are independent and identically distributed? Similar questions for classical probabilities, quantum states, and quantum channels are beautifully answered by so-called “de Finetti theorems”, which connect a simple and easy-to-justify condition — symmetry under exchange — with a very particular multipartite structure: a mixture of identical states/channels. Here we extend the result to processes with arbitrary causal structure, including indefinite causal order and multi-time, non-Markovian processes applicable to noisy quantum devices. The result also implies a new class of de Finetti theorems for quantum states subject to a large class of linear constraints, which can be of independent interest.

In this Letter, we introduce a notion of local fraction for experiments taking place against arbitrary static causal backgrounds—greatly generalising previous results on no-signalling scenarios—and we explicitly formulate a linear program to compute this quantity. We derive a free characterisation of causal functions which allows us to efficiently construct the matrices required to perform concrete calculations. We demonstrate our techniques by analysing the local fraction of a novel example involving two Bell tests in interleaved causal order.

Recent progress in table-top experiments offers the opportunity to show for the first time that gravity is not compatible with a classical description. In all current experimental proposals, such as the generation of gravitationally induced entanglement between two quantum sources of gravity, gravitational effects can be explained with the Newton potential, namely in a regime that is consistent with the weak-field limit of general relativity and does not probe the field nature of gravity. Hence, the Newtonian origin of the effects is a limitation to the conclusions on the nature of gravity that can be drawn from these experiments. Here, we identify two effects that overcome this limitation: they cannot be reproduced using the Newton potential and are independent of graviton emission. First, we show that the interaction between a generic quantum source of gravity, e.g. in a wide Gaussian state, and a test particle cannot be reproduced with the Newton potential nor with a known classical theory or gravity. Hence, observing the form of this interaction would require either a modification to classical gravity or its quantum description. Second, we show that the quantum commutator between the gravitational field and its canonically conjugate momentum appears as an additional term in the relative phase of a generic quantum source interacting with a test particle. Observing this term in the phase would be a test of the gravitational field as a quantum mediator. Identifying stronger quantum aspects of gravity than those reproducible with the Newton potential is crucial to prove the nonclassicality of the gravitational field and to plan a new generation of experiments testing quantum aspects of gravity in a broader sense than what proposed so far.

Information-theoretic insights have proven fruitful in many areas of quantum physics. But can the fundamental dynamics of quantum systems be derived from purely information-theoretic principles, without resorting to Hilbert space structures such as unitary evolution and self-adjoint observables? Here we provide a model where the dynamics originates from a condition of informational non-equilibrium, the deviation of the system’s state from a reference state associated to a field of identically prepared systems. Combining this idea with three basic information-theoretic principles, we derive a notion of energy that captures the main features of energy in quantum theory: it is observable, bounded from below, invariant under time-evolution, in one-to-one correspondence with the generator of the dynamics, and quantitatively related to the speed of state changes. Our results provide an information-theoretic reconstruction of the Mandelstam-Tamm bound on the speed of quantum evolutions, establishing a bridge between dynamical and information-theoretic notions.

The study of quantum reference frames (QRFs) is motivated by the idea of taking into account the quantum properties of the reference frames that we use, explicitly or implicitly, in our description of physical systems. Like a classical reference frame, a QRF can be used to define physical quantities such as time, position, momentum, and spin relationally. Unlike its classical analogue, it relativises the notions of superposition and entanglement. Here, we provide a novel explanation for the frame-dependence of superposition and entanglement by tracing it back to the question of how configurations or locations are identified across different branches in superposition. We show that, in the presence of symmetries, whether a system is in ‘the same’ or ‘different’ configurations across the branches depends on the choice of QRF. Thus, sameness and difference-and, as a result, superposition and entanglement-lose their absolute meaning. We apply these ideas to semi-classical spacetimes in superposition and use coincidences of four scalar fields to construct a comparison map between the spacetime points in the different branches. This allows us to determine whether a given event is located at ‘the same’ or ‘different’ points in the superposed spacetimes. Since this feature depends on the choice of QRF, we argue that the localisation of an event should not be seen as an inherent property. This alleviates previously voiced concerns that QRF changes could have empirical consequences for interference experiments, such as the BMV proposal. Moreover, it implies that the number of events is equal in both the flat and the curved spacetime implementations of indefinite causal order. We conclude with the ‘quantum hole argument’ as a generalisation of Einstein’s hole argument, arguing that not just spacetime points but also their identification across a superposition lose their absolute physical meaning.