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Recent studies have shown that quantum information may be effectively transmitted by a finite collection of completely depolarizing channels in a coherent superposition of different orders, via an operation known as the quantum $tt SWITCH$. Such results are quite remarkable, as completely depolarizing channels taken in isolation and in a definite order can only output white noise. For general channels however, little is known about the potential communication enhancement provided by the quantum $tt SWITCH$. In this Letter, we define an easily computable quantity $mathcal{P}_n$ associated with the quantum ${tt SWITCH}$ of $n$ copies of a fixed channel, and we conjecture that $mathcal{P}_n>0$ is both a necessary and sufficient condition for communication enhancement via the quantum $tt SWITCH$. In support of our conjecture, we derive a simple analytic expression for the classical capacity of the quantum $tt SWITCH$ of $n$ copies of an arbitrary Pauli channel in terms of the quantity $mathcal{P}_n$, which we then use to show that our conjecture indeed holds in the space of all Pauli channels. Utilizing such results, we then formulate a communication protocol involving the quantum $tt SWITCH$ which enhances the private capacity of the BB84 channel.

The Causaloid framework is an operational approach aimed to house both the radical aspects of General Relativity — dynamic causal structure, and Quantum Theory — indefiniteness, to provide a scaffolding that might be suitable for Quantum Gravity by providing a landscape of theories that allow for indefinite causal structure. One may consider it as a generalisation of generalised probability theories (or GPTs) where a priori regions are not assumed to have any given causal relationship, to incorporate the possibility of indefinite causal structure. Since its conception, there have been many advances in the field of indefinite causal structure mostly stemming from the work of Chiribella et al. on the quantum switch and supermaps and from Oreshkov et al. on causal inequalities and process matrices. These approaches have systems moving along wires and use Hilbert space structure. They violate the standard causality constraints of Quantum Theory and, in this sense, can be regarded as post-quantum. The Causaloid approach does not necessarily have systems moving along wires or Hilbert spaces. This is the first paper in a trilogy of papers aiming to close the gap between the Causaloid (that allows for GPTs) and post-quantum studies that employ Hilbert spaces. To do so in the present paper, we provide a diagrammatic language for the Causaloid framework along with new terminology for the three levels of physical compression (called Tomographic, Compositional, and Meta compression).

Artificial intelligence (AI) is currently based largely on black-box machine learning models which lack interpretability. The field of eXplainable AI (XAI) strives to address this major concern, being critical in high-stakes areas such as the finance, legal and health sectors. We present an approach to defining AI models and their interpretability based on category theory. For this we employ the notion of a compositional model, which sees a model in terms of formal string diagrams which capture its abstract structure together with its concrete implementation. This comprehensive view incorporates deterministic, probabilistic and quantum models. We compare a wide range of AI models as compositional models, including linear and rule-based models, (recurrent) neural networks, transformers, VAEs, and causal and DisCoCirc models. Next we give a definition of interpretation of a model in terms of its compositional structure, demonstrating how to analyse the interpretability of a model, and using this to clarify common themes in XAI. We find that what makes the standard ‘intrinsically interpretable’ models so transparent is brought out most clearly diagrammatically. This leads us to the more general notion of compositionally-interpretable (CI) models, which additionally include, for instance, causal, conceptual space, and DisCoCirc models. We next demonstrate the explainability benefits of CI models. Firstly, their compositional structure may allow the computation of other quantities of interest, and may facilitate inference from the model to the modelled phenomenon by matching its structure. Secondly, they allow for diagrammatic explanations for their behaviour, based on influence constraints, diagram surgery and rewrite explanations. Finally, we discuss many future directions for the approach, raising the question of how to learn such meaningfully structured models in practice.

Time-reversal symmetry is a prevalent feature of microscopic physics, including operational quantum theory and classical general relativity. Previous works have studied indefinite causal structure using the language of operational quantum theory, however, these rely on time-asymmetric conditions to constrain both operations and the process matrix. Here, we use time-symmetric, operational probabilistic theory to develop a time-symmetric process matrix formalism for indefinite causal structure. This framework allows for more processes than previously considered and a larger set of causal inequalities. We demonstrate that this larger set of causal inequalities offers new opportunities for device-independent certification of causal non-separability by violating new inequalities. Additionally, we determined that the larger class of time-symmetric processes found here is equivalent to those with Indefinite Causal Order and Time Direction (ICOTD) considered by Chiribella and Liu, thereby providing a description of these processes in terms of process matrices.

Recent work on quantum reference frames (QRFs) has demonstrated that superposition and entanglement are properties that change under QRF transformations. Given their utility in quantum information processing, it is important to understand how a mere change of perspective can produce or reduce these resources. Here we find a trade-off between entanglement and subsystem coherence under a QRF transformation, in the form of a conservation theorem for their sum, for two pairs of measures. Moreover, we find a weaker trade-off for any possible pair of measures. Finally, we discuss the implications of this interplay for violations of Bell’s inequalities, clarifying that for any choice of QRF, there is a quantum resource responsible for the violation. These findings contribute to a better understanding of the quantum information theoretic aspects of QRFs, offering a foundation for future exploration in both quantum theory and quantum gravity.

We show that finite physical clocks always have well-behaved signals, namely that every waiting-time distribution generated by a physical process on a system of finite size is guaranteed to be bounded by a decay envelope. Following this consideration, we show that one can reconstruct the distribution using only operationally available information, namely, that of the ordering of the ticks of one clock with the respect to those of another clock (which we call the reference), and that the simplest possible reference clock — a Poisson process — suffices.

Observing spatial entanglement in the Bose-Marletto-Vedral (BMV) experiment would demonstrate the existence of non-classical properties of the gravitational field. We show that the special relativistic invariance of the linear regime of general relativity implies that all the components of the gravitational potential must be non-classical. This is simply necessary in order to describe the BMV entanglement consistently across different inertial frames of reference. On the other hand, we show that the entanglement in accelerated frames could differ from that in stationary frames.

Motivated by recent advances in non-Lorentzian physics, we revisit the light-cone formulation of quantum field theories. We discuss some interesting subalgebras within the light-cone Poincar’e algebra, with a key emphasis on the Carroll, Bargmann, and Galilean kinds. We show that theories on the light front possess a Hamiltonian of the magnetic Carroll type, thereby proposing a straightforward method for deriving magnetic Carroll Hamiltonian actions from Lorentzian field theories.

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.

Quantum homogenization is a reservoir-based quantum state approximation protocol, which has been successfully implemented in state transformation on quantum hardware. In this work we move beyond that and propose the homogenization as a novel platform for quantum state stabilization and information protection. Using the Heisenberg exchange interactions formalism, we extend the standard quantum homogenization protocol to the dynamically equivalent (SWAP) formulation. We then demonstrate its applicability on the available noisy intermediate-scale quantum (NISQ) processors by presenting a shallow quantum circuit implementation consisting of a sequence of cnot and single-qubit gates. In light of this, we employ the Beny-Oreshkov generalization of the Knill-Laflamme (KL) conditions for near-optimal recovery channels to show that our proposed (SWAP) quantum homogenization protocol yields a completely positive, trace-preserving (CPTP) map under which the code subspace is correctable. Therefore, the protocol protects quantum information contained in a subsystem of the reservoir Hilbert space under CPTP dynamics.