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We propose terminology to classify interpretations of quantum mechanics and models that modify or complete quantum mechanics. Our focus is on models which have previously been referred to as superdeterministic (strong or weak), retrocausal (with or without signalling, dynamical or non-dynamical), future-input-dependent, atemporal and all-at-once, not always with the same meaning or context. Sometimes these models are assumed to be deterministic, sometimes not, the word deterministic has been given different meanings, and different notions of causality have been used when classifying them. This has created much confusion in the literature, and we hope that the terms proposed here will help to clarify the nomenclature. The general model framework that we will propose may also be useful to classify other interpretations and modifications of quantum mechanics. This document grew out of the discussions at the 2022 Bonn Workshop on Superdeterminism and Retrocausality.

Protocols for observing gravity induced entanglement typically comprise the interaction of two particles prepared either in a superposition of two discrete paths, or in a continuously delocalized (harmonic oscillator) state of motion. An important open question has been whether these two different approaches allow to draw the same conclusions on the quantum nature of gravity. To answer this question, we analyse using the path-integral approach a setup that contains both features: a superposition of two highly delocalized center of mass states. We conclude that the two usual protocols are of similar epistemological relevance. In both cases the appearance of entanglement, within linearised quantum gravity, is due to gravity being in a highly non-classical state: a superposition of distinct geometries.

Here we investigate the role of quantum interference in the quantum homogenizer, whose convergence properties model a thermalization process. In the original quantum homogenizer protocol, a system qubit converges to the state of identical reservoir qubits through partial-swap interactions, that allow interference between reservoir qubits. We design an alternative, incoherent quantum homogenizer, where each system-reservoir interaction is moderated by a control qubit using a controlled-swap interaction. We show that our incoherent homogenizer satisfies the essential conditions for homogenization, being able to transform a qubit from any state to any other state to arbitrary accuracy, with negligible impact on the reservoir qubits’ states. Our results show that the convergence properties of homogenization machines that are important for modelling thermalization are not dependent on coherence between qubits in the homogenization protocol. We then derive bounds on the resources required to re-use the homogenizers for performing state transformations. This demonstrates that both homogenizers are universal for any number of homogenizations, for an increased resource cost.

Predicting whether an observable will dynamically evolve to thermal equilibrium in an isolated quantum system is an important open problem, as it determines the applicability of thermodynamics and statistical mechanics. The Observable Thermalization framework has been proposed as a solution, characterizing observables that thermalize using an observable-specific maximum entropy principle. In this paper, we achieve three results. First, we confirm the dynamical relaxation of local observables towards maximum entropy, in a 1D Ising chain. Second, we provide the most general solution to the maximization problem and numerically verify some general predictions about equilibrium behavior in the same model. Third, we explore the emergence and physical meaning of an observable-specific notion of energy. Our results mark significant progress towards a fully predictive theory of thermalization in isolated quantum systems and open interesting questions about observable-specific thermodynamic quantities.

Recent works by Chandrasekaran, Penington, and Witten have shown in various special contexts that the quantum-corrected Ryu-Takayanagi (RT) entropy (or its covariant Hubeny-Rangamani-Takayanagi (HRT) generalization) can be understood as computing an entropy on an algebra of bulk observables. These arguments do not rely on the existence of a holographic dual field theory. We show that analogous-but-stronger results hold in any UV-completion of asymptotically anti-de Sitter quantum gravity with a Euclidean path integral satisfying a simple and familiar set of axioms. We consider a quantum context in which a standard Lorentz-signature classical bulk limit would have Cauchy slices with asymptotic boundaries $B_L sqcup B_R$ where both $B_L$ and $B_R$ are compact manifolds without boundary. Our main result is then that (the UV-completion of) the quantum gravity path integral defines type I von Neumann algebras ${cal A}^{B_L}_L$, ${cal A}^{B_R}_{R}$ of observables acting respectively at $B_L$, $B_R$ such that ${cal A}^{B_L}_L$, ${cal A}^{B_R}_{R}$ are commutants. The path integral also defines entropies on ${cal A}^{B_L}_L, {cal A}^{B_R}_R$. Positivity of the Hilbert space inner product then turns out to require the entropy of any projection operator to be quantized in the form $ln N$ for some $N in {mathbb Z}^+$ (unless it is infinite). As a result, our entropies can be written in terms of standard density matrices and standard Hilbert space traces. Furthermore, in appropriate semiclassical limits our entropies are computed by the RT-formula with quantum corrections. Our work thus provides a Hilbert space interpretation of the RT entropy. Since our axioms do not severely constrain UV bulk structures, they may be expected to hold equally well for successful formulations of string field theory, spin-foam models, or any other approach to constructing a UV-complete theory of gravity.

Quantum nonlocality, pioneered in Bell’s seminal work and subsequently verified through a series of experiments, has drawn substantial attention due to its practical applications in various protocols. Evaluating and comparing the extent of nonlocality within distinct quantum correlations holds significant practical relevance. Within the resource theoretic framework this can be achieved by assessing the inter-conversion rate among different nonlocal correlations under free local operations and shared randomness. In this study we, however, present instances of quantum nonlocal correlations that are incomparable in the strongest sense. Specifically, when starting with an arbitrary many copies of one nonlocal correlation, it becomes impossible to obtain even a single copy of the other correlation, and this incomparability holds in both directions. Remarkably, these incomparable quantum correlations can be obtained even in the simplest Bell scenario, which involves two parties, each having two dichotomic measurements setups. Notably, there exist an uncountable number of such incomparable correlations. Our result challenges the notion of a ‘unique gold coin’, often referred to as the ‘maximally resourceful state’, within the framework of the resource theory of quantum nonlocality, which has nontrivial implications in the study of nonlocality distillation.

Neural networks have shown their effectiveness in various tasks in the realm of quantum computing. However, their application in quantum error mitigation, a crucial step towards realizing practical quantum advancements, has been restricted by reliance on noise-free statistics. To tackle this critical challenge, we propose a data augmentation empowered neural model for error mitigation (DAEM). Our model does not require any prior knowledge about the specific noise type and measurement settings and can estimate noise-free statistics solely from the noisy measurement results of the target quantum process, rendering it highly suitable for practical implementation. In numerical experiments, we show the model’s superior performance in mitigating various types of noise, including Markovian noise and Non-Markovian noise, compared with previous error mitigation methods. We further demonstrate its versatility by employing the model to mitigate errors in diverse types of quantum processes, including those involving large-scale quantum systems and continuous-variable quantum states. This powerful data augmentation-empowered neural model for error mitigation establishes a solid foundation for realizing more reliable and robust quantum technologies in practical applications.

Quantum state teleportation represents a pillar of quantum information and a milestone on the roadmap towards quantum networks with a large number of nodes. Successful photonic demonstrations of this protocol have been carried out employing different qubit encodings. However, demonstrations in the Fock basis encoding are challenging, due to the impossibility of creating a coherent superposition of vacuum-one photon states on a single mode with linear optics. Previous realizations using such an encoding strongly relied on ancillary modes of the electromagnetic field, which only allowed the teleportation of subsystems of entangled states. Here, we enable quantum teleportation of genuine vacuum-one photon states avoiding ancillary modes, by exploiting coherent control of a resonantly excited semiconductor quantum dot in a micro-cavity. Within our setup, we can teleport vacuum-one-photon qubits and perform entanglement swapping in such an encoding. Our results may disclose new potentialities of quantum dot single-photon sources for quantum information applications.

Recently there has been significant interest in using causal modelling techniques to understand the structure of physical theories. However, the notion of `causation’ is limiting – insisting that a physical theory must involve causal structure already places significant constraints on the form that theory may take. Thus in this paper, we aim to set out a more general structural framework. We argue that any quantitative physical theory can be represented in the form of a generative program, i.e. a list of instructions showing how to generate the empirical data; the information-processing structure associated with this program can be represented by a directed acyclic graph (DAG). We suggest that these graphs can be interpreted as encoding relations of `ontological priority,’ and that ontological priority is a suitable generalisation of causation which applies even to theories that don’t have a natural causal structure. We discuss some applications of our framework to philosophical questions about realism, operationalism, free will, locality and fine-tuning.

We perform a detailed study of the covariance properties of the gravitational symplectic potential on a null hypersurface, and of the different polarizations that can be used to study conservative as well as leaky boundary conditions. We study the symmetry groups that arise with different %boundary conditions in the phase space prescriptions, and determine the fields that have anomalous transformations. This allows us to identify a one-parameter family of covariant symplectic potentials. Imposing stationarity as in the original Wald-Zoupas prescription, one recovers the unique symplectic potential of Chandrasekaran, Flanagan and Prabhu. The associated charges are all conserved on non-expanding horizons, but not on flat spacetime. We show that it is possible to demand a weaker notion of stationarity which selects another symplectic potential, again in a unique way, and whose charges are conserved on both non-expanding horizons and flat light-cones. Furthermore, the flux of future-pointing diffeomorphisms at leading-order around an outgoing flat light-cone is positive and reproduces the tidal heating term plus a memory-like term. Our results have applications for dynamical notions of entropy, and are useful to clarify the interplay between different boundary conditions, charge prescriptions, and symmetry groups that can be associated with a null boundary. We also study the conformal conservative boundary conditions suggested by the alternative polarization and identify under which conditions they define a non-ambiguous variational principle.