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Probing quantum entanglement with macroscopic objects allows to test quantum mechanics in new regimes. One way to realize such behavior is to couple a macroscopic mechanical oscillator to a continuous light field via radiation pressure. In view of this, the system that is discussed comprises an optomechanical cavity driven by a coherent optical field in the unresolved sideband regime where we assume Gaussian states and dynamics. We develop a framework to quantify the amount of entanglement in the system numerically. Different from previous work, we treat non-Markovian noise and take into account both the continuous optical field and the cavity mode. We apply our framework to the case of the Advanced Laser Interferometer Gravitational-Wave Observatory (Advanced LIGO) and discuss the parameter regimes where entanglement exists, even in the presence of quantum and classical noises.

A universal framework for quantum-classical dynamics based on information-theoretic approaches is presented. Based on this, we analyze the interaction between quantum matter and a classical gravitational field. We point out that, under the assumption of conservation of momentum or energy, the classical gravitational field cannot cause the change of the momentum or energy of the quantum system, which is not consistent with the observation of existing experiments (e.g. the free fall experiment), while on the contrary the quantum gravitational field can do so. Our analysis exposes the fundamental relationship between conservation laws and the quantum properties of objects, offering new perspectives for the study of quantum gravity.

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.

Discrimination of quantum states under local operations and classical communication (LOCC) is an intriguing question in the context of local retrieval of classical information, encoded in the multipartite quantum systems. All the local quantum state discrimination premises, considered so far, mimic a basic communication set-up, where the spatially separated decoding devices are independent of any additional input. Here, exploring a generalized communication scenario we introduce a framework for input-dependent local quantum state discrimination, which we call local random authentication (LRA). Referring to the term nonlocality, often used to indicate the impossibility of local state discrimination, we coin the term conditional nonlocality for the impossibility associated with the task LRA. We report that conditional nonlocality necessitates the presence of entangled states in the ensemble, a feature absent from erstwhile nonlocality arguments based on local state discrimination. Conversely, all the states in a complete basis set being entangled implies conditional nonlocality. However, the impossibility of LRA also exhibits more conditional nonlocality with less entanglement. The relation between the possibility of LRA and local state discrimination for sets of multipartite quantum states, both in the perfect and conclusive cases, has also been established. The results highlight a completely new aspect of the interplay between the security of information in a network and quantum entanglement under the LOCC paradigm.

The AdS/CFT correspondence states that certain conformal field theories are equivalent to string theories in a higher-dimensional anti-de Sitter space. One aspect of the correspondence is an equivalence of density matrices or, if one ignores normalizations, of positive operators. On the CFT side of the correspondence, any two positive operators $A,B$ will satisfy the trace inequality $operatorname{Tr}(AB) leq operatorname{Tr}(A) operatorname{Tr}(B)$. This relation holds on any Hilbert space ${cal H}$ and is deeply associated with the fact that the algebra $B({cal H})$ of bounded operators on ${cal H}$ is a type I von Neumann factor. Holographic bulk theories must thus satisfy a corresponding condition, which we investigate below. In particular, we argue that the Euclidean gravitational path integral respects this inequality at all orders in the semi-classical expansion and with arbitrary higher-derivative corrections. The argument relies on a conjectured property of the classical gravitational action, which in particular implies a positive action conjecture for quantum gravity wavefunctions. We prove this conjecture for Jackiw-Teitelboim gravity and we also motivate it for more general theories.