April 2025

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.

The eigenstate thermalization hypothesis (ETH) is foundational to modern discussions of thermalization in closed quantum systems. In this work, we expand on traditional explanations for the prevalence of ETH by emphasizing the role of operator locality. We introduce an operator-specific perturbation problem that can be thought of as a means of understanding the onset or breakdown of ETH for specific classes of operators in a given system. We derive explicit functional forms for the off-diagonal variances of operator matrix elements for typical local operators under various `scrambling ansatzes’, expressed in terms of system parameters and parameters of the corresponding perturbation problem. We provide simple tests and illustrations of these ideas in chaotic spin chain systems.

A common way to avoid divergent integrals in homogeneous spatially non-compact gravitational systems is to introduce a fiducial cell by cutting-off the spatial slice at a finite region $V_o$. This is usually considered as an auxiliary regulator to be removed after computations by sending $V_otoinfty$. In this paper, we analyse the dependence of the classical and quantum theory of homogeneous, isotropic and spatially flat cosmology on $V_o$. We show that each fixed $V_o$ regularisation leads to a different canonically independent theory. At the classical level, the dynamics of observables is not affected by the regularisation on-shell. For the quantum theory, however, this leads to a family of regulator dependent quantum representations and the limit $V_otoinfty$ becomes then more subtle. First, we construct a novel isomorphism between different $V_o$-regularisations, which allows us to identify states in the different $V_o$-labelled Hilbert spaces to ensure equivalent dynamics for any value of $V_o$. The $V_otoinfty$ limit would then correspond to choosing a state for which the volume assigned to the fiducial cell becomes infinite as appropriate in the late-time regime. As second main result of our analysis, quantum fluctuations of observables smeared over subregions $Vsubset V_o$, unlike those smeared over the full $V_o$, explicitly depend on the size of the fiducial cell through the ratio $V/V_o$ interpreted as the (inverse) number of subcells $V$ homogeneously patched together into $V_o$. Physically relevant fluctuations for a finite region, as e.g. in the early-time regime, which would be unreasonably suppressed in a na”ive $V_otoinfty$ limit, become appreciable at small volumes. Our results suggest that the fiducial cell is not playing the role of a mere regularisation but is physically relevant at the quantum level and complement previous statements in the literature.

It was recently noted that different internal quantum reference frames (QRFs) partition a system in different ways into subsystems, much like different inertial observers in special relativity decompose spacetime in different ways into space and time. Here we expand on this QRF relativity of subsystems and elucidate that it is the source of all novel QRF dependent effects, just like the relativity of simultaneity is the origin of all characteristic special relativistic phenomena. We show that subsystem relativity, in fact, also arises in special relativity with internal frames and, by implying the relativity of simultaneity, constitutes a generalisation of it. Physical consequences of the QRF relativity of subsystems, which we explore here systematically, and the relativity of simultaneity may thus be seen in similar light. We focus on investigating when and how subsystem correlations and entropies, interactions and types of dynamics (open vs. closed), as well as quantum thermodynamical processes change under QRF transformations. We show that thermal equilibrium is generically QRF relative and find that, remarkably, QRF transformations not only can change a subsystem temperature, but even map positive into negative temperature states. We further examine how non-equilibrium notions of heat and work exchange, as well as entropy production and flow depend on the QRF. Along the way, we develop the first study of how reduced subsystem states transform under QRF changes. Focusing on physical insights, we restrict to ideal QRFs associated with finite abelian groups. Besides being conducive to rigour, the ensuing finite-dimensional setting is where quantum information-theoretic quantities and quantum thermodynamics are best developed. We anticipate, however, that our results extend qualitatively to more general groups and frames, and even to subsystems in gauge theory and gravity. [abridged]

We construct relational observables in group field theory (GFT) in terms of covariant positive operator-valued measures (POVMs), using techniques developed in the context of quantum reference frames. We focus on matter quantum reference frames; this can be generalized to other types of frames within the same POVM-based framework. The resulting family of relational observables provides a covariant framework to extract localized observables from GFT, which is typically defined in a perspective-neutral way. Then, we compare this formalism with previous proposals for relational observables in GFT. We find that our quantum reference frame-based relational observables overcome the intrinsic limitations of previous proposals while reproducing the same continuum limit results concerning expectation values of the number and volume operators on coherent states. Nonetheless, there can be important differences for more complex operators, as well as for other types of GFT states. Finally, we also use a specific class of POVMs to show how to project states and operators from the more general perspective-neutral GFT Fock space to a perspective-dependent one where a scalar matter field plays the role of a relational clock.

We present a Group Field Theory (GFT) quantization of the Husain-Kuchav{r} (HK) model formulated as a non-interacting GFT. We demonstrate that the path-integral formulation of this HK-GFT provides a completion of a corresponding spinfoam model developed earlier

It has been recently realized that the bulk dual of the double-scaled SYK (DSSYK) model has both positive and negative Ricci curvature and is described by a dilaton-gravity theory with a $sin(Phi)$ potential arXiv:2404.03535. We study T$^2$-deformations in the DSSYK model after performing the ensemble averaging to probe regions of positive and approximately constant curvature. The dual finite cutoff interpretation of the deformation allows us to place the DSSYK model in the stretched horizon of the bulk geometry, partially realizing a conjecture of Susskind arXix:2109.14104. We show that the energy spectrum and thermodynamic entropy are well-defined for a contour reaching these regions. Importantly, the system displays a phase transition from a thermodynamically stable to an unstable configuration by varying its microcanonical temperature; unless it is located on any of the stretched horizons, which is always unstable. The thermodynamic properties in this model display an enhanced growth as the system approaches the stretched horizon, and it scrambles information at a (hyper)-fast rate.

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.

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.

In a gauge theory, a collection of kinematical degrees of freedom is used to redundantly describe a smaller amount of gauge-invariant information. In a quantum error correcting code (QECC), a collection of computational degrees of freedom that make up a device’s physical layer is used to redundantly encode a smaller amount of logical information. We elaborate this clear parallel in terms of quantum reference frames (QRFs), which are a universal toolkit for quantization in the presence of symmetries. The result is a precise dictionary between QECCs and QRFs within the perspective-neutral framework for constrained systems. Concepts from quantum error correction like error sets and correctability translate to novel insights into the informational architecture of gauge theories. Conversely, the dictionary provides a systematic procedure for constructing symmetry-based QECCs and characterizing their error correcting properties. In this initial work, we scrutinize the dictionary between Pauli stabilizer codes and their corresponding QRF setups, which possess symmetry groups that are isomorphic to the stabilizer group. We show that there is a one-to-one correspondence between maximal correctable error sets and tensor factorizations splitting system from frame degrees of freedom, relative to which errors corrupt only redundant frame data. When passed through the dictionary, standard Pauli errors from the code essentially behave as electric excitations that are exactly dual, via Pontryagin duality, to magnetic excitations related to gauge-fixing. We comprehensively illustrate our findings in surface codes, which themselves manifestly connect quantum error correction with gauge systems. The exploratory investigations in this article pave the way for deeper foundational applications to quantum gauge theories and for eventual practical applications to quantum simulation.