MIT Center for Theoretical Physics – a Leinweber Institute

A fundamental task in quantum information is to approximate a pure quantum state in terms of sparse states or, for a bipartite system, states of bounded Schmidt rank. The optimal deterministic approximation in each case is straightforward, and maximizes the fidelity: keep the largest entries or singular values. On the other hand, random mixtures of sparse states can achieve quadratically improved trace distances, and yield nontrivial bounds on other distance measures like the robustness. In this work, we give efficient algorithms for finding mixtures of sparse states that optimally approximate a given pure state in either trace distance or robustness. These algorithms also yield descriptions of efficiently samplable ensembles of sparse, or less-entangled, states that correspond to these optimal mixed approximations. This can be used for the truncation step of algorithms for matrix product states, improving their accuracy while using no extra memory, and we demonstrate this improvement numerically. Our proofs use basic facts about convex optimization and zero-sum games, as well as rigorous guarantees for computing maximum-entropy distributions.

In this Letter, we initiate a systematic study of the $n$-point correlation functions (CF) in gauge theories in the sequential light-cone (SLC) limit. Focusing on QCD, we formulate a factorization theorem for the CF of four vector currents in this limit using tools from soft-collinear effective field theory (SCET). This result unveils a duality between CF and Wilson loops in non-conformal field theories, according to which the singular structure of the CF is described by a null polygonal Wilson loop dressed by universal jet functions and current form factors, directly related to well-known ingredients in collider physics. We employ this new factorization theorem to obtain the singular terms of the four-point CF in QCD in the SLC limit up to three loops. This constitutes the first determination of terms beyond one loop and in particular determines, for the first time, conformal-symmetry-breaking terms induced by the non-vanishing $β$-function of QCD. As a stringent check, we verify that our result satisfies the anomalous conformal Ward identities and its leading-transcendental term reproduces the known correlation function in $\mathcal{N}=4$ SYM to three loops. Our results are easily generalized to the multi-point case, offering a powerful tool for future applications of SCET to the study of the fundamental structure of gauge theories.

We review recent developments in the use of von Neumann algebras to analyze the entanglement structure of quantum gravity and the emergence of spacetime in the semi-classical limit. Von Neumann algebras provide a natural framework for describing quantum subsystems when standard tensor factorizations are unavailable, capturing both kinematic and dynamical aspects of entanglement. The first part of the review introduces the fundamentals of von Neumann algebras, including their classification, and explains how they can be applied to characterize entanglement. Topics covered include modular and half-sided modular flows and their role in the emergence of time, as well as the crossed-product construction of von Neumann algebras. The second part turns to applications in quantum gravity, including an algebraic formulation of AdS/CFT in the large-$N$ limit, the emergence of bulk spacetime structure through subregion-subalgebra duality, and an operator-algebraic perspective on gravitational entropy. It also discusses simple operator-algebraic models of quantum gravity, which provide concrete settings in which to explore these ideas. In addition, several original conceptual contributions are presented, including a diagnostic of firewalls and an algebraic formulation of entanglement islands. The review concludes with some speculative remarks on the mathematical structures underlying quantum gravity.

We report on our investigation in arXiv:2509.08881 of how recent jet substructure measurements constrain the resolution length $L_{\rm res}$ of the quark-gluon plasma formed in heavy-ion collisions. $L_{\rm res}$ is defined such that high-energy partons within a jet shower are resolved by the medium if and only if they are separated by a distance greater than $L_{\rm res}$. Using the Hybrid Model, we reproduce ALICE data on the scaled Soft Drop angle $θ_g$ for $R=0.2$ charged-particle jets and ATLAS data on the Hard Group angle $ΔR_{12}$ for $R=1$ jets reclustered from skinny $R = 0.2$ inclusive subjets. We find that the narrowing of the $θ_g$-distribution in PbPb collisions observed by ALICE and the suppression of $R=1$ jets with multiple skinny subjets in PbPb collisions observed by ATLAS rule out $L_{\rm res} = \infty$, where each entire parton shower loses energy to the plasma coherently as if it were a single colored object. We then compare Hybrid Model calculations to ATLAS measurements of $R_{\rm AA}$ of $R=1$ jets reclustered from $R=0.2$ subjets, as a function of the Soft Drop angle $dR_{12}$ obtained by grooming all charged-particle tracks associated with each $R=1$ jet. We demonstrate, for the first time, that the ATLAS data is inconsistent with $L_{\rm res} = 0$, where the plasma resolves every splitting in a parton shower. Our results agree best with the data when QGP possesses a finite, nonzero $L_{\rm res}\sim (1-2)/(πT)$.