A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Quantum states are not entangled if submanifold is a product.
Study on quantum state entanglement using Kaehler manifolds.
Locates entanglement in curves using knot intensity distribution.
Kauffman and Lomonaco explored the idea of understanding quantum entanglement (the non-local correlation of certain properties of particles) topologically by viewing unitary entangling operators as braiding operators. In the work of G. Alagic, M. Jarret, and S. Jordan it is shown that entanglement is a necessary condit…
q-CNN learns data features through entangled states.
The paper uncovers the mathematical structure enabling value decomposition in multi-agent systems.
Study uses holography to analyze entanglement entropy in deformed CFTs.
Paper defines untangling number to measure entanglement complexity in 3-periodic networks.
Any solution to the Yang-Baxter equation yields a family of representations of braid groups. Under certain conditions, identified by Turaev, the appropriately normalized trace of these representations yields a link invariant. Any Yang-Baxter solution can be interpreted as a two-qudit quantum gate. Here we show that if …
This work introduces 'Artificial Entanglement' to understand LLMs' fine-tuning effectiveness.
When a spacetime has boundaries, the entangling surface does not have to be necessarily compact and it may have boundaries as well. Then there appear a new, boundary, contribution to the entanglement entropy due to the intersection of the entangling surface with the boundary of the spacetime. We study the boundary cont…
We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface that separates two subsystems of quantum strongly coupled SU(N) superconformal gauge theory. We extend this result and calculate en…
A relation between the conformal anomaly and the logarithmic term in the entanglement entropy is known to exist for CFT's in even dimensions. In odd dimensions the local anomaly and the logarithmic term in the entropy are absent. As was observed recently, there exists a non-trivial integrated anomaly if an odd-dimensio…
We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, o…
We analyze the Ricci flow of a noncompact metric that describes a two-dimensional black hole. We consider entanglement entropy of a 2d black hole which is due to the quantum correlations between two subsystems: one is inside and the other is outside the black hole horizon. It is demonstrated that the entanglement entro…
Paper introduces untangling number to quantify 3-periodic tangle complexity.
We define the local periodic linking number, LK, between two oriented closed or open chains in a system with three-dimensional periodic boundary conditions. The properties of LK indicate that it is an appropriate measure of entanglement between a collection of chains in a periodic system. Using this measure of linking …
New kernels allow learning from non-separable data.
New methods assess topological entanglement in periodic systems.
Quantum datasets improve QML performance.
We propose a conceptual design for a quantum blockchain. Our method involves encoding the blockchain into a temporal GHZ (Greenberger-Horne-Zeilinger) state of photons that do not simultaneously coexist. It is shown that the entanglement in time, as opposed to an entanglement in space, provides the crucial quantum adva…
New machine learning method detects quantum separability in large-scale systems.
A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter (adS) is generalized to include entanglement entropy of black holes living on the boundary of adS. The generalized proposal is verified in boundary dimensio…
Study tackles causal effects of close contact on MRSA infections from entangled treatment data.
We present the quantum model of Bertrand duopoly and study the entanglement behavior on the profit functions of the firms. Using the concept of optimal response of each firm to the price of the opponent, we found only one Nash equilibirum point for maximally entangled initial state. The very presence of quantum entangl…
New metric for disentangling multivariate representations, accounting for more complex entanglements.
For a very ample line bundle L on a compact connected complex manifold X, with a real structure, we discuss entanglement properties of certain sequences of vectors in tensor products of spaces of holomorphic sections of powers of L.
The study bounds entanglement entropy for coherent states on Kähler manifolds.
Fibonacci anyons are attractive for use in topological quantum computation because any unitary transformation of their state space can be approximated arbitrarily accurately by braiding. However there is no known braid that entangles two qubits without leaving the space spanned by the two qubits. In other words, there …
The abstract explores a new wave equation linking quantum mechanics and complex adaptive systems.
Tensor networks improve image classification but require more expressive states.
For a given quantum field theory, provided the area of the entangling surface is fixed, what surface maximizes entanglement entropy? We analyze the answer to this question in four and higher dimensions. Surprisingly, in four dimensions the answer is related to a mathematical problem of finding surfaces which minimize t…
It is a fundamental, but still elusive question whether the schemes based on quantum mechanics, in particular on quantum entanglement, can be used for classical information processing and machine learning. Even partial answer to this question would bring important insights to both fields of machine learning and quantum…
We address several problems concerning the geometry of the space of Hermitian operators on a finite-dimensional Hilbert space, in particular the geometry of the space of density states and canonical group actions on it. For quantum composite systems we discuss and give examples of measures of entanglement.
New diagrams classify triply periodic entanglements.
Entangled bisimulation improves policy learning from visual input.
Few quantum measurements limit learning entanglement.
New knot models analyze local entanglement for robust curve analysis.
Bit threads provide an alternative description of holographic entanglement, replacing the Ryu-Takayanagi minimal surface with bulk curves connecting pairs of boundary points. We use bit threads to prove the monogamy of mutual information (MMI) property of holographic entanglement entropies. This is accomplished using t…
A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational O(2) symmetry in a subspace orthogonal to a singular surface so that the surfa…
We review supervised learning and deep neural network design for learning membership on algebraic varieties. We demonstrate that these trained artificial neural networks can predict the entanglement type for quantum states. We give examples for detecting degenerate states, as well as border rank classification for up t…
The paper estimates common mean of entangled Gaussians with bounded variances.
A new approach uses circuit topology to study complex polymer interactions.
A method for estimating parameters from entangled single-sample distributions, robust to high-noise data.
Geometrically constructs twist-field correlation functions in CFT.
New formula connects holographic entanglement entropy to Willmore energy in 5D.
The backbone of most proteins forms an open curve. To study their entanglement, a common strategy consists in searching for the presence of knots in their backbones using topological invariants. However, this approach requires to close the curve into a loop, which alters the geometry of curve. Knoto-ID allows evaluatin…
Study on entanglement complexity of confined ring polymers in lattice tubes.