Related papers: Subsystem Trace Distance in Quantum Field Theory
We study the entanglement and Renyi entropies of two disjoint intervals in minimal models of conformal field theory. We use the conformal block expansion and fusion rules of twist fields to define a systematic expansion in the elliptic…
Optimal transport has been very successful for various machine learning tasks; however, it is known to suffer from the curse of dimensionality. Hence, dimensionality reduction is desirable when applied to high-dimensional data with…
Various approaches to alignment-free sequence comparison are based on the length of exact or inexact word matches between two input sequences. Haubold {\em et al.} (2009) showed how the average number of substitutions between two DNA…
We develop a linear-programming method to extract dynamical information from static ground-state correlators in quantum field theory. We recast the K\"all\'en-Lehmann inversion as a convex optimization problem, in a spirit similar to the…
The reduced-density-matrix method is an promising candidate for the next generation electronic structure calculation method; it is equivalent to solve the Schr\"odinger equation for the ground state. The number of variables is the same as a…
Phenomenological models of quantum gravity often consider the existence of some form of minimal length. This feature is commonly described in the context of quantum mechanics and using the corresponding formalism and techniques. Although…
This paper addresses the problem of finding a representation of a subtree distance, which is an extension of the tree metric. We show that a minimal representation is uniquely determined by a given subtree distance, and give a linear time…
This paper is on the normal approximation of singular subspaces when the noise matrix has i.i.d. entries. Our contributions are three-fold. First, we derive an explicit representation formula of the empirical spectral projectors. The…
We calculate equilibrium solutions for Ising spin models on `small world' lattices, which are constructed by super-imposing random and sparse Poissonian graphs with finite average connectivity c onto a one-dimensional ring. The nearest…
We introduce an analytical iterative method, the density matrix recursion method, to generate arbitrary reduced density matrices of superpositions of short-range dimer coverings on periodic or non-periodic quantum spin-1/2 ladder lattices,…
We study the best approximation and distance problems in the operator space $\B(\HS)$ and in the space of trace class operators $\LS^1(\B(\HS))$. Formulations of distances are obtained in both cases. The case of finite-dimensional…
The huge amount of information stored in text form makes methods that deal with texts really interesting. This thesis focuses on dealing with texts using compression distances. More specifically, the thesis takes a small step towards…
We construct a bosonic quantum field on a general quantum graph. Consistency of the construction leads to the calculation of the total scattering matrix of the graph. This matrix is equivalent to the one already proposed using generalized…
Partial trace is a very important mathematical operation in quantum mechanics. It is not only helpful in studying the subsystems of a composite quantum system but also used in computing a vast majority of quantum entanglement measures.…
We investigate the ground-state Riemannian metric and the cyclic quantum distance of an inhomogeneous quantum Ising spin-1/2 chain in a transverse field. This model can be diagonalized by using a general canonical transformation to the…
A subspace method is introduced to solve large-scale trace ratio problems. This approach is matrix-free, requiring only the action of the two matrices involved in the trace ratio. At each iteration, a smaller trace ratio problem is…
We propose a scheme for using an unmodulated and unmeasured spin-chain as a channel for short distance quantum communications. The state to be transmitted is placed on one spin of the chain and received later on a distant spin with some…
The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains…
This paper presents TRACE, a tool to analyze the quality of 2D embeddings generated through dimensionality reduction techniques. Dimensionality reduction methods often prioritize preserving either local neighborhoods or global distances,…
Leveraging the Wasserstein distance -- a summation of sample-wise transport distances in data space -- is advantageous in many applications for measuring support differences between two underlying density functions. However, when supports…