相关论文: Emergent Distance and Metricity of Mutual Informat…

We introduce a geometric scaling relation that characterizes the local scale behavior of correlations using the informational distance $d_E = K_0/\sqrt{I}$, where $I$ is the mutual information. We define a geometric conversion factor, $G…

This paper presents a unified framework, integrating information theory and statistical mechanics, to connect metric failure in high-dimensional data with emergence in complex systems. We propose the "Information Dilution Theorem,"…

We investigate dimensional reduction, the property that the critical behavior of a system in the presence of quenched disorder in dimension d is the same as that of its pure counterpart in d-2, and its breakdown in the case of the…

Many real networks are embedded in space, where in some of them the links length decay as a power law distribution with distance. Indications that such systems can be characterized by the concept of dimension were found recently. Here, we…

This paper is concerned with factor of i.i.d. processes on the $d$-regular tree for $d \geq 3$. We study the mutual information of the values on two given vertices. If the vertices are neighbors (i.e., their distance is $1$), then a known…

Higher-form symmetries act on sub-dimensional spatial manifolds of a quantum system. They can emerge as an exact symmetry at low energies even when they are explicitly broken at the microscopic level, making them difficult to characterize.…

We extend the Prometheus framework for unsupervised phase transition discovery from two-dimensional classical systems to three-dimensional classical systems and quantum many-body systems. Building upon preliminary observations from a 2D…

I consider the tradeoff between the information gained about an initially unknown quantum state, and the disturbance caused to that state by the measurement process. I show that for any distribution of initial states, the…

How quantum information is scrambled in the global degrees of freedom of non-equilibrium many-body systems is a key question to understand local thermalization. Here we propose that the scaling of the mutual information between two…

We study the R\'enyi mutual information $\tilde{I}_n$ of the ground state of different critical quantum chains. The R\'enyi mutual information definition that we use is based on the well established concept of the R\'enyi divergence. We…

In this work we derive a number of chain rules for mutual information quantities, suitable for analyzing quantum cryptography with imperfect devices that leak additional information to an adversary. First, we derive a chain rule between…

A dispersive medium becomes entangled with zero-point fluctuations in the vacuum. We consider an arbitrary array of material bodies weakly interacting with a quantum field and compute the quantum mutual information between them. It is shown…

We propose a systematic scheme to reach the properties of two-dimensional (2D) statistical and quantum systems by studying the effective (1+1)-dimensional theory that is constructed from the tensor network representation. On on hand, we…

Quantifying entanglement of multiple subsystems is a challenging open problem in interacting quantum systems. Here, we focus on two subsystems of length $\ell$ separated by a distance $r=\alpha\ell$ and quantify their entanglement…

In quantum physics, measurement error and disturbance were first naively thought to be simply constrained by the Heisenberg uncertainty relation. Later, more rigorous analysis showed that the error and disturbance satisfy more subtle…

We quantify the emergent complexity of quantum states near quantum critical points on regular 1D lattices, via complex network measures based on quantum mutual information as the adjacency matrix, in direct analogy to quantifying the…

We prove that any one-dimensional (1D) quantum state with small quantum conditional mutual information in all certain tripartite splits of the system, which we call a quantum approximate Markov chain, can be well-approximated by a Gibbs…

We study the generic scaling properties of the mutual information between two disjoint intervals, in a class of one-dimensional quantum critical systems described by the c=1 bosonic field theory. A numerical analysis of a spin-chain model…

We study the concept of entanglement distance between two quantum states which quantifies the amount of information shared between their reduced density matrices (RDMs). Using analytical arguments combined with…

This paper delves into a fundamental aspect of quantum statistical mechanics -- the absence of thermal phase transitions in one-dimensional (1D) systems. Originating from Ising's analysis of the 1D spin chain, this concept has been pivotal…