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Quantum networks hold the potential to revolutionize a variety of fields by surpassing the capabilities of their classical counterparts. Many of these applications necessitate the sharing of high-fidelity entangled pairs among communicating…
We show that the entropy of a message can be tested in a device-independent way. Specifically, we consider a prepare-and-measure scenario with classical or quantum communication, and develop two different methods for placing lower bounds on…
The characterization of quantum correlations in many-body systems is instrumental to understanding the nature of emergent phenomena in quantum materials. The correlation entropy serves as a key metric for assessing the complexity of a…
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…
We consider the evolution of variance of entropy (varentropy) in the course of a polar transform operation on binary data elements (BDEs). A BDE is a pair $(X,Y)$ consisting of a binary random variable $X$ and an arbitrary side information…
Sensitive detection of low-abundance molecular targets is widely assumed to require enzymatic amplification, such as PCR, to achieve low detection limits. In amplification-free platforms, sensitivity is traditionally constrained by…
In contemporary scientific research, understanding the distinction between correlation and causation is crucial. While correlation is a widely used analytical standard, it does not inherently imply causation. This paper addresses the…
We propose a new estimator to measure directed dependencies in time series. The dimensionality of data is first reduced using a new non-uniform embedding technique, where the variables are ranked according to a weighted sum of the amount of…
Entanglement measures find frequent application in the study of topologically ordered systems, where the presence of topological order is reflected in an additional contribution to the entanglement of the system. Obtaining this topological…
Byte-Pair Encoding (BPE) has become a widely adopted subword tokenization method in modern language models due to its simplicity and strong empirical performance across downstream tasks. However, applying BPE to unsegmented languages such…
The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…
This is an extended version of the previous paper arXiv:2103.05303 to study entanglement entropy (EE) of a half space in interacting field theories. In the previous paper, we have proposed a novel method to calculate EE based on the notion…
Coping with distributional shifts is an important part of transfer learning methods in order to perform well in real-life tasks. However, most of the existing approaches in this area either focus on an ideal scenario in which the data does…
A central task in analyzing complex dynamics is to determine the loci of information storage and the communication topology of information flows within a system. Over the last decade and a half, diagnostics for the latter have come to be…
We analyse the entanglement structure of states generated by random constant-depth two-dimensional quantum circuits, followed by projective measurements of a subset of sites. By deriving a rigorous lower bound on the average entanglement…
Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information…
This paper develops a framework for identification, estimation, and inference on the causal mechanisms driving endogenous social network formation. Identification is challenging because of unobserved confounders and reverse causality;…
The structure entropy is one of the most important parameters to describe the structure property of the complex networks. Most of the existing struc- ture entropies are based on the degree or the betweenness centrality. In order to describe…
Entanglement is a key quantum phenomena and understanding transitions between phases of matter with different entanglement properties are an interesting probe of quantum mechanics. We numerically study a model of a 2D tensor network…
Topological phases are unique states of matter which support non-local excitations which behave as particles with fractional statistics. A universal characterization of gapped topological phases is provided by the topological entanglement…