Related papers: How Hidden are Hidden Processes? A Primer on Crypt…
We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…
We propose here a new model of encryption of binary data taking advantage of the complexity associated with delayed dynamics. In this scheme, the encryption process is a coupling dynamics with various time delays between different bits in…
We derive dynamics of the entanglement wedge cross section from the reflected entropy for local operator quench states in the holographic CFT. By comparing between the reflected entropy and the mutual information in this dynamical setup, we…
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…
Entropy is a very useful concept from physics that tries to explain how a system behaves from a point of view of the thermodynamics. However, there are two ways to explain entropy, and it depends on if we are studying a microsystem or a…
The entanglement entropy in clean, as well as in random quantum spin chains has a logarithmic size-dependence at the critical point. Here, we study the entanglement of composite systems that consist of a clean and a random part, both being…
Part 1 has studied the conversion of observed random process with its hidden information to related dynamic process, applying entropy functional measure (EF) of the random process and path functional information measure (IPF) of the dynamic…
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…
Machine learning on encrypted data has received a lot of attention thanks to recent breakthroughs in homomorphic encryption and secure multi-party computation. It allows outsourcing computation to untrusted servers without sacrificing…
Opacity is a generic security property, that has been defined on (non probabilistic) transition systems and later on Markov chains with labels. For a secret predicate, given as a subset of runs, and a function describing the view of an…
Circuit complexity, defined as the minimum circuit size required for implementing a particular Boolean computation, is a foundational concept in computer science. Determining circuit complexity is believed to be a hard computational problem…
The secrecy performance of a source-channel model is studied in the context of lossy source compression over a noisy broadcast channel. The source is causally revealed to the eavesdropper during decoding. The fidelity of the transmission to…
We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of…
Predictive equivalence in discrete stochastic processes have been applied with great success to identify randomness and structure in statistical physics and chaotic dynamical systems and to inferring hidden Markov models. We examine the…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…
We prove that under mild positivity assumptions the entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. A general principle to determine the domain of analyticity is stated. An…
Quantum informatic quantities such as entanglement entropy are useful in detecting quantum phase transitions. Recently, a new entanglement measure called pseudo-entropy was proposed which is a generalization of the more well-known…
Many non-equilibrium, active processes are observed at a coarse-grained level, where different microscopic configurations are projected onto the same observable state. Such "lumped" observables display memory, and in many cases the…
A randomized algorithm for finding sparse cuts is given which is based on constructing a dual markov chain called multiscale rings process(MRP) and a new concept of entropy. It is shown how the time to absorption of the dual process…