Related papers: Telescopic Relative Entropy

A new form of zero-discord state via Petz's monotonicity condition on relative entropy with equality has been derived systematically. A generalization of symmetric zero-discord states is presented and the related physical implications are…

We study the exponential decay of relative entropy functionals for zero-range processes on the complete graph. For the standard model with rates increasing at infinity we prove entropy dissipation estimates, uniformly over the number of…

We revisit the connection between index and relative entropy for an inclusion of finite von Neumann algebras. We observe that the Pimsner-Popa index connects to sandwiched Renyi $p$-relative entropy for all $1/2\le p\le \infty$, including…

An alternative method is presented for extracting the von Neumann entropy $-\operatorname{Tr} (\rho \ln \rho)$ from $\operatorname{Tr} (\rho^n)$ for integer $n$ in a quantum system with density matrix $\rho$. Instead of relying on direct…

We conclude a sequence of work by giving near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves on prior results that obtain…

The optimality and sensitivity of the empirical risk minimization problem with relative entropy regularization (ERM-RER) are investigated for the case in which the reference is a sigma-finite measure instead of a probability measure. This…

We derive entropic uncertainty relations for successive generalized measurements by using general descriptions of quantum measurement within two {distinctive operational} scenarios. In the first scenario, by merging {two successive…

We use large-$N$ diagrammatic techniques to calculate the relative entropy of symmetric random states drawn from the Wishart ensemble. These methods are specifically designed for symmetric sectors, allowing us to determine the relative…

This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…

We study the relative entanglement entropies of one interval between excited states of a 1+1 dimensional conformal field theory (CFT). To compute the relative entropy $S(\rho_1 \| \rho_0)$ between two given reduced density matrices $\rho_1$…

We demonstrate that the stabilizer R\'{e}nyi entropy (SRE), a computable measure of quantum magic, can serve as an information-theoretic probe for universal properties associated with conformal defects in one-dimensional quantum critical…

We prove that the quantum relative entropy decreases monotonically under the application of any positive trace-preserving linear map, for underlying separable Hilbert spaces. This answers in the affirmative a natural question that has been…

Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…

For a special class of bipartite states we calculate explicitly the asymptotic relative entropy of entanglement $E_R^\infty$ with respect to states having a positive partial transpose (PPT). This quantity is an upper bound to distillable…

Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…

Holevo introduced a fidelity between quantum states that is symmetric and as effective as the trace norm in evaluating their similarity. This fidelity is bounded by a function of the trace norm, a relationship to which we will refer as…

The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…

The long-standing problem of finding a closed formula for the relative entropy of entanglement (REE) for two qubits is addressed. A compact-form solution to the inverse problem, which characterizes an entangled state for a given closest…

Topological entanglement entropy has been regarded as a smoking-gun signature of topological order in two dimensions, capturing the total quantum dimension of the topological particle content. An extrapolation method on cylinders has been…

It is known that the Maximum relative Entropy (MrE) method can be used to both update and approximate probability distributions functions in statistical inference problems. In this manuscript, we apply the MrE method to infer magnetic…