Related papers: Relations between different quantum R\'enyi diverg…
We introduce an improved one-shot characterisation of randomness extraction against quantum side information (privacy amplification), strengthening known one-shot bounds and providing a unified derivation of the tightest known asymptotic…
A theory of thermodynamics has been recently formulated and derived on the basis of R\'enyi entropy and its relative versions. In this framework, we define the concepts of partition function, internal energy and free energy, and fundamental…
Channel simulation is to simulate a noisy channel using noiseless channels with unlimited shared randomness. This can be interpreted as the reverse problem to Shannon's noisy coding theorem. In contrast to previous works, our approach…
Fidelity is the standard measure for quantifying the similarity between two quantum states. It is equal to the square of the minimum Bhattacharyya coefficient between the probability distributions induced by quantum measurements on the two…
It is well-known that any quantum channel $\mathcal{E}$ satisfies the data processing inequality (DPI), with respect to various divergences, e.g., quantum $\chi^2_{\kappa}$divergences and quantum relative entropy. More specifically, the…
We identify a universal structural principle underlying the smoothing of classical divergences: the optimizer of the smoothing problem is a clipped probability vector, independently of the specific divergence. This yields a…
We study the dynamics of (R\'enyi) mutual information, logarithmic negativity, and (R\'enyi) reflected entropy after exciting the ground state by a local operator. Together with recent results from Ref. [1], we are able to conjecture a…
We extend from the hyperfinite setting to general von Neumann algebras Mosonyi and Ogawa's (2015) and Mosonyi and Hiai's (2023) results showing the operational interpretation of sandwiched relative R\'enyi entropy in the strong converse of…
Information divergence that measures the difference between two nonnegative matrices or tensors has found its use in a variety of machine learning problems. Examples are Nonnegative Matrix/Tensor Factorization, Stochastic Neighbor…
A quantitative and predictive theory of quantum light-matter interactions in ultra thin materials involves several fundamental challenges. Any realistic model must simultaneously account for the ultra-confined plasmonic modes and their…
Data-processing inequalities capture the phenomenon that two probability distributions can only become less distinguishable under any common post-processing. For more fine-grained inequalities, one turns to strong data-processing inequality…
We present an approximate inference method, based on a synergistic combination of R\'enyi $\alpha$-divergence variational inference (RDVI) and rejection sampling (RS). RDVI is based on minimization of R\'enyi $\alpha$-divergence…
Regularized optimal transport (OT) has received much attention in recent years starting from Cuturi's introduction of Kullback-Leibler (KL) divergence regularized OT. In this paper, we propose regularizing the OT problem using the family of…
The concept of distinguishability lies at the heart of quantum information theory. We introduce \textit{left-right relative entropy} as a quantitative measure of distinguishability within the space of boundary states in two-dimensional…
The symmetry-resolved R\'enyi entanglement entropy is the R\'enyi entanglement entropy of each symmetry sector of a density matrix $\rho$. This experimentally relevant quantity is known to have rich theoretical connections to conformal…
It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is…
We derive a strengthened monotonicity inequality for quantum relative entropy by employing properties of $\alpha$-R\'{e}nyi relative entropy. We develop a unifying treatment towards the improvement of some quantum entropy inequalities. In…
This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…
We study the behavior of the R\'enyi entropies for the toric code subject to a variety of different perturbations, by means of 2D density matrix renormalization group and analytical methods. We find that R\'enyi entropies of different index…
The interplay of quantum and classical fluctuations in the vicinity of a quantum critical point (QCP) gives rise to various regimes or phases with distinct quantum character. In this work, we show that the R\'enyi entropy is a precious tool…