Related papers: Strong converse theorems using R\'enyi entropies
This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations…
We determine the exact strong converse exponent for entanglement-assisted classical communication of a quantum channel. Our main contribution is the derivation of an upper bound for the strong converse exponent which is characterized by the…
In their seminal work, Bennett et al. [IEEE Trans. Inf. Theory (2002)] showed that, with sufficient shared randomness, one noisy channel can simulate another at a rate equal to the ratio of their capacities. We establish that when coding…
Strong converse theorems refer to the study of impossibility results in information theory. In particular, Mosonyi and Ogawa established a one-shot strong converse bound for quantum hypothesis testing [Comm. Math. Phys, 334(3), 2014], which…
Quantum entanglement can be used in a communication scheme to establish a correlation between successive channel inputs that is impossible by classical means. It is known that the classical capacity of quantum channels can be enhanced by…
We provide the sandwiched R\'enyi divergence of order $\alpha\in(\frac{1}{2},1)$, as well as its induced quantum information quantities, with an operational interpretation in the characterization of the exact strong converse exponents of…
A strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of…
Recently, a new notion of quantum R\'enyi divergences has been introduced by M\"uller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J.Math.Phys. 54:122203, (2013), and Wilde, Winter, Yang, Commun.Math.Phys. 331:593--622, (2014), that has…
The fully quantum reverse Shannon theorem establishes the optimal rate of noiseless classical communication required for simulating the action of many instances of a noisy quantum channel on an arbitrary input state, while also allowing for…
Quantum information processing is limited, in practice, to efficiently implementable operations. This motivates the study of quantum divergences that preserve their operational meaning while faithfully capturing these computational…
We consider a distributed quantum hypothesis testing problem with communication constraints, in which the two hypotheses correspond to two different states of a bipartite quantum system, multiple identical copies of which are shared between…
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…
Partially smoothed information measures are fundamental tools in one-shot quantum information theory. In this work, we determine the exact strong converse exponents of these measures for both pure quantum states and classical states.…
The strong converse for a coding theorem shows that the optimal asymptotic rate possible with vanishing error cannot be improved by allowing a fixed error. Building on a method introduced by Gu and Effros for centralized coding problems, we…
Entanglement criteria for an $n$-partite quantum system with continuous variables are formulated in terms of R\'{e}nyi entropies. R\'{e}nyi entropies are widely used as a good information measure due to many nice properties. Derived…
The sandwiched R\'enyi divergences of two finite-dimensional density operators quantify their asymptotic distinguishability in the strong converse domain. This establishes the sandwiched R\'enyi divergences as the operationally relevant…
One possibility of defining a quantum R\'enyi $\alpha$-divergence of two quantum states is to optimize the classical R\'enyi $\alpha$-divergence of their post-measurement probability distributions over all possible measurements (measured…
This paper is twofold. In the first part, we present a refinement of the R\'enyi Entropy Power Inequality (EPI) recently obtained in \cite{BM16}. The proof largely follows the approach in \cite{DCT91} of employing Young's convolution…
The entropy accumulation theorem, and its subsequent generalized version, is a powerful tool in the security analysis of many device-dependent and device-independent cryptography protocols. However, it has the drawback that the finite-size…
In this article we establish new bounds on the quantum communication complexity of distributed problems. Specifically, we consider the amount of communication that is required to transform a bipartite state into another, typically more…