Related papers: R\'enyi generalizations of quantum information mea…
Quantum generalizations of the Fisher information are important in quantum information science, with applications in high energy and condensed matter physics and in quantum estimation theory, machine learning, and optimization. One can…
In this work we investigate the conditions for quantum back action to result in a phase transition in the information dynamics of a monitored system. We introduce a framework that captures a wide range of experiments encompassing probes…
Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the…
We pedagogically present the information theory as originally established, explaining its essential ideas and paying attention to the expression employed to measure the amount of information. Also we discussed relationships between…
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…
We introduce ways to measure information storage in quantum systems, using a recently introduced computation-theoretic model that accounts for measurement effects. The first, the quantum excess entropy, quantifies the shared information…
Lieb and Ruskai's strong subadditivity theorem, which shows that the conditional mutual information must be nonnegative, is fundamental in quantum theory. It has numerous applications, such as in quantum error correction. When the mutual…
Quantum key distribution requires tight and reliable bounds on the secret key rate to ensure robust security. This is particularly so for the regime of finite block sizes, where the optimization of generalized R\'enyi entropic quantities is…
Quantum physical layer security protocols offer significant advantages, particularly in space communications, but their achievable secrecy rates are often limited to the asymptotic regime. Realistic communication systems, however, demand…
Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is…
The leading term for the mutual R\'enyi information is studied for two widely separated identical compound systems for free scalar fields in $(d+1)$ Euclidean space. The compound system consists of two identical spheres in contact, with a…
The primary entropic measures for quantum states are additive under the tensor product. In the analysis of quantum information processing tasks, the minimum entropy of a set of states, e.g., the minimum output entropy of a channel, often…
Quantum mutual information (QMI) not only displays the mutual information in the system but also demonstrates some quantum correlation beyond entanglement. We explore here the two alternatives of multipartite quantum mutual information…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
In this note, we provide analytic expressions for the R\'enyi common information of orders in $(1,\infty)$ for the doubly symmetric binary source (DSBS). Until now, analytic expressions for the R\'enyi common information of all orders in…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
In this paper, we present several novel representations of $\alpha$-mutual information ($\alpha$-MI) in terms of R{\' e}nyi divergence and conditional R{\' e}nyi entropy. The representations are based on the variational characterizations of…
We give systematic ways of defining monotone quantum relative entropies and (multi-variate) quantum R\'enyi divergences starting from a set of monotone quantum relative entropies. Despite its central importance in information theory, only…
We analyze the geometry of a joint distribution over a set of discrete random variables. We briefly review Shannon's entropy, conditional entropy, mutual information and conditional mutual information. We review the entropic information…
A framework for a quantum information theory is introduced that is based on the measure of quantum information associated with probability distribution predicted by quantum measuring of state. The entanglement between states of measured…