Related papers: On the quantum f-relative entropy and generalized …
The study of conditional $q$-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The $q$-entropies depend on the density matrix $\rho$…
A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily…
The precise one-shot characterisation of operational tasks in classical and quantum information theory relies on different forms of smooth entropic quantities. A particularly important connection is between the hypothesis testing relative…
We present a quantum information theory that allows for a consistent description of entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices (rather than probability distributions) for the…
Mutual information is used as a purely geometrical regularization of entanglement entropy applicable to any QFT. A coefficient in the mutual information between concentric circular entangling surfaces gives a precise universal prescription…
Over the last few years, machine learning unlocked previously infeasible features for compression, such as providing guarantees for users' privacy or tailoring compression to specific data statistics (e.g., satellite images or audio…
Quantum channels, also called quantum operations, are linear, trace preserving and completely positive transformations in the space of quantum states. Such operations describe discrete time evolution of an open quantum system interacting…
Generalizations of the quantum Fano inequality are considered. The notion of $q$-entropy exchange is introduced. This quantity is concave in each of its two arguments. For $q\geq0$, the inequality of Fano type with $q$-entropic functionals…
We prove a version of the data-processing inequality for the relative entropy for general von Neumann algebras with an explicit lower bound involving the measured relative entropy. The inequality, which generalizes previous work by Sutter…
We consider both known and not previously studied trace functions with applications in quantum physics. By using perspectives we obtain convexity statements for different notions of residual entropy, including the entropy gain of a quantum…
Any reasonable measure of distinguishability of quantum states must satisfy a data processing inequality, that is, it must not increase under the action of a quantum channel. We can ask about the proportion of information lost or preserved…
It is observed that the entropy reduction (the information gain in the initial terminology) of an efficient (ideal or pure) quantum measurement coincides with the generalized quantum mutual information of a q-c channel mapping an a priori…
We investigate bounds in the transmission of classical information through quantum systems. Our focus lies in the generalized Holevo theorem, which provides a single-letter Holevo-like inequality from arbitrary quantum distance measures.…
Let $S(\rho)=- Tr (\rho \log\rho)$ be the von Neumann entropy of an $N$-dimensional quantum state $\rho$ and $e_2(\rho)$ the second elementary symmetric polynomial of the eigenvalues of $\rho$. We prove the inequality $S(\rho) \le c(N)…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
The concept of classical $f$-divergences gives a unified framework to construct and study measures of dissimilarity of probability distributions; special cases include the relative entropy and the R\'enyi divergences. Various quantum…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
We give an explicit characterisation of the quantum states which saturate the strong subadditivity inequality for the von Neumann entropy. By combining a result of Petz characterising the equality case for the monotonicity of relative…
Recently, various non-classical properties of quantum states and channels have been characterized through an advantage they provide in specific quantum information tasks over their classical counterparts. Such advantage can be typically…
In the last decades, it has been understood that a wide variety of phenomena in quantum field theory (QFT) can be characterised using quantum information measures, such as the entanglement entropy of a state and the relative entropy between…