Related papers: Strong Subadditivity Lower Bound and Quantum Chann…
Quantum channel capacity is a fundamental quantity in order to understand how good can quantum information be transmitted or corrected when subjected to noise. However, it is generally not known how to compute such quantities, since the…
In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…
In this paper, we derive a new generalisation of the strong subadditivity of the entropy to the setting of general conditional expectations onto arbitrary finite-dimensional von Neumann algebras. The latter inequality, which we call…
We investigate the additivity properties for both bipartite and multipartite systems by using entropic uncertainty relations (EUR) defined in terms of the joint Shannon entropy of probabilities of local measurement outcomes. In particular,…
The entanglement content of superpositions of quantum states is investigated based on a measure called {\it concurrence}. Given a bipartite pure state in arbitrary dimension written as the quantum superposition of two other such states, we…
By carrying out appropriate continuous quantum measurements with a family of projection operators, a unitary channel can be approximated in an arbitrary precision in the trace norm sense. In particular, the quantum Zeno effect is described…
This manuscript introduces a computationally efficient method to calculate the nonlinearity of a quantum feature map, as well as a method for determining whether a quantum feature map will have a high concentration of quantum states. The…
We show that the von Neumann's algorithm of reduction (i.e. the algorithm of calculating the density matrix of the observable subsystem from the density matrix of the closed quantum system) corresponds to the special approximation at which…
Quantum entropy is an important measure for describing the uncertainty of a quantum state, more uncertainty in subsystems implies stronger quantum entanglement between subsystems. Our goal in this work is to quantify bipartite entanglement…
Entanglement of pure states of bipartite quantum systems has been shown to have a unique measure in terms of the von Neumann entropy of the reduced states of either of its subsystems. The measure is established under entanglement…
The entanglement entropy of a pure quantum state of a bipartite system $A \cup B$ is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local…
We consider two-dimensional states of matter satisfying an uniform area law for entanglement. We show that the topological entanglement entropy is equal to the minimum relative entropy distance from the reduced state to the set of thermal…
Given an arbitrary quantum state ($\sigma$), we obtain an explicit construction of a state $\rho^*_\varepsilon(\sigma)$ (resp. $\rho_{*,\varepsilon}(\sigma)$) which has the maximum (resp. minimum) entropy among all states which lie in a…
For a quantum state undergoing unitary Schr\"odinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum…
The quantum probability distribution arising from single-copy von Neumann measurements on an arbitrary two-qubit state is decomposed into the local and nonlocal parts, in the approach of Elitzur, Popescu and Rohrlich [A. Elitzur, S.…
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…
Information theory has become an increasingly important research field to better understand quantum mechanics. Noteworthy, it covers both foundational and applied perspectives, also offering a common technical language to study a variety of…
Determining capacities of quantum channels is a fundamental question in quantum information theory. Despite having rigorous coding theorems quantifying the flow of information across quantum channels, their capacities are poorly understood…
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…
The proof of additivity of entanglement of formation for some special cases is given. The strong concavity of von Neumann entropy due to strong subadditivity of von Neumann entropy is presented. Some general relations concerning about the…