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Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…
A new interpretation of entanglement entropy is proposed: entanglement entropy of a pure state with respect to a division of a Hilbert space into two subspaces 1 and 2 is an amount of information, which can be transmitted through 1 and 2…
The topological entropy dimension is mainly used to distinguish the zero topological entropy systems. Two types of topological entropy dimensions, the classical entropy dimension and the Pesin entropy dimension, are investigated for…
We study the quantification of coherence in infinite dimensional systems, especially the infinite dimensional bosonic systems in Fock space. We show that given the energy constraints, the relative entropy of coherence serves as a…
Superconducting microwave quantum networks is a rapidly developing field, enabling distributed quantum computing and holding a promise for hybrid architectures in quantum internet. Quantum secret sharing (QSS) is one of the key protocols…
Quantum networks, which can exceed the framework of standard bell theorem, flourish the investigation of quantum nonlocality further. Recently, a concept of full quantum network nonlocality (FNN) which is stronger than network nonlocality,…
A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balanceable quantities. These flows are first…
Quantum conditional entropies play a fundamental role in quantum information theory. In quantum key distribution, they are exploited to obtain reliable lower bounds on the secret-key rates in the finite-size regime, against collective…
We view DHR superselection sectors with finite statistics as Quantum Field Theory analogs of elliptic operators where KMS functionals play the role of the trace composed with the heat kernel regularization. We extend our local holomorphic…
In the present work we are studying a bosonic quantum field system at finite temperature, and at zero and non-zero chemical potential. For a simple spatial partition we derive the corresponding mutual information, a quantity that measures…
We investigate fundamental connections between thermodynamics and quantum information theory. First, we show that the operational framework of thermal operations is nonequivalent to the framework of Gibbs-preserving maps, and we comment on…
Using the relative entropy of total correlation, we derive an expression relating the mutual information of $n$-partite pure states to the sum of the mutual informations and entropies of its marginals and analyze some of its implications.…
The von Neumann entropy plays a vital role in quantum information theory. The von Neumann entropy determines, e.g., the capacities of quantum channels. Also, entropies of composite quantum systems are important for future quantum networks,…
We consider scaling of the entanglement entropy across a topological quantum phase transition in one dimension. The change of the topology manifests itself in a sub-leading term, which scales as $L^{-1/\alpha}$ with the size of the…
We consider entropy in Generalized Non-Signalling Theory (also known as box world) where the most common definition of entropy is the measurement entropy. In this setting, we completely characterize the set of allowed entropies for a…
Landauer's principle provides a link between Shannon's information entropy and Clausius' thermodynamical entropy. We set up here a basic formula for the incremental free energy of a quantum channel, possibly relative to infinite systems,…
Issues related to quantum entanglement in systems of indistinguishable particles, as discussed in the information theoretic approach, are extended to anyonic statistics. Local and non-local measurements discussed in this framework are…
Superdiffusion is an anomalous transport behavior. Recently, a new mechanism, termed the ``nodal mechanism," has been proposed to induce superdiffusion in quantum models. However, existing realizations of the nodal mechanism have so far…
In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent…
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…