Related papers: Tip of the Quantum Entropy Cone
We review aspects of entanglement entropy in the quantum mechanics of $N\times N$ matrices, i.e. matrix quantum mechanics (MQM), at large $N$. In doing so we review standard models of MQM and their relation to string theory, D-brane…
We normalize the combinatorial Laplacian of a graph by the degree sum, look at its eigenvalues as a probability distribution and then study its Shannon entropy. Equivalently, we represent a graph with a quantum mechanical state and study…
Entanglement is considered a fundamental ingredient for quantum technologies and condensed matter systems are among the good candidates for quantum devices. For bipartite pure states the von Neumann entropy is a proper measure of…
We study one-dimensional systems of $N$ particles in a one-dimensional harmonic trap with an inverse power law interaction $\sim|x|^{-d}$. Within the framework of the harmonic approximation we derive, in the strong interaction limit, the…
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon)…
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 provide a generalized treatment of uncertainties, von Neumann entropy, and squeezing in entangled bipartite pure state of two-level atoms. We observe that when the bipartite state is entangled, though the von Neumann entropy of the…
A `whole-part' theory is developed for a set of finite quantum systems $\Sigma (n)$ with variables in ${\mathbb Z}(n)$. The partial order `subsystem' is defined, by embedding various attributes of the system $\Sigma (m)$ (quantum states,…
A system of interacting qubits can be viewed as a non-i.i.d quantum information source. A possible model of such a source is provided by a quantum spin system, in which spin-1/2 particles located at sites of a lattice interact with each…
A large class of strongly correlated quantum systems can be described in certain large-N limits by quadratic in field actions along with self-consistency equations that determine the two-point functions. We use the replica approach and the…
The entropic uncertainty relations are a very active field of scientific inquiry. Their applications include quantum cryptography and studies of quantum phenomena such as correlations and non-locality. In this work we find…
Quantum coherence is the most distinguished signature of quantum mechanics, also recognized to be an essential resource for many promising quantum technologies, playing a central role in phenomena related to quantum information science,…
The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact…
Information inequalities govern the ultimate limitations in information theory and as such play an pivotal role in characterizing what values the entropy of multipartite states can take. Proving an information inequality, however, quickly…
The min-cut function of weighted hypergraphs and the von Neumann entropy of pure quantum states are both symmetric submodular functions. In this note, we explain this coincidence by proving that the min-cut function of any weighted…
In classical and quantum information theory, operational quantities such as the amount of randomness that can be extracted from a given source or the amount of space needed to store given data are normally characterized by one of two…
A general inequality between entanglement entropy and a number of topologically ordered states is derived, even without using the properties of the parent Hamiltonian or the formalism of topological quantum field theory. Given a quantum…
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…
Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…
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…