相关论文: Infinitely many constrained inequalities for the v…
In recent years, various quantum inequalities have been established on quantum symmetries in the framework of quantum Fourier analysis. We provide a detailed introduction to quantum inequalities including Hausdorff-Young inequality, Young's…
The entropic region is formed by the collection of the Shannon entropies of all subvectors of finitely many jointly distributed discrete random variables. For four or more variables, the structure of the entropic region is mostly unknown.…
Uncertainty relations are central to quantum physics. While they were originally formulated in terms of variances, they have later been successfully expressed with entropies following the advent of Shannon information theory. Here, we…
After a brief introduction to the concept of entanglement in quantum systems, I apply these ideas to many-body systems and show that the von Neumann entropy is an effective way of characterising the entanglement between the degrees of…
Entropic uncertainty relations demonstrate the intrinsic uncertainty of nature from an information-theory perspective. Recently, a quantum-memory-assisted entropic uncertainty relation for multiple measurements was proposed by Wu $et\ al.$…
Claude Shannon coined entropy to quantify the uncertainty of a random distribution for communication coding theory. We observe that the uncertainty nature of entropy also limits its direct usage in mathematical modeling. Therefore we…
I show that non-decreasing entropy provides a necessary and sufficient condition to convert the state of a physical system into a different state by a reversible transformation that acts on the system of interest and a further "catalyst"…
It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the…
We generalize, improve and unify theorems of Rumin, and Maassen--Uffink about classical entropies associated to quantum density matrices. These theorems refer to the classical entropies of the diagonals of a density matrix in two different…
Entropy is a fundamental property of both classical and quantum systems, spanning myriad theoretical and practical applications in physics and computer science. We study the problem of obtaining estimates to within a multiplicative factor…
K. He, J. Hou, and M. Li have recently given a sufficient and necessary condition for unitary equivalence of quantum states. This condition is based on the von Neumann entropy. In this note we first give a short proof of their result, and…
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…
We employ some techniques involving projections in a von Neumann algebra to establish some maximal inequalities such as the strong and weak symmetrization, Levy, Levy-Skorohod, and Ottaviani inequalities in the realm of the quantum…
The R{\'e}nyi entropy is one of the important information measures that generalizes Shannon's entropy. The quantum R{\'e}nyi entropy has a fundamental role in quantum information theory, therefore, bounding this quantity is of vital…
We derive fundamental constraints for the Schur complement of positive matrices, which provide an operator strengthening to recently established information inequalities for quantum covariance matrices, including strong subadditivity. This…
It has long been conjectured that the entropy of quantum fields across boundaries scales as the boundary area. This conjecture has not been easy to test in spacetime dimensions greater than four because of divergences in the von Neumann…
We derive an inequality for the linear entropy, that gives sharp bounds for all finite dimensional systems. The derivation is based on generalised Bloch decompositions and provides a strict improvement for the possible distribution of…
Relations between Shannon entropy and Renyi entropies of integer order are discussed. For any N-point discrete probability distribution for which the Renyi entropies of order two and three are known, we provide an lower and an upper bound…
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…
We study the von Neumann entropy of the partial trace of a system of two two-level atoms (qubits) in a dispersive cavity where the atoms are interacting collectively with a single mode electromagnetic field in the cavity. We make a contrast…