Related papers: From quasi-entropy to skew information
It is here proposed a geometric approach for the problem of describing entropy in a quantum system. We make use of an extension of tensor calculus called morphogenetic calculus. By using such formalism we express the entropy of a quantum…
We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information and show these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. These…
We establish analogues of the Bergstr\"om and Bonnesen inequalities, related to determinants and volumes respectively, for the entropy power and for the Fisher information. The obtained inequalities strengthen the well-known convolution…
In this paper, we first provide three general norm inequalities, which are used to give new uncertainty relations of any finite observables and quantum channels via metric-adjusted skew information. The results are applicable to its special…
The pure quantum entanglement is generalized to the case of mixed compound states on an operator algebra to include the classical and quantum encodings as particular cases. The true quantum entanglements are characterized by quantum…
We study different aspects of quantum field theory at finite density using methods from quantum information theory. For simplicity we focus on massive Dirac fermions with nonzero chemical potential, and work in $1+1$ space-time dimensions.…
Firstly the fluctuation theorems (FT) for expended work in a driven nonequilibrium system, isolated or thermostatted, together with the ensuing Jarzynski work-energy (W-E) relationships, will be discussed and reobtained. Secondly, the…
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) R\'{e}nyi entropy and its related entropy power. This…
We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results from a certain…
We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is fully expressive for irreversible quantum computing, including…
Given a positive function $f$ on $(0,\infty)$ and a non-zero real parameter $\theta$, we consider a function $I_f^\theta(A,B,X)=Tr X^*(f(L_AR_B^{-1})R_B)^\theta(X)$ in three matrices $A,B>0$ and $X$. In the literature $\theta=\pm1$ has been…
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…
Uncertainty principle is one of the most essential features in quantum mechanics and plays profound roles in quantum information processing. We establish tighter summation form uncertainty relations based on metric-adjusted skew information…
We develop notions of Rota-Baxter structures and associated Birkhoff factorizations, in the context of min-plus semirings and their thermodynamic deformations, including deformations arising from quantum information measures such as the von…
Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical…
We propose a new approach to study quantum phase transitions in low-dimensional fermionic or spin models that go from uniform to spatially inhomogeneous phases such as dimerized, trimerized, or incommensurate phases. It is based on studying…
We investigate quantum average correlations and complementarity relations based on metric-adjusted skew information. Several natural averaging procedures are considered, including complete families of mutually unbiased bases, all…
We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von…
Fisher's information measure plays a very important role in diverse areas of theoretical physics. The associated measures as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the…
Quantum Information is a new area of research which has been growing rapidly since the last decade. This topic is very close to potential applications to the so called Quantum Computer. In our point of view it makes sense to develop a more…