Related papers: R\'enyi Entropy, Signed Probabilities, and the Qub…
The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…
The asymptotics of the weighted $L_{p}$-norms of Hermite polynomials, which describes the R\'enyi entropy of order $p$ of the associated quantum oscillator probability density, is determined for $n\to\infty$ and $p>0$. Then, it is applied…
The random matrix ensembles (RME), especially Gaussian random matrix ensembles GRME and Ginibre random matrix ensembles, are applied to following quantum systems: nuclear systems, molecular systems, and two-dimensional electron systems…
We derive entropic inseparability criteria for the phase space representation of quantum states. In contrast to criteria involving differential entropies of marginal phase space distributions, our criteria are based on a joint distribution…
Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…
Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here we express it as an effective amount (measure) of distinct outcomes…
R\'enyi entropy is a one-parameter generalization of Shannon entropy, which has been used in various fields of physics. Despite its wide applicability, the physical interpretations of the R\'enyi entropy are not widely known. In this paper,…
The study of conditional $q$-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The $q$-entropies depend on the density matrix $\rho$…
It is proposed to map the quantum information qubit not to individual spin 1/2 states, but to the collective spin states being eigenfunctions of the Hamiltonian including spin-spin interactions, which may be not small. Such an approach…
After Shannon, entropy becomes a fundamental quantity to describe not only uncertainity or chaos of a system but also information carried by the system. Shannon's important discovery is to give a mathematical expression of the mutual…
The efficient simulation of correlated quantum systems is the most promising near-term application of quantum computers. Here, we present a measurement of the second Renyi entropy of the ground state of the two-site Fermi-Hubbard model on a…
The entropy of probability distribution defined by Shannon has several extensions. R\'enyi entropy is one of the general extensions of Shannon entropy and is widely used in engineering, physics, and so on. On the other hand, the quantum…
We investigate quantum phase transitions (QPTs) in spin chain systems characterized by local Hamiltonians with matrix product ground states. We show how to theoretically engineer such QPT points between states with predetermined properties.…
The two-parameter Minkowski like inequality written for composite quantum system state is obtained for arbitrary Hermitian nonnegative matrix with trace equal to unity. The inequality can be used as entropic and information inequality for…
In this article we establish new bounds on the quantum communication complexity of distributed problems. Specifically, we consider the amount of communication that is required to transform a bipartite state into another, typically more…
The R\'enyi entropy is a mathematical generalization of the concept of entropy and it encodes the total information of a system as a funtion of its order parameter $\alpha$. The meaning of the R\'enyi entropy in physics is not completely…
We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…
R\'enyi complexity ratio of two density functions is introduced for three and multidimensional quantum systems. Localization property of several density functions are defined and five theorems about near continuous property of R\'enyi…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
The aim of the present paper is twofold. First, to give the main ideas behind quantum computingand quantum information, a field based on quantum-mechanical phenomena. Therefore, a shortreview is devoted to (i) quantum bits or qubits (and…