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Density matrices and entropies

Ingemar Bengtsson, Karol Zyczkowski

Cambridge University Press eBooksMay 11, 20061 citation

A generalized quantum relative entropy

Luiza Helena Félix de Andrade, Rui F. Vigelis, Charles C. Cavalcante

We propose a generalization of the quantum relative entropy by considering the geodesic on a manifold formed by all the invertible density matrices $ \mathcal{P} $. This geodesic is defined from a deformed exponential function $ \varphi $ which allows to work with a wider class of families of probability distributions. Such choice allows important flexibility in the statistical model. We show and discuss some properties of this proposed generalized quantum relative entropy.

Advances in Mathematics of CommunicationsJan 1, 20202 citations

The quantum Bayes rule and generalizations from the quantum maximum entropy method

Kevin Vanslette

The recent article 'Entropic Updating of Probability and Density Matrices' [ 1 ] derives and demonstrates the inferential origins of both the standard and quantum relative entropies in unison. Operationally, the standard and quantum relative entropies are shown to be designed for the purpose of inferentially updating probability distributions and density matrices, respectively, when faced with incomplete information. We call the inferential updating procedure for density matrices the 'quantum maximum entropy method'. Standard inference techniques in probability theory can be criticized for lacking concrete physical consequences in physics; but here, because we are updating quantum mechanical density matrices, the quantum maximum entropy method has direct physical and experimental consequences. The present article gives a new derivation of the Quantum Bayes Rule, and some generalizations, using the quantum maximum entropy method while discuss some of the limitations the quantum maximum entropy method puts on the measurement process in Quantum Mechanics.The recent article 'Entropic Updating of Probability and Density Matrices' [ 1 ] derives and demonstrates the inferential origins of both the standard and quantum relative entropies in unison. Operationally, the standard and quantum relative entropies are shown to be designed for the purpose of inferentially updating probability distributions and density matrices, respectively, when faced with incomplete information. We call the inferential updating procedure for density matrices the 'quantum maximum entropy method'. Standard inference techniques in probability theory can be criticized for lacking concrete physical consequences in physics; but here, because we are updating quantum mechanical density matrices, the quantum maximum entropy method has direct physical and experimental consequences. The present article gives a new derivation of the Quantum Bayes Rule, and some generalizations, using the quantum maximum entropy method while discuss some of the limitations the quantum maximum entropy method puts on the measurement process in Quantum Mechanics.

arXiv:1710.10949Journal of Physics CommunicationsJan 23, 20188 citations

Density matrices and entropies

Ingemar Bengtsson, Karol Życzkowski

Cambridge University Press eBooksAug 14, 20170 citations

Derivation of density operators for generalized entropies with quantum analysis

M. Ishihara

arXiv:1904.03363Physica A Statistical Mechanics and its ApplicationsNov 6, 20196 citations

Modified relative entropy of entanglement for multi-party systems

An Min Wang

We present the modified relative entropy of entanglement for multi-party systems by a given relative density matrix which is spanned by a linear combination of the direct products of so-called basis of relative density matrices and reduced density matrices for every party. For three qubit system in a pure state we derive out the explicit and closed expression of our relative density matrix which is a function of the components of the state vector of three qubits. Through computing the modified relative entropy of entanglement of some important and interesting examples, we display the main behaviors and elementary properties of the modified relative entropy of entanglement and compare it with the generalized entanglement of formation. Moreover, we also propose an assistant, as the upper bound, of the modified relative entropy of entanglement.We present the modified relative entropy of entanglement for multi-party systems by a given relative density matrix which is spanned by a linear combination of the direct products of so-called basis of relative density matrices and reduced density matrices for every party. For three qubit system in a pure state we derive out the explicit and closed expression of our relative density matrix which is a function of the components of the state vector of three qubits. Through computing the modified relative entropy of entanglement of some important and interesting examples, we display the main behaviors and elementary properties of the modified relative entropy of entanglement and compare it with the generalized entanglement of formation. Moreover, we also propose an assistant, as the upper bound, of the modified relative entropy of entanglement.

arXiv:quant-ph/0012029Dec 6, 20001 citation

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