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Entanglement measures and the Hilbert–Schmidt distance

Masanao Ozawa

arXiv:quant-ph/0002036Physics Letters AApr 1, 2000190 citations

A new entanglement measure induced by the Hilbert-Schmidt norm

Christopher Witte, Mathias Trucks

In this letter we discuss a new entanglement measure. It is based on the Hilbert-Schmidt norm of operators. We give an explicit formula for calculating the entanglement of a large set of states on C^2 \\times C^2. Furthermore we find some relations between the entanglement of relative entropy and the Hilbert-Schmidt entanglement. A rigorous definition of partial transposition is given in the appendix.

Jan 1, 199872 citations

The Hilbert-Schmidt norm as a measure of entanglement in spin-1/2 Heisenberg chain: generalized Bell inequality and distance between states

Saulo L L da Silva, Daniel H. T. Franco

In this letter, we show that the measure of entanglement using the generalized Bell inequality and the distance between states coincide when we use the Hilbert-Schmidt norm. Our conclusions apply to the spin-1/2 Heisenberg chains with interaction between the first neighbors.

arXiv:2104.09661Apr 19, 20210 citations

MEASURES OF ENTANGLEMENT - A HILBERT SPACE APPROACH

W. A. Majewski, Joint work with M. Ohya T. Matsuoka

Quantum Bio-InformaticsFeb 1, 20093 citations

Measures of Quantum Entanglement

P. K. Aravind

Springer eBooksJan 1, 19962 citations

A Holevo-Type Bound for a Hilbert Schmidt Distance Measure

Boaz Tamir, Eliahu Cohen

We prove a new version of the Holevo bound employing the Hilbert-Schmidt norm instead of the Kullback-Leibler divergence. Suppose Alice is sending classical information to Bob by using a quantum channel while Bob is performing some projective measurements. We bound the classical mutual information in terms of the Hilbert-Schmidt norm by its quantum Hilbert-Schmidt counterpart. This constitutes a Holevo-type upper bound on the classical information transmission rate via a quantum channel. The resulting inequality is rather natural and intuitive relating classical and quantum expressions using the same measure.We prove a new version of the Holevo bound employing the Hilbert-Schmidt norm instead of the Kullback-Leibler divergence. Suppose Alice is sending classical information to Bob by using a quantum channel while Bob is performing some projective measurements. We bound the classical mutual information in terms of the Hilbert-Schmidt norm by its quantum Hilbert-Schmidt counterpart. This constitutes a Holevo-type upper bound on the classical information transmission rate via a quantum channel. The resulting inequality is rather natural and intuitive relating classical and quantum expressions using the same measure.

arXiv:1502.04691Journal of Quantum Information ScienceJan 1, 201527 citations

A new entanglement measure induced by the Hilbert–Schmidt norm

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