Quantifying Entanglement

Quantifying Entanglement

(February 1, 2008) | V. Vedral, M.B. Plenio, M.A. Rippin, P. L. Knight
The paper by V. Vedral, M.B. Plenio, M.A. Rippin, and P.L. Knight presents a framework for quantifying entanglement in quantum systems. They define conditions that any measure of entanglement must satisfy and construct a class of "good" entanglement measures. These measures are geometrically intuitive and can be generalized to systems with more than two particles. The authors introduce the concept of purification procedures, which involve local general measurements and classical communication, and show that entangled states can be purified to maximally entangled states. They propose a measure of entanglement based on the minimum distance between a given state and all possible disentangled states, ensuring that the measure is zero for separable states and invariant under local unitary operations. The measure is shown to satisfy the necessary conditions for a valid entanglement measure. The paper also discusses specific examples, such as Bell-diagonal states and Werner states, and suggests that the Bures metric can be used to quantify entanglement with a statistical operational basis. The authors conclude by highlighting the potential for experimental determination of entanglement degrees using these measures.The paper by V. Vedral, M.B. Plenio, M.A. Rippin, and P.L. Knight presents a framework for quantifying entanglement in quantum systems. They define conditions that any measure of entanglement must satisfy and construct a class of "good" entanglement measures. These measures are geometrically intuitive and can be generalized to systems with more than two particles. The authors introduce the concept of purification procedures, which involve local general measurements and classical communication, and show that entangled states can be purified to maximally entangled states. They propose a measure of entanglement based on the minimum distance between a given state and all possible disentangled states, ensuring that the measure is zero for separable states and invariant under local unitary operations. The measure is shown to satisfy the necessary conditions for a valid entanglement measure. The paper also discusses specific examples, such as Bell-diagonal states and Werner states, and suggests that the Bures metric can be used to quantify entanglement with a statistical operational basis. The authors conclude by highlighting the potential for experimental determination of entanglement degrees using these measures.
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[slides and audio] Quantifying Entanglement