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arXiv:quant-ph/9906098 · Physical Review A

Entanglement quantification and purification in continuous-variable systems

Scott Parker, Sougato Bose, Martin Bodo Plenio

Published Feb 10, 2000• 189 citations
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Abstract

We develop theoretical and numerical tools for the quantification of entanglement in systems with continuous degrees of freedom. Continuous variable entanglement swapping is introduced and based on this idea we develop methods of entanglement purification for continuous variable systems. The success of these entanglement purification methods is then assessed using these tools.

DOI
10.1103/physreva.61.032305

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We develop theoretical and numerical tools for the quantification of entanglement in systems with continuous degrees of freedom. Continuous variable entanglement swapping is introduced and based on this idea we develop methods of entanglement purification for continuous variable systems. The success of these entanglement purification methods is then assessed using these tools.
A profound comprehension of quantum entanglement is crucial for the progression of quantum technologies. The degree of entanglement can be assessed by enumerating the entangled degrees of freedom, leading to the determination of a parameter known as the Schmidt number. In this paper, we develop an efficient analytical tool for characterizing high Schmidt number witnesses for bipartite quantum states in arbitrary dimensions. Our methods not only offer viable mathematical methods for constructing high-dimensional Schmidt number witnesses in theory but also simplify the quantification of entanglement and dimensionality. Most notably, we develop high-dimensional Schmidt number witnesses within arbitrary-dimensional systems, with our Schmidt witness coefficients relying solely on the operator Schmidt coefficient. Subsequently, we demonstrate our theoretical advancements and computational superiority by constructing Schmidt number witnesses in arbitrary dimensional bipartite quantum systems with Schmidt numbers four and five.