dorsal/arxiv
View SchemaLewenstein-Sanpera decomposition of a generic 2x2 density matrix by using Wootters's basis
| Authors | S. J. Akhtarshenas, M. A. Jafarizadeh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0211051 |
| URL | https://arxiv.org/abs/quant-ph/0211051 |
Abstract
The Lewenstein-Sanpera decomposition for a generic two-qubit density matrix is obtained by using Wootters's basis. It is shown that the average concurrence of the decomposition is equal to the concurrence of the state. It is also shown that all the entanglement content of the state is concentrated in the Wootters's state $|x_1>$ associated with the largest eigenvalue $\lambda_1$ of the Hermitian matrix $\sqrt{\sqrt{\rho}\tilde{\rho}\sqrt{\rho}}$ >. It is shown that a given density matrix $\rho$ with corresponding set of positive numbers $\lambda_i$ and Wootters's basis can transforms under $SO(4,c)$ into a generic $2\times2$ matrix with the same set of positive numbers but with new Wootters's basis, where the local unitary transformations correspond to $SO(4,r)$ transformations, hence, $\rho$ can be represented as coset space $SO(4,c)/SO(4,r)$ together with positive numbers $\lambda_i$. By giving an explicit parameterization we characterize a generic orbit of group of local unitary transformations.
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"abstract": "The Lewenstein-Sanpera decomposition for a generic two-qubit density matrix\nis obtained by using Wootters\u0027s basis. It is shown that the average concurrence\nof the decomposition is equal to the concurrence of the state. It is also shown\nthat all the entanglement content of the state is concentrated in the\nWootters\u0027s state $|x_1\u003e$ associated with the largest eigenvalue $\\lambda_1$ of\nthe Hermitian matrix $\\sqrt{\\sqrt{\\rho}\\tilde{\\rho}\\sqrt{\\rho}}$ \u003e. It is shown\nthat a given density matrix $\\rho$ with corresponding set of positive numbers\n$\\lambda_i$ and Wootters\u0027s basis can transforms under $SO(4,c)$ into a generic\n$2\\times2$ matrix with the same set of positive numbers but with new Wootters\u0027s\nbasis, where the local unitary transformations correspond to $SO(4,r)$\ntransformations, hence, $\\rho$ can be represented as coset space\n$SO(4,c)/SO(4,r)$ together with positive numbers $\\lambda_i$. By giving an\nexplicit parameterization we characterize a generic orbit of group of local\nunitary transformations.",
"arxiv_id": "quant-ph/0211051",
"authors": [
"S. J. Akhtarshenas",
"M. A. Jafarizadeh"
],
"categories": [
"quant-ph"
],
"title": "Lewenstein-Sanpera decomposition of a generic 2x2 density matrix by using Wootters\u0027s basis",
"url": "https://arxiv.org/abs/quant-ph/0211051"
},
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