dorsal/arxiv
View SchemaNew considerations on the separability of very noisy mixed states and implications for NMR quantum computing
| Authors | J. D. Bulnes, R. S. Sarthour, E. R. de Azevedo, F. A. Bonk, J. C. C. Freitas, A. P. Guimarães, T. J. Bonagamba, I. S. Oliveira |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0404020 |
| URL | https://arxiv.org/abs/quant-ph/0404020 |
Abstract
We revise the problem first addressed by Braunstein and co-workers (Phys. Rev. Lett. {\bf 83} (5) (1999) 1054) concerning the separability of very noisy mixed states represented by general density matrices with the form $\rho_\epsilon = (1-\epsilon)M_d+\epsilon\rho_1$. From a detailed numerical analysis, it is shown that: (1) there exist infinite values in the interval taken for the density matrix expansion coefficients, $-1\le c_{\alpha_1,...,\alpha_N}\le 1$, which give rise to {\em non-physical density matrices}, with trace equal to 1, but at least one {\em negative} eigenvalue; (2) there exist entangled matrices outside the predicted entanglement region, and (3) there exist separable matrices inside the same region. It is also shown that the lower and upper bounds of $\epsilon$ depend on the coefficients of the expansion of $\rho_1$ in the Pauli basis. If $\rho_{1}$ is hermitian with trace equal to 1, but is allowed to have {\em negative} eigenvalues, it is shown that $\rho_\epsilon$ can be entangled, even for two qubits.
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"abstract": "We revise the problem first addressed by Braunstein and co-workers (Phys.\nRev. Lett. {\\bf 83} (5) (1999) 1054) concerning the separability of very noisy\nmixed states represented by general density matrices with the form\n$\\rho_\\epsilon = (1-\\epsilon)M_d+\\epsilon\\rho_1$. From a detailed numerical\nanalysis, it is shown that: (1) there exist infinite values in the interval\ntaken for the density matrix expansion coefficients, $-1\\le\nc_{\\alpha_1,...,\\alpha_N}\\le 1$, which give rise to {\\em non-physical density\nmatrices}, with trace equal to 1, but at least one {\\em negative} eigenvalue;\n(2) there exist entangled matrices outside the predicted entanglement region,\nand (3) there exist separable matrices inside the same region. It is also shown\nthat the lower and upper bounds of $\\epsilon$ depend on the coefficients of the\nexpansion of $\\rho_1$ in the Pauli basis. If $\\rho_{1}$ is hermitian with trace\nequal to 1, but is allowed to have {\\em negative} eigenvalues, it is shown that\n$\\rho_\\epsilon$ can be entangled, even for two qubits.",
"arxiv_id": "quant-ph/0404020",
"authors": [
"J. D. Bulnes",
"R. S. Sarthour",
"E. R. de Azevedo",
"F. A. Bonk",
"J. C. C. Freitas",
"A. P. Guimar\u00e3es",
"T. J. Bonagamba",
"I. S. Oliveira"
],
"categories": [
"quant-ph"
],
"title": "New considerations on the separability of very noisy mixed states and implications for NMR quantum computing",
"url": "https://arxiv.org/abs/quant-ph/0404020"
},
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