New considerations on the separability of very noisy mixed states and implications for NMR quantum computing

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dc.creatorBulnes, J. D.
dc.creatorSarthour, R. S.
dc.creatorde Azevedo, E. R.
dc.creatorBonk, F. A.
dc.creatorFreitas, J. C. C.
dc.creatorGuimarães, A. P.
dc.creatorBonagamba, T. J.
dc.creatorOliveira, I. S.
dc.date2004-04-03
dc.date.accessioned2026-07-07T06:09:28Z
dc.date.available2026-07-07T06:09:28Z
dc.descriptionWe 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 $ρ_ε= (1-ε)M_d+ερ_1$. From a detailed numerical analysis, it is shown that: (1) there exist infinite values in the interval taken for the density matrix expansion coefficients, $-1\le c_{α_1,...,α_N}\le 1$, 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 $ε$ depend on the coefficients of the expansion of $ρ_1$ in the Pauli basis. If $ρ_{1}$ is hermitian with trace equal to 1, but is allowed to have {\em negative} eigenvalues, it is shown that $ρ_ε$ can be entangled, even for two qubits.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/quant-ph/0404020
dc.identifierhttp://arxiv.org/abs/quant-ph/0404020
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/91971
dc.subjectQuantum Physics
dc.titleNew considerations on the separability of very noisy mixed states and implications for NMR quantum computing
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