Maximally entangled mixed states for qubit-qutrit systems

Paulo E.M.F. Mendonça; Marcelo A. Marchiolli; Samuel R. Hedemann

doi:10.1103/PhysRevA.95.022324

Maximally entangled mixed states for qubit-qutrit systems

Paulo E.M.F. Mendonça
, Marcelo A. Marchiolli
, Samuel R. Hedemann

Department of Physics

Stevens Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the latter, partial solutions are obtained by imposing extra spectral constraints such as rank deficiency and degeneracy, which enable a semidefinite programming treatment for the optimization problem at hand. Despite the technically motivated assumptions, we provide strong numerical evidence that threefold degenerate X states of purity P reach the highest entanglement negativity accessible to arbitrary qubit-qutrit density matrices of the same purity, hence characterizing a sparse family of likely qubit-qutrit maximally entangled mixed states.

Original language	English
Article number	022324
Journal	Physical Review A
Volume	95
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevA.95.022324
State	Published - Feb 21 2017

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics

Access to Document

10.1103/PhysRevA.95.022324

Cite this

@article{c3511d93d33b45e5a56f2594bee23bfd,

title = "Maximally entangled mixed states for qubit-qutrit systems",

abstract = "We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the latter, partial solutions are obtained by imposing extra spectral constraints such as rank deficiency and degeneracy, which enable a semidefinite programming treatment for the optimization problem at hand. Despite the technically motivated assumptions, we provide strong numerical evidence that threefold degenerate X states of purity P reach the highest entanglement negativity accessible to arbitrary qubit-qutrit density matrices of the same purity, hence characterizing a sparse family of likely qubit-qutrit maximally entangled mixed states.",

author = "Mendon{\c c}a, \{Paulo E.M.F.\} and Marchiolli, \{Marcelo A.\} and Hedemann, \{Samuel R.\}",

note = "Publisher Copyright: {\textcopyright} 2017 American Physical Society.",

year = "2017",

month = feb,

day = "21",

doi = "10.1103/PhysRevA.95.022324",

language = "English",

volume = "95",

journal = "Physical Review A",

issn = "2469-9926",

publisher = "American Physical Society",

number = "2",

}

TY - JOUR

T1 - Maximally entangled mixed states for qubit-qutrit systems

AU - Mendonça, Paulo E.M.F.

AU - Marchiolli, Marcelo A.

AU - Hedemann, Samuel R.

PY - 2017/2/21

Y1 - 2017/2/21

N2 - We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the latter, partial solutions are obtained by imposing extra spectral constraints such as rank deficiency and degeneracy, which enable a semidefinite programming treatment for the optimization problem at hand. Despite the technically motivated assumptions, we provide strong numerical evidence that threefold degenerate X states of purity P reach the highest entanglement negativity accessible to arbitrary qubit-qutrit density matrices of the same purity, hence characterizing a sparse family of likely qubit-qutrit maximally entangled mixed states.

AB - We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the latter, partial solutions are obtained by imposing extra spectral constraints such as rank deficiency and degeneracy, which enable a semidefinite programming treatment for the optimization problem at hand. Despite the technically motivated assumptions, we provide strong numerical evidence that threefold degenerate X states of purity P reach the highest entanglement negativity accessible to arbitrary qubit-qutrit density matrices of the same purity, hence characterizing a sparse family of likely qubit-qutrit maximally entangled mixed states.

UR - https://www.scopus.com/pages/publications/85013745131

UR - https://www.scopus.com/pages/publications/85013745131#tab=citedBy

U2 - 10.1103/PhysRevA.95.022324

DO - 10.1103/PhysRevA.95.022324

M3 - Article

SN - 2469-9926

VL - 95

JO - Physical Review A

JF - Physical Review A

IS - 2

M1 - 022324

ER -

Maximally entangled mixed states for qubit-qutrit systems

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this