### Abstract

For every possible spectrum of 2^{N}-dimensional density operators, we construct an N-qubit X-state of the same spectrum and maximal genuine multipartite (GM-) concurrence, hence characterizing a global unitary transformation that - constrained to output X-states - maximizes the GM-concurrence of an arbitrary input mixed state of N qubits. We also apply semidefinite programming methods to obtain N-qubit X-states with maximal GM-concurrence for a given purity and to provide an alternative proof of optimality of a recently proposed set of density matrices for the purpose, the so-called XMEMS. Furthermore, we introduce a numerical strategy to tailor a quantum operation that converts between any two given density matrices using a relatively small number of Kraus operators. We apply our strategy to design short operator-sum representations for the transformation between any given N-qubit mixed state and a corresponding X-MEMS of the same purity.

Original language | English (US) |
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Article number | 215304 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 48 |

Issue number | 21 |

DOIs | |

State | Published - May 29 2015 |

### Keywords

- Entanglement
- Genuine Multipartite Concurrence
- N-qubit X-states

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

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## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*48*(21), [215304]. https://doi.org/10.1088/1751-8113/48/21/215304