arXiv:0707.3007 · Physical Review A

Relation between three-qubit entanglement invariants and two-qubit concurrence

Wen-Long Yang, Jing‐Ling Chen

Published Sep 10, 2007• 3 citations

Abstract

In this Brief Report we show the relation between three-qubit entanglement invariants and two-qubit concurrence with the help of projective measurements. How to use these invariants to represent the entanglement property of three-qubit pure states is also investigated.

DOI: 10.1103/physreva.76.034301

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arXiv:0707.3007 · Physical Review A

Relation between three-qubit entanglement invariants and two-qubit concurrence

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Published Sep 10, 2007• 3 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreva.76.034301

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{C}_{AB}

and the $AB\text{\ensuremath{-}}C$ three-qubit concurrence

{C}_{(AB)C}

, which represents the entanglement between qubits

\mathit{A}

and

\mathit{B}

as a whole and the third qubit

\mathit{C}

. It is found that the entanglement between any two qubits in a three-qubit system is limited by the entanglement between these two qubits and another qubit. As a consequence, we present the upper bounds for the concurrence

{C}_{AB}

, when the concurrence between qubits

\mathit{A}

and

\mathit{C}

({C}_{AC})

and the concurrence between qubits

\mathit{B}

and

\mathit{C}

({C}_{BC})

are both given or one of the two is provided.

For pure symmetric three-qubit states there are only three algebraically independent entanglement measures; one choice is the pairwise concurrence

\mathcal{C}

, the three-tangle $\ensuremath{\tau}$, and the Kempe invariant $\ensuremath{\kappa}$. Using a canonical form for symmetric

n

-qubit states derived from their Majorana representation, we derive the explicit achievable region of triples $(\mathcal{C},\ensuremath{\tau},\ensuremath{\kappa})$.