An entangled state is called $m$ resistant if it remains entangled after losing an arbitrary subset of $m$ particles but becomes fully separable after losing any number of particles larger than $m$. Quinta et al. [Phys. Rev. A 100, 062329 (2019)] conjectured that for any $N$-particle systems, there always exists an $m$-resistant pure state of some local dimension $d$. In this paper, we give two general constructions of $m$-resistant pure states. One is from the mixtures of Dicke states, which provides strong $(N-k)$-resistant pure $N$-qubit states with $k=4$ or 5. The other is from classical error-correcting codes, which provides new $m$-resistant pure qudit states for certain $m<N/2$.

Close

PrevNext

View figure in article

• Quantum entanglement