Most robust and fragile two-qubit entangled states under deploarizing
channels (pp0645-0660)
Chao-Qian
Pang, Fu-Lin Zhang, Yue Jiang, Mai-Lin Liang, and Jing-Ling Chen
doi:
https://doi.org/10.26421/QIC13.7-8-6
Abstracts:
For a two-qubit system under local depolarizing channels,
the most robust and most fragile states are derived for a given
concurrence or negativity. For the one-sided channel, the pure states
are proved to be the most robust ones, with the aid of the evolution
equation for entanglement given by Konrad et al. [Nat. Phys. 4, 99
(2008)]. Based on a generalization of the evolution equation for
entanglement, we classify the ansatz states in our investigation by the
amount of robustness, and consequently derive the most fragile states.
For the two-sided channel, the pure states are the most robust for a
fixed concurrence. Under the uniform channel, the most fragile states
have the minimal negativity when the concurrence is given in the region
[1/2, 1]. For a given negativity, the most robust states are the ones
with the maximal concurrence, and the most fragile ones are the pure
states with minimum of concurrence. When the entanglement approaches
zero, the most fragile states under general nonuniform channels tend to
the ones in the uniform channel. Influences on robustness by
entanglement, degree of mixture, and asymmetry between the two qubits
are discussed through numerical calculations. It turns out that the
concurrence and negativity are major factors for the robustness. When
they are fixed, the impact of the mixedness becomes obvious. In the
nonuniform channels, the most fragile states are closely correlated with
the asymmetry, while the most robust ones with the degree of mixture.
Key words:
Entanglement sudden death; Evolution equation of
entanglement; Most robust state; Most fragile state |