  We study the dynamics of entanglement of two electron spins in two quantum
dots, in which each electron is interacting with its nuclear spin environment.
Focusing on the case of uncoupled dots, and starting from either Bell or Werner
states of two qubits, we calculate the decay of entanglement due to the
hyperfine interaction with the nuclei. We mostly focus on the regime of
magnetic fields in which the bath-induced electron spin flips play a role, for
example their presence leads to the appearance of entanglement sudden death at
finite time for two qubits initialized in a Bell state. For these fields the
intrabath dipolar interactions and spatial inhomogeneity of hyperfine couplings
are irrelevant on the time scale of coherence (and entanglement) decay, and
most of the presented calculations are performed using the uniform-coupling
approximation to the exact hyperfine Hamiltonian. We provide a comprehensive
overview of entanglement decay in this regime, considering both free evolution
of the qubits, and an echo protocol with simultaneous application of $\pi$
pulses to the two spins. All the currently relevant for experiments bath states
are considered: the thermal state, narrowed states (characterized by diminished
uncertainty of one of the components of the Overhauser field) of two
uncorrelated baths, and a correlated narrowed state with a well-defined value
of the $z$ component of the Overhauser field interdot gradient. While we mostly
use concurrence to quantify the amount of entanglement in a mixed state of the
two electron spins, we also show that their entanglement dynamics can be
reconstructed from measurements of the currently relevant for experiments
entanglement witnesses, and the fidelity of quantum teleportation performed
using a partially disentangled state as a resource.
