Limitations on the maximal level of entanglement of two singlet–triplet qubits in GaAs quantum dots

We analyze in detail a procedure of entangling of two singlet–triplet (S– T_0 ) qubits operated in a regime when energy associated with the magnetic field gradient, Δ B_z , is an order of magnitude smaller than the exchange energy, J, between singlet and triplet states (Shulman et al. in Science 336:202, 2012). We have studied theoretically a single S– T_0 qubit in free induction decay and spin echo experiments. We have obtained analytical expressions for the time dependence of components of its Bloch vector for quasistatic fluctuations of Δ B_z and quasistatic or dynamical 1/f^β -type fluctuations of J. We have then considered the impact of fluctuations of these parameters on the efficiency of the entangling procedure which uses an Ising-type coupling between two S– T_0 qubits. In particular, we have obtained an analytical expression for evolution of two qubits affected by 1/f^β -type fluctuations of J. This expression indicates the maximal level of entanglement that can be generated by performing the entangling procedure. Our results deliver also an evidence that in the above-mentioned experiment S– T_0 qubits were affected by uncorrelated 1/f^β charge noises.