We propose two schemes for splitting single- and two-qubit states by using four-particle genuine entangled state as the quantum channel. After the sender performs Bell-basis (or three-partite GHZ- basis) measurements on her particles, and the cooperators operate single-particle measurements on their particles, the state receiver can reconstruct the original state of the sender by applying the appropriate unitary operation. In particular, in the scheme for splitting two-qubit state, the receiver needs to introduce an auxiliary particle and carries out a C-NOT operation.
Cooper pair splitters are promising candidates for generating spin-entangled electrons. However, the splitting of Cooper pairs is a random and noisy process, which hinders further synchronized operations on the entangled electrons. To circumvent this problem, we here propose and analyze a dynamic Cooper pair splitter that produces a noiseless and regular flow of spin-entangled electrons. The Cooper pair splitter is based on a superconductor coupled to quantum dots, whose energy levels are tuned in and out of resonance to control the splitting process. We identify the optimal operating conditions for which exactly one Cooper pair is split per period of the external drive and the flow of entangled electrons becomes noiseless. To characterize the regularity of the Cooper pair splitter in the time domain, we analyze the g^{(2)} function of the output currents and the distribution of waiting times between split Cooper pairs. Our proposal is feasible using current technology, and it paves the way for dynamic quantum information processing with spin-entangled electrons.
Proposals to probe the quantum nature of gravity through entanglement between spatially separated masses have attracted considerable interest. In such schemes, spatial superpositions are prepared through controlled splitting operations that produce several interferometric branches. Here we propose and analyse protocols involving repeated splitting stages, each of which doubles the number of occupied paths. We show that the density matrix after
n splitting stages is related to that of the
(n−1)-splitting protocol through local parity dephasing. Two of the resulting sectors reproduce the preceding state, while the other two acquire additional gravitational phases. Removing the locally generated parts gives an exact lower bound on the change in negativity, expressed in terms of the preceding state's negative partial-transpose eigenspace. For two splitting stages, this leads to an explicit condition on three gravitational phases under which the additional split cannot reduce negativity. We also show that further splitting cannot shorten the lifetime of the generated entanglement. If the local internal system preserves the full branch label, the positional entanglement is retained upon recombination. We describe an implementation using a reusable two-level system and local memories, and compare it with a readout without a memory register. For the latter, we derive an exact condition for when an additional splitting stage improves the readout, based on a
2×2 Schur complement. Numerical simulations show an advantage in positional negativity over the rates considered, with an improvement surviving the restricted readout at all decoherence rates considered at the final readout time.