Charge qubit entanglement in double quantum dots

– We study entanglement of charge qubits in a vertical tunnel-coupled double quantum dot containing two interacting electrons. Exact diagonalization is used to compute the negativity characterizing entanglement. We find that entanglement can be efficiently generated and controlled by sidegate voltages, and describe how it can be detected. For large enough tunnel coupling, the negativity shows a pronounced maximum at an intermediate interaction strength within the Wigner molecule regime. Semiconductor few-electron quantum dots (QDs) continue to attract a lot of interest, as it has now become possible to experimentally control both the electronic spin and charge in a condensed-phase environment in an unprecedented manner. In particular, double quantum dots (DQDs) can be fabricated in a well-controlled fashion in high-quality semiconductor devices, and are currently under intense study [1–9]. Vertical or lateral tunnel-coupled DQDs are among the most promising candidates for realizing spin or charge qubits in a quantum information processor [10–12]. Their main advantages are scalability, good control of physical properties via tunable external (sidegate-) voltages or magnetic fields, and spatial separation of the individual QDs (allowing to perform oneor two-qubit operations). Recent progress has been very swift, and present-day experiments are performed on DQDs containing just one or two electrons. We present an exact diagonalization study of ground-state entanglement in a vertical tunnel-coupled DQD containing two interacting electrons. In general, entanglement provides a crucial resource for quantum computing, making certain tasks faster or more secure [13]. While coherent single-electron dynamics has been successfully realized in DQDs, see, e.g., Refs. [8,9], systematic studies of the two-electron dynamics and of entanglement are only now coming into reach [4]. In view of these developments, it seems timely to provide theoretical predictions for two-electron charge entanglement in DQDs, including both the effects of electron-electron interactions and of spin-orbit (SO) couplings. Entanglement of two ‘charge qubits’, which here arise because an electron may reside in the upper or the lower dot, in such a bipartite mixed state can, for instance, be determined by the Peres-Horodecki measure (the ‘negativity’ N) [14, 15] in a mathematically sufficient and necessary way. Other entanglement measures exist [16], for instance, the commonly used concurrence C [17], which is mathematically equivalent. It obeys the inequality C ≥ N [18, 19], although we find only