Quantum entanglement of space domains occupied by interacting electrons

Spin-entanglement of two electrons occupying two spatial regions – domains – is expressed in a compact form in terms of spin-spin correlation functions. The power of the formalism is demonstrated on several examples ranging from generation of entanglement by scattering of two electrons to the entanglement of a pair of qubits represented by a double quantum dot coupled to leads. In the latter case the collapse of entanglement due to the Kondo effect is analyzed. 1 Introduction Based on the peculiar behaviour of entangled quantum states, in 1935 Einstein, Podolsky and Rosen argued that quantum mechanical description of reality is not complete [1]. Today this article is Einstein's most cited publication, but quantum entanglement is not considered a paradox. In fact, the ability to establish entangle-ment between quantum particles in a controlled manner is a crucial ingredient of any quantum information processing system [2]. Also, the study of entanglement provides insight into the nature of many-body states in the vicinity of crossovers between various regimes or points of quantum phase transition [3]. In realistic hardware designed for quantum information processing, several criteria for qubits (DiVincenzo's checklist) must be fulfilled [4]: the existence of multiple identifiable qubits, the ability to initialize and manipulate qubits, small decoherence, and the ability to measure qubits, i.e., to determine the outcome of computation. Quite generally, the parts of an interacting system are to some extent entangled. However, fully entangled qubit pairs are required for such applications [2]. This leads to the question of how to quantify the entanglement. The entanglement of binary quantum objects (qubits) can be quantified by the entanglement of formation, a notion which for pure states reduces to the von Neumann en