The quantum correlations present in a system of three coupled spins 12 in a thermal state are investigated. Localizable entanglement, as well as concurrence function, is exactly evaluated. The results obtained show the existence of a temperature range corresponding to which it is impossible to localize entanglement.
We consider systems of interacting spins and study the entanglement that can be localized, on average, between two separated spins by performing local measurements on the remaining spins. This concept of localizable entanglement (LE) leads naturally to notions like entanglement length and entanglement fluctuations. For both spin-1∕2 and spin-1 systems, we prove that the LE of a pure quantum state can be lower bounded by connected correlation functions. We further propose a scheme, based on matrix-product states and the Monte Carlo method, to efficiently calculate the LE for quantum states of a large number of spins. The virtues of LE are illustrated for various spin models. In particular, characteristic features of a quantum phase transition such as a diverging entanglement length can be observed. We also give examples for pure quantum states exhibiting a diverging entanglement length but finite correlation length. We have numerical evidence that the ground state of the antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum channel. Furthermore, we apply the numerical method to mixed states and study the entanglement as a function of temperature.
We consider pure quantum states of N>>1 spins or qubits and study the average entanglement that can be localized between two separated spins by performing local measurements on the other individual spins. We show that all classical correlation functions provide lower bounds to this localizable entanglement, which follows from the observation that classical correlations can always be increased by doing appropriate local measurements on the other qubits. We analyze the localizable entanglement in familiar spin systems and illustrate the results on the hand of the Ising spin model, in which we observe characteristic features for a quantum phase transition such as a diverging entanglement length.
We investigate the possibility of the existence of different types of thermal entanglement in the two-spin Heisenberg XY model, which are distinguished by the behavior of the concurrence as a function of the model parameters. Singularities in the temperature threshold for thermal entanglement and in the ground-state energy as a function of the model parameters are used to construct diagrams containing boundary lines separating the several types of thermal entanglement in the system, showing an unexpected rich structure. We discuss a procedure to extract a pure quantum component from the spin-correlation function at arbitrary temperatures, by using the explicit form of the decomposition that minimizes the concurrence, and show that it is highly sensitive to the different patterns of thermal entanglement.