Quantum correlations and measurements in tri-partite quantum systems.

Abstract

Correlations and entanglement in a chain of three oscillators A,B,C with nearest neighbour coupling is studied. Oscillators A,B and B,C are coupled but there is no direct coupling between oscillators A,C. Examples with initial factorizable states are considered, and the time evolution is calculated. It is shown that the dynamics of the tri-partite system creates correlations and entanglement among the three oscillators and in particular, between oscillators A,C which are not coupled directly. We have performed photon number selective and non-selective measurements on oscillator A and we investigated their effects on the correlations and entanglement. It is shown that, before the measurement, the correlations between oscillators A,C can be stronger than the correlations of oscillators A,B. Moreover, some entanglement witness shows that oscillators A,C are entangled but the oscillators A,B might or might not be entangled. By using quantum discord, which measures the quantumness of correlations, it is shown that there are quantum correlations between oscillators A,B and after the measurements in both cases of selective and non-selective measurements, oscillators A,B and A,C become classically correlated.