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Quantum correlations and measurements in tri-partite quantum systems.

Bahari Idrus

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Correlations and entanglement in a chain of three oscillators A,B,C with \nnearest neighbour coupling is studied. Oscillators A,B and B,C are coupled \nbut there is no direct coupling between oscillators A,C. Examples with initial \nfactorizable states are considered, and the time evolution is calculated. It \nis shown that the dynamics of the tri-partite system creates correlations and \nentanglement among the three oscillators and in particular, between oscillators \nA,C which are not coupled directly. We have performed photon number \nselective and non-selective measurements on oscillator A and we investigated \ntheir effects on the correlations and entanglement. It is shown that, before \nthe measurement, the correlations between oscillators A,C can be stronger \nthan the correlations of oscillators A,B. Moreover, some entanglement witness \nshows that oscillators A,C are entangled but the oscillators A,B might \nor might not be entangled. By using quantum discord, which measures the \nquantumness of correlations, it is shown that there are quantum correlations \nbetween oscillators A,B and after the measurements in both cases of selective \nand non-selective measurements, oscillators A,B and A,C become classically \ncorrelated.

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Correlations and entanglement in a chain of three oscillators A,B,C with \nnearest neighbour coupling is studied. Oscillators A,B and B,C are coupled \nbut there is no direct coupling between oscillators A,C. Examples with initial \nfactorizable states are considered, and the time evolution is calculated. It \nis shown that the dynamics of the tri-partite system creates correlations and \nentanglement among the three oscillators and in particular, between oscillators \nA,C which are not coupled directly. We have performed photon number \nselective and non-selective measurements on oscillator A and we investigated \ntheir effects on the correlations and entanglement. It is shown that, before \nthe measurement, the correlations between oscillators A,C can be stronger \nthan the correlations of oscillators A,B. Moreover, some entanglement witness \nshows that oscillators A,C are entangled but the oscillators A,B might \nor might not be entangled. By using quantum discord, which measures the \nquantumness of correlations, it is shown that there are quantum correlations \nbetween oscillators A,B and after the measurements in both cases of selective \nand non-selective measurements, oscillators A,B and A,C become classically \ncorrelated.
In this talk we will discuss how entanglement is defined with respect to separability, and how the strategies for quantifying two-party entanglement can be extended to multiple parties. Though residual entanglement (i.e., what is left when two-party entanglement is subtracted away) is a popular concept for measuring three-party entanglement, we criticize this and expand on a new resource-based measure known as the tri-partite entanglement of formation. Though there remain multiple fundamental questions to be answered on measures of multi-partite entanglement, we show how the tri-partite entanglement of formation can be bounded from below using experimental correlations in much the same way as was done for two parties. Moreover, we give examples showing how much tripartite entanglement may be present in entangled photon triplets generated in nonlinear optics, and provide a general witness for N-partite entanglement. In our development of the N-partite witness, we also discovered something interesting about the nature of quantum correlations. Though there is no quantum-imposed limit to the correlations two parties can share (e.g., in both position and in momentum), there is such a limit for three or more parties.
Time evolution dynamics of three non-coupled two-level atoms independently interacting with their reservoirs is solved exactly by considering a damping Lorentzian spectral density. For three atoms initially prepared in Greenberger—Horne—Zeilinger-type state, quantum correlation dynamics in a Markovian reservoir is compared with that in a non-Markovian reservoir. By increasing detuning quantity in the non-Markovian reservoir, three-atom correlation dynamics measured by negative eigenvalue presents a trapping phenomenon which provides long-time quantum entanglement. Then we compare the correlation dynamics of three atoms with that of two atoms, measured by quantum entanglement and quantum discord for an initial robuster-entangled type state. The result further confirms that quantum discord is indeed different from quantum entanglement in identifying quantum correlation of many bodies.
A system comprised of three oscillators A, B and C is studied. The oscillators B and C are interacting with each other, while the oscillator A does not interact with any of them. At t = 0 the system is in the state ρAB(0) ⊗ ρC(0). Two examples in which ρAB(0) is in separable and entangled states, are considered. It is shown that the oscillators A, C become entangled and that a measurement in C whose result is communicated classically to A , affects the state of the oscillator A. The work studies how the collapse due to the measurement at C , affects the state of the oscillator A .
We investigate the prominent impacts of coupling strengths on the evolution of entanglement and quantum discord for a three-qubit system coupled to an XY spin-chain environment. In the case of a pure W state, more robust, even larger nonzero quantum correlations can be obtained by tailoring the coupling strengths between the qubits and the environment. For a mixed state consisting of the GHZ and W states, the dynamics of entanglement and quantum discord can characterize the critical point of quantum phase transition. Remarkably, a large nonzero quantum discord is generally retained, while the nonzero entanglement can only be obtained as the system-environment coupling satisfies certain conditions. We also find that the impact of each qubit’s coupling strength on the quantum correlation dynamics strongly depends on the variation schemes of the system-environment couplings.