In a tripartite quantum system, research has shown how the dynamics can create correlations and entanglement especially for indirect correlation between the particles. Although, there is no direct correlation between the particles in some cases, however, after evolution or transformation they become entangled. In this paper, we demonstrate the use of one type of von Neumann measurement called the non-selective measurement. The objective of this paper is to investigate the effects of non-selective measurement on a chain of three oscillators A, B, C with nearest neighbour coupling when we performed the photon number measurement on A. We are interested to investigate the effects of quantum measurement on the correlation and entanglement, that is, whether it will increase or decrease and also the effects on the whole tripartite quantum system. It was discovered that, after the measurement on A, the correlation of oscillators A, B and A, C collapse to factorizable states and do not effect the entanglement of oscillator B,C.
In a tripartite quantum system, research has shown how the dynamics can create correlations and entanglement especially for indirect correlation between the particles. Although, there is no direct correlation between the particles in some cases, however, after evolution or transformation they become entangled. In this paper, we demonstrate the use of one type of von Neumann measurement called the non-selective measurement. The objective of this paper is to investigate the effects of non-selective measurement on a chain of three oscillators A, B, C with nearest neighbour coupling when we performed the photon number measurement on A. We are interested to investigate the effects of quantum measurement on the correlation and entanglement, that is, whether it will increase or decrease and also the effects on the whole tripartite quantum system. It was discovered that, after the measurement on A, the correlation of oscillators A, B and A, C collapse to factorizable states and do not effect the entanglement of oscillator B,C.
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.
The process of measurement plays an important role in quantum theory. Measurements can be direct, if the physical system S interacts directly with the measurement apparatus M (as we have assumed until now), or indirect. In the latter case, the physical system first interacts with an ancillary system B , which may have a space of states that is very different from that of S , for instance much larger; after this interaction has finished, M is used to perform a measurement on B , without any direct interaction with A . Because S is then “protected” from any direct interaction with the measurement apparatus, the state of S is not necessarily strongly modified, and may even be only weakly affected. In both cases, the process implies entanglement between several physical systems. In this chapter, we study how this entanglement is created and used for measurements as well as the notion of weak and continuous measurements. These questions play an important role in several of the interpretations of quantum mechanics that we discuss in Chapter 10. Direct measurements The Von Neumann model of quantum measurement [4] provides a general frame for describing the process in terms of correlations appearing (or disappearing) in the state vector associated with the whole system S + M . In this model, the two systems S and M are initially described by a product state ∣ψ 0 〈 and interact during the time of measurement, so that they become entangled; they then reach a final state ∣ψ′〈 and do not interact anymore.
We describe an efficient theoretical criterion suitable for the evaluation of the tripartite entanglement of any mixed three-boson or three-fermion state, based on the notion of the entanglement of particles for bipartite systems of identical particles. Our approach allows one to quantify the accessible number of quantum correlations in the systems without any violation of the local particle number superselection rule. A generalization of the tripartite negativity is here applied to some correlated systems including the continuous-time quantum walks of identical particles (for both bosons and fermions) and compared with other criteria recently proposed in the literature. Our results show the dependence of the entanglement dynamics upon the quantum statistics: The bosonic bunching results in a low number of quantum correlations while Fermi-Dirac statistics allows for higher values of the entanglement.
Quantum entanglement is one of most remarkable features of quantum mechanics,and in recent years it has played a more and more important role in quantum information.However,real quantum system inevitably interacts with the environment,resulting in the entanglement decay or even entanglement sudden death,so it is necessary to study the entanglement dynamical properties of an open system under different environments.In this paper,we investigate the entanglement dynamic behaviors of three interacting two-level atoms in an optical cavity which is coupled to a structured zero-temperature bosonic reservoir.Laplace transform,LBC and other methods are utilized,through numerical method we analyze the entanglement dynamic behavios of tripartite of three atoms and bipartite of cavity and reservoir.We also discuss how the coupling parameters affect the entanglement dynamics.Results show that in a short time,the entanglement of tripartite increases with coupling strength of three atoms increasing,and a periodic oscillation appears, but entanglement of bipartite decreases.The entanglement of tripartite decreases with the coupling strength between atoms and cavity increasing and damping oscillation appears,but the entanglement of bipartite increases.In a long-time limit,the entanglement approaches to a steady value.The non-Markovian dynamics of the qubits is determined by both the coupling strength and the spectral width.The strong system-reservoir coupling regime results in the non-Markovian dynamics of system.As the spectral width increases,the system of three atoms transforms from non-Markovian regime to Markovian regime.The increasing of spectral width results in the Markovian dynamic behavior of system,but the system of the atoms falls into the non-Markovian regime once more.When the coupling between the cavity and reservoir is weak,the entanglement of three atoms increases as the detuning of the cavity and reservoir increases,but it is not obvious.When the coupling between the cavity and reservoir is strong,the entanglement of three atoms increases and a periodic oscillation appears with increasing the detuning between the cavity and reservoir,so we can effectively restrain the effects of dissipation of reservoir on entanglement decay by adjusting the detuning between the cavity and reservoir.
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 .
Qubits A, B and C, initially prepared in a like-GHZ state, are distributed to three remote receivers through a decoherence environment. A weak measurement is firstly performed on each qubit before experiencing the decoherence channel, and then the receivers carry out a quantum measurement reversal on individual qubit after receiving them. The qubits’ entanglement is evaluated by means of negativity. The results show the pre- and post-measurements’ strength has an important influence on tripartite entanglement for the initially given state, and proper pre- and post-measurements’ strength always effectively improves tripartite entanglement, which is significant to protect entanglement from decoherence.