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 .
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 .
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.
Throughout this project, the case of a composite system formed by a harmonic oscillator and a two-state atom will be studied; considering both affect each other as \na consequence of a Jaynes-Cummings interaction, and being both coupled to different reservoirs that are assumed to be independent from each other. The effects \nof the decoherence in the evolution of the populations and coherences will be analyzed; specifically the energy dissipation and the coherence loss, as well as the stationary states and the relevance of the Jaynes-Cummings interaction. Finally, the \nsolution of stochastic equations will be analyzed, particularly the evolution of the \nexpectation value of the position operator for the harmonic oscilator; for the case of \nsimultaneous measurements in both subsystems, as well as for a measurement in \nthe harmonic oscillator when the two-state atom undergoes a decoherence process.
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.
Measurements on a bipartite system AB are classified into ones that are freely implementable with only classical communication between A and B (LOCC measurements), and the others that require consumption of entanglement if they are to be implemented with classical communication. When we notice that measurements on a bipartite system can also be used to create entanglement, we have another natural classification: measurements that are capable of creating entanglement, and the others that have no ability of producing entanglement (separable measurements). Interestingly, there exists a separable measurement that is not an LOCC measurement, namely, a measurement that requires entanglement to implement, but is not capable of creating entanglement at all. Such an example was found for a pair of three-level systems, in conjunction with a discrimination task of an intricate set of eight or nine states. Here we show an example of such a measurement on a pair of two-level systems (qubits), which arises in a discrimination task of just two states that look quite simple and have little intricacy. Such an example suggests that this kind of irreversibility is not only shown by a limited set of cleverly constructed measurements, but is also exhibited by a much larger class of measurements than we had expected.
We consider a multilevel system coupled to a bosonic measurement apparatus. We derive exact expressions for the time-dependent expectation values of a large class of physically relevant observables that depend on degrees of freedom of both systems. We find that, for this class, though the two systems become entangled as a result of their interaction, they appear classically correlated for long enough times. The unique corresponding time-dependent separable state is determined explicitly. To better understand the physical parameters that control the time scale of this effective disentanglement process, we study a one-dimensional measurement apparatus.
We study entanglement in a system comprising two coupled quartic oscillators. It is shown that the entanglement, as measured by the von Neumann entropy, increases with the classical chaos parameter for generic chaotic eigenstates. We consider certain isolated periodic orbits whose bifurcation sequence affects a class of strongly scarred quantum eigenstates, called the channel localized states. For these states, the entanglement is a local minima in the vicinity of a pitchfork bifurcation but is a local maxima near an antipitchfork bifurcation. We place these results in the context of the close connections that may exist between entanglement measures and conventional measures of localization. We also point to an interesting near degeneracy that arises in the spectrum of reduced density matrices of certain states as an interplay between localization and symmetry.