Sequential Weak Measurements with Correlated Pointers

Sammanfattning

This project studies the measurement process of two quantum mechanical observables using two coupled entangled measuring devices (correlated pointers). We assume Gaussian entanglement between the pointers and express their wave function with that of a two-mode squeezed state. The measurement process is modeled with the von Neumann Hamiltonian H = g(t)Ap where we assume the coupling strength ∫ g(t) dt = g is small. We explicitly derive expressions for the expected values of the pointers’ canonical variables and their products, expressed using only the relevant weak values and the entanglement. We show that in the no entanglement case these expressions agree with previously known results while in the high entanglement limit we can no longer neglect terms of higher order in g which means that the analysis is not valid. An example of a spin-1/2 system is given where the results indicate that in the presence of entanglement we can measure both the observables’ weak values from only one of the pointers.