Quantum Weak Measurement And Its Applications In Quantum Metrology And Tomography

Originating from the investigation of time-symmetric formalism of quantum mechanics,Yakir Aharonov and Lev Vaidman proposed the two-state vector formalism to describe a quantum state.Several peculiar effects arise in this time-symmetrized framework.In practice,the state described by two-state vector formalism is typically created by pre-and post-selection on an ensemble.To reveal the properties of the intellectual state between the pre-and post-selection,the measurement process is required not to significantly disturb the two-state vector.Compared to the standard Von Neumann measurement,weak measurement aims to make the coupling strength between the quantum system and the measuring apparatus sufficiently weak so that the measurement disturbance to the state is negligible.Consequently,weak measurement is often employed to acquire the value of an observable A performed on the two-state vector system,with outcome<A>w which is defined as weak value.With appropriate pre-and post-selected states,<A>w can lie far outside the eiginvalue spectrum of observables A or even be complex.The peculiar properties of weak value provide us with rich physical contents for both fundamental investigation and practical implementation.The research contents of this thesis focus on the applications of weak measurement on quantum metrology and quantum tomography.The application of weak measurement on quantum metrology is known as weak value amplification(WVA).WVA has been used as an effective metrological protocol for amplifying the minute physical effect.Unfortunately,the amplified outcomes tend to occur with highly suppressed probabilities due to post-selection.It is proved that the precision of WVA fails to surpass that of conventional measurement(CM)with ideal setup.Nevertheless,the optimal precision WVA protocol can achieve as good precision as CM,implying that the tiny minority of postselected photons contains most of the metrological information.This inspired us to implement WVA to avoid the saturation of detectors and enlarge the dynamic range of the system.We experimentally investigate the measurement precision of WVA and CM in an optical system with a generic scientific Charge-coupled Device(CCD).Our experimental results demonstrate that WVA offers metrological advantages over the CM in the presence of classical noise and detector saturation which are ubiquitous in scientific CCDs.The formula of weak value provides us large degrees of freedom to adjust the pre-and post-selected states as well as the observable,thus exhibiting a new physical meaning.In 2011,Jeff.S.Lundeen et al.realized a direct measurement of quantum state through mapping the weak value to the expanded coefficient of a quantum wavefunction.Soon after,the direct scheme was applied to various kinds of quantum states or even a quantum process.However,this direct method for tomography is still incomplete so far.For example,the reported experiments on direct tomography of quantum states are limited to single-particle states.Besides,as the crucial ingredient of the 'triad',direct tomography of a quantum measurement is still absent.What we do next is to fill these two gaps.We deduce the theoretical derivation to directly measure an arbitrary two-photon polarized state based on the general procedure of direct tomography.To directly measure the element of density matrix,the joint weak value of non-local variables is required.We propose three experimental approaches to extract the joint weak value from the correlated readouts of two individually coupled meter states.From the retrodictive approach,the quantum measurement can be decomposed to the retrodictive state multiplying the measurement efficiency.Through assigning the retrodictive state as post-selected state in weak measurement,we realize the direct measurement of positive operator-valued measures(POVMs)of a quantum measurement.We have also applied our scheme to characterizing the projective measurements as well as a symmetric informationally complete(SIC)POVM of a polarized qubit.Our work opens new doors to characterize a quantum measurement and especially an effective option for the tomography of a high-dimensional and multi-output quantum measurement.