As quantum technologies grow in complexity, the need for efficient, non-destructive measurement schemes become increasingly important. Photonic systems, while in many ways ideal for quantum information processing, offer only a limited number of degrees of freedom per mode - placing fundamental restrictions on the number and type of observables that can be simultaneously accessed. Weak measurement provides a framework to circumvent some of these limitations, enabling joint measurements, minimal back-action, and alternative pathways for quantum state characterization.
This thesis presents two contributions to the theory and implementation of weak measurements in optics. First, we design, simulate, and experimentally realize a scheme to measure joint weak values of position and momentum projectors - building on Lundeen and Bamber’s framework. We employ a glass sliver to weakly measure x position and use a spatial light modulator (SLM) to couple polarization to x momentum in a way that the strength this interaction is conditional on the y position. We show that a binary conditionality is able to achieve the same results as the linear conditionality initially proposed, while enabling simpler setups and larger signals.
Second, we analyze how weak interactions arising from bulk optical nonlinearities can be harnessed for quantum measurements. Using both the von Neumann and Positive Operator-Valued Measure (POVM) formalisms, we explore a range of nonlinear processes. We identify that information about photon number and field quadratures are accessible via nonlinear interactions, and propose that certain POVM based schemes may offer practical alternatives to standard homodyne detection of field quadratures.
This work contributes to the ongoing development of quantum measurement techniques in optics and presents how weak measurements provide a useful framework in which to consider alternative measurement schemes.
