Motivated by the challenges and limitation of existing experimental techniques, this work elaborates our recent proposal for the precision measurement of atomic parity nonconservation by quantum metrology with an entangled pair of trapped ions. Although the technique is fundamentally based on an existing proposal, it can potentially reach a figure of merit twice as high for an exceedingly tiny observable, yet to be measured in any ion trap experiment. The systematic of the technique have been shown to be better controlled as compared to other experiments. Since the goal of the experiment is...