Importantly, it was argued that the JWVA scheme permits the removal of systematic error, background noise, and fluctuations in alignments of the experimental setup 32, 33, 34. This proposal was referred to as joint-weak-measurement or joint WVA (JWVA) scheme. However, aside from the singular amplification regime, viewing that the discarding data by post-selection encode considerable information, a different strategy of amplification was proposed by considering to use all the post-selection accepted (PSA) and rejected (PSR) data 30, 31, 32, 33, 34, 35, 36. In the singular amplification regime, this novel quantum effect allows the WVA measurement to put almost all of the Fisher information about the parameter under estimation into the small portion of the remained data 13, 14, 15, which leads thus to some important technical advantages. Physically speaking, the WVA is rooted in the quantum nature of interference effect between the pre- and post-selected (PPS) states. The WVA technique involves an essential procedure termed as post-selection, which discards a large portion of output data. The WVA technique allows probe sensitivity beyond the detector’s resolution and can outperform conventional measurement in the presence of detector saturation and technical imperfections 21, 22, 23. Similar content being viewed by othersĪpplying the concept of quantum weak values (WVs) proposed by Aharonov, Albert and Vaidman (AAV) 1, 2, a novel scheme of precision metrology termed as weak-value amplification (WVA) has caused great interest over the past decade and a half 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29. The proposed classical DSA technique holds similar technical advantages of the JWVA and may find interesting applications in practice. We also discuss how to implement the post-selection of a classical mixed state. We obtain a simple expression for the amplified signal, carry out characterization of precision, and point out the optimal working regime. In this work, after erasing the quantum coherence, we analyze the difference-signal amplification (DSA) technique, which serves as a classical counterpart of the JWVA, and show that similar amplification effect can be achieved. And, an alternative version, termed as joint WVA (JWVA), which employs the difference-signal from the post-selection accepted and rejected results, has been found possible to achieve even better sensitivity (two orders of magnitude higher) under some technical limitations (e.g. The novel weak-value-amplification (WVA) scheme of precision metrology is deeply rooted in the quantum nature of destructive interference between the pre- and post-selection states.
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