Quantum-coherence-free precision metrology by means of difference-signal amplifification

The novel weak-value-amplifification (WVA) scheme of precision metrology is deeply rooted in the quantum nature of destructive interference between the pre- and post-selection states. 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. misalignment errors). In this work, after erasing the quantum coherence, we analyze the difference-signal amplifification (DSA) technique, which serves as a classical counterpart of the JWVA, and show that similar amplifification effect can be achieved. We obtain a simple expression for the amplifified signal, carry out characterization of precision, and point out the optimal working regime. We also discuss how to implement the post-selection of a classical mixed state. The proposed classical DSA technique holds similar technical advantages of the JWVA and may find interesting applications in practice.