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Bulletin of the American Physical Society

The meaning of negative weak values

James E. Troupe, Jeff Tollaksen

Published Mar 10, 2008• 0 citations
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We propose a usage of a weak value for a quantum processing between preselection and postselection. While the weak value of a projector of 1 provides a process with certainty like the probability of 1, the weak value of -1 negates the process completely. Their mutually opposite effect is approved without a conventional `weak' condition. In addition the quantum process is not limited to be unitary; in particular we consider the dissipation of photons and experimentally demonstrate the negation of the dissipation by using the negative weak value of -1 against the positive weak value of 1.
We propose a usage of a weak value for a quantum processing between preselection and postselection. While the weak value of a projector of 1 provides a process with certainty like the probability of 1, the weak value of −1 negates the process completely. Their mutually opposite effect is approved without a conventional 'weak' condition. In addition the quantum process is not limited to be unitary; in particular we consider a loss of photons and experimentally demonstrate the negation of the photon loss by using the negative weak value of −1 against the positive weak value of 1.
Weak values and measurements have been proposed as a means to achieve dramatic enhancements in metrology based on the greatly increased range of possible measurement outcomes. Unfortunately, the very large values of measurement outcomes occur with highly suppressed probabilities. This raises three vital questions in weak-measurement-based metrology. Namely, (Q1) Does postselection enhance the measurement precision? (Q2) Does weak measurement offer better precision than strong measurement? (Q3) Is it possible to beat the standard quantum limit or to achieve the Heisenberg limit with weak measurement using only classical resources? We analyze these questions for two prototypical, and generic, measurement protocols and show that while the answers to the first two questions are negative for both protocols, the answer to the last is affirmative for measurements with phase-space interactions, and negative for configuration space interactions. Our results, particularly the ability of weak measurements to perform at par with strong measurements in some cases, are instructive for the design of weak-measurement-based protocols for quantum metrology.