Negation of photon loss provided by negative weak value

Abstract

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.

The real and imaginary parts of a weak value appearing as back-actions via a post-selection

“…Although such a symmetric relation of the positive weak value 1 and the negative one −1 was also confirmed as linearpolarization shift in [47], I have shown that the symmetric relation is also found in the post-selection probability without another system of polarization. Actually the supplementary result of Figure .5(b) in [46] implies such a symmetric relation when T is large (i.e. R << 1).…”

“…In this discussion of [46], the negative weak value of −1 by itself does not make sense, since the negative value cannot be related to 'negation' without the positive value. In other words the negative weak value of −1 is meaningful in the equation, 1 − 1 = 0.…”

“…In [46] it was already shown that a real weak value is useful in estimating how the post-selection probability is change by dissipations which are placed between the prepost-selection: A negative real weak value well represents a negation of a dissipation against a positive one. Especially, when |k k| w = 1 in equation ( 9) without the approximation, the post-selection probability decreases as if a photon has passed the attenuator with certainty, i.e.…”

“…where P rob(1|φ) represents the probability of observing the meter as |1 m under the success of the post-selection, |φ s . Actually a polarization has been often used as the meter for a weak measurement on the path state of a photon [15,46,47] as shown in figure 2 (b).…”

Linear optics for direct observation of quantum violation of pigeonhole principle by joint weak measurement

“…It also has been a beneficial measurement tool in application [30]- [37]. Moreover weak value itself has been found to be useful for description of a quantum phenomenon [38]- [44].…”