Weak measurements and negative probabilities

Xuanmin Zhu, Qun Wei, Quanhui Liu +1 more

Sooryansh Asthana, V. Ravishankar

Xuanmin Zhu, Qun Wei, Quanhui Liu +1 more

We study the outcomes in a general measurement with postselection, and derive upper bounds for the pointer readings in weak measurement. Using the idea of weak measurement, we study Hardy's gedanken experiment and show how the negative probabilities emerge in weak measurement. By calculating the information gain of the measuring device about which path the particles pass through, we show that the negative probabilities only emerge for cases when the information gain is little due to very weak coupling between the measuring device and the particles. When the coupling strength increases, we can unambiguously determine whether a particle passes through a given path every time, hence the average shifts always represent true probabilities, and the strange negatives probabilities disappear.

D. Sokolovski

Kazuhiro Yokota, Nobuyuki Imoto

When the weak value of a projector is 1, a quantum system behaves as in that eigenstate with probability 1. By definition, however, the weak value may take an anomalous value lying outside the range of probability like −1. From the viewpoint of a physical effect, we show that such a negative weak value of −1 can be regarded as the counterpart of the ordinary value of 1. Using photons, we experimentally verify it as the symmetrical shift in polarization depending on the weak value given by pre-postselection of the path state. Unlike observation of a weak value as an ensemble average via weak measurements, the effect of a weak value is definitely confirmed in Hong–Ou–Mandel effect: the symmetrical shift corresponding to the weak value can be directly observed as the rotation angle of a half wave plate.

Lars M. Johansen