Null weak values in multi-level systems

A two-step measurement protocol of a quantum system, known as the weak value (WV), was introduced more than two decades ago by Aharonov et al (1988 Phys. Rev. Lett. 60 1351) and has since then been studied in various contexts. In this paper, we discuss another two-step measurement protocol that we dub the null weak value (NWV). The protocol consists of a partial-collapse measurement followed by quantum manipulation on the system and finally a strong measurement. The first step is a strong measurement which takes place with a small probability. The second strong measurement is used as a postselection on the outcome of the earlier step. Not being measured in the partial-collapse stage (null outcome) leads to a nontrivial correlation between the two measurements. The NVW protocol, first defined for a two-level system (Zilberberg et al 2012 arXiv:1205.3877), is then generalized to a multi-level system and compared with the standard-WV protocol