Null weak values in multi-level systems

TL;DR

This paper introduces and analyzes the null weak value (NWV) protocol, a two-step quantum measurement process involving partial-collapse and strong measurements, generalized from two-level to multi-level systems, revealing new correlations.

Contribution

It generalizes the null weak value protocol from two-level to multi-level quantum systems and compares its properties to standard weak values.

Findings

NWV protocol exhibits non-trivial correlations in multi-level systems.

Comparison shows differences between NWV and standard weak values.

Generalization broadens potential applications in quantum measurement theory.

Abstract

A two-step measurement protocol of a quantum system, known as weak value (WV), has been introduced more than two decades ago by Aharonov et al. [1], and has since been studied in various contexts. Here we discuss another two-step measurement protocol which we dub 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 small probability. The second strong measurement is used as postselection on the outcome of the earlier step. Not being measured in the partial-collapse stage (null outcome) leads to a non-trivial correlation between the two measurements. The NVW protocol, first defined for a two-level system [2], is generalized to a multi-level system, and compared to the standard-WV protocol.