Anomalous Weak Values Without Post-Selection

TL;DR

This paper demonstrates that anomalous weak values can occur without post-selection in sequential weak measurements, challenging previous beliefs and raising questions about their interpretation and causal implications.

Contribution

It shows that anomalous weak values are possible without post-selection in sequential measurements, expanding understanding of weak measurement phenomena.

Findings

Anomalous weak values can occur without post-selection.

Sequential weak measurements can produce anomalous values.

Implications for causal structure distinctions.

Abstract

A weak measurement performed on a pre- and post-selected quantum system can result in an average value that lies outside of the observable's spectrum. This effect, usually referred to as an "anomalous weak value", is generally believed to be possible only when a non-trivial post-selection is performed, i.e., when only a particular subset of the data is considered. Here we show, however, that this is not the case in general: in scenarios in which several weak measurements are sequentially performed, an anomalous weak value can be obtained without post-selection, i.e., without discarding any data. We discuss several questions that this raises about the subtle relation between weak values and pointer positions for sequential weak measurements. Finally, we consider some implications of our results for the problem of distinguishing different causal structures.