Security in a prepare-and-measure quantum key distribution protocol when the receiver uses weak values to guess the sender's bits

TL;DR

This paper investigates the use of weak values in a quantum key distribution protocol and finds that employing weak values for mixed states leads to inaccuracies, challenging their interpretation as elements of reality.

Contribution

It demonstrates that weak values for mixed states can produce unreliable results in quantum communication, questioning their foundational role.

Findings

Weak values for mixed states can generate inaccurate measurement outcomes.

Using weak values in quantum communication protocols may compromise security.

Weak values may not represent elements of physical reality as previously thought.

Abstract

The weak values and weak measurement formalism were initially limited to pure states, which were later extended to mixed states, leading to intriguing applications in quantum information processing tasks. Weak values are considered to be abstract properties of systems describing a complete picture between successive measurements in the two-state vector formalism (TSVF). The remarkable achievements of the weak value formalism in experimental quantum mechanics have persuaded most quantum physicists that it is impeccable. However, we explore a scenario where the formalism of weak values for mixed states is employed in a quantum communication protocol, but discover that it generates inaccurate outcomes. This reinforces our previous conclusion that the weak values may not be elements of the reality of weak measurements, contrary to what the proponents of weak values proposed.