Security in a Prepare-and-Measure Quantum Key Distribution Protocol when the Receiver Uses Weak Values to Guess the Sender’s Bits

The weak values and weak measurement formalism were initially limited to pure states which was 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 of 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 pioneers of weak values proposed.