Quantum preparation uncertainty and lack of information

TL;DR

This paper investigates whether quantum uncertainty, especially in measurement outcomes, can be interpreted as a lack of information, linking quantum uncertainty to classical-like ignorance in the context of quantum cryptography.

Contribution

It demonstrates that for BB84 measurements, quantum uncertainty can be partially explained by a lack of information, offering new insights into quantum measurement and cryptographic security.

Findings

Uncertainty in BB84 measurements relates to available information about measurement choices.

Other quantum measurements also show a connection between uncertainty and lack of information.

Implications for cryptographic protocol security are discussed.

Abstract

The quantum uncertainty principle famously predicts that there exist measurements that are inherently incompatible, in the sense that their outcomes cannot be predicted simultaneously. In contrast, no such uncertainty exists in the classical domain, where all uncertainty results from ignorance about the exact state of the physical system. Here, we critically examine the concept of preparation uncertainty and ask whether similarly in the quantum regime, some of the uncertainty that we observe can actually also be understood as a lack of information (LOI), albeit a lack of quantum information. We answer this question affirmatively by showing that for the well known measurements employed in BB84 quantum key distribution, the amount of uncertainty can indeed be related to the amount of available information about additional registers determining the choice of the measurement. We proceed to show that also for other measurements the amount of uncertainty is in part connected to a LOI. Finally, we discuss the conceptual implications of our observation to the security of cryptographic protocols that make use of BB84 states.