Quantum security and theory of decoherence

TL;DR

This paper explores the intersection of quantum decoherence and cryptography, analyzing how environmental interactions can compromise quantum data privacy, exemplified through a quantum random number generator vulnerability.

Contribution

It introduces a novel relation linking decoherence and cryptographic security, highlighting how environmental effects can threaten quantum data privacy.

Findings

Derived a trade-off relation between eavesdropper's guessing probability and decoherence.

Illustrated potential security breaches in quantum random number generators.

Connected decoherence mechanisms with cryptographic assumptions.

Abstract

We sketch a relation between two crucial, yet independent, fields in quantum information research, viz. quantum decoherence and quantum cryptography. We investigate here how the standard cryptographic assumption of shielded laboratory, stating that data generated by a secure quantum device remain private unless explicitly published, is disturbed by the einselection mechanism of quantum Darwinism explaining the measurement process by interaction with the external environment. We illustrate the idea with a paradigmatic example of a quantum random number generator compromised by an analog of the Van Eck phreaking. In particular, we derive a trade-off relation between eavesdropper's guessing probability $P_{guess}$ and the collective decoherence factor $\Gamma$ of the simple form $P_{guess} + \Gamma \geq 1$.