Randomness quantification in spontaneous emission

TL;DR

The paper develops a first-principles quantum-information-theoretic framework to quantify intrinsic randomness in QRNGs based on spontaneous emission, identifying two adversary models: direct access to the atom (Adversary I) and access to the atom's purification (Adversary II). It analyzes four QRNG implementations—single-photon detection, temporal mode, spatial mode, and quantum phase fluctuation—deriving exact and bound expressions for extractable randomness under each adversary scenario. The results reveal that single-photon and temporal-mode schemes can be insecure against atom-access adversaries but retain a provable randomness lower bound if only purification is leaked, whereas spatial-mode and phase-fluctuation schemes remain secure against both adversaries. This framework connects spontaneous emission physics with coherence-based randomness certification, providing practical formulas for intrinsic randomness and guiding robust design of spontaneous-emission-based QRNGs.

Abstract

Quantum coherence serves as a fundamental resource for generating intrinsic randomness, yet the quantification of randomness in quantum random number generators (QRNGs) based on spontaneous emission has remained largely phenomenological. Existing randomness analysis lacks rigorous adversarial models and a clear characterization of the role of quantum coherence in these systems. In this work, we develop a comprehensive quantum information-theoretic framework for randomness generation in spontaneous emission processes. We characterize two distinct eavesdropping strategies: one where the adversary directly accesses the atom ensemble, and the other where the adversary accesses only its purification. Our analysis reveals that when randomness is generated through single-photon detection and temporal mode measurements, the QRNG is vulnerable to the first adversary scenario, though it still guarantees a lower bound on intrinsic randomness against the second adversary scenario even under maximal information leakage from the atoms. In contrast, QRNGs based on spatial mode detection and phase fluctuations demonstrate security against both types of adversaries, providing robust randomness generation. Furthermore, we provide a quantitative calculation of intrinsic randomness for these spontaneous-emission-based QRNG schemes.

Figures (2)

• Figure 1: Schematic illustration of the adversary scenario. We consider the systems $A$, $R$, and $R'$, which correspond to the atom, the emitted radiation, and the purification of the initial atomic system. The input state for $R$ is the vacuum state $\ketbra{0}{0}_R$ with no photons. The spontaneous emission process is described as a unitary evolution $U_{AR}$. The two types of adversary have access to $AR'$ and $R'$, respectively. The user performs a POVM $M$ on system $R$ and the measurement outcome is used to generate random numbers. Different implementations of $M$ correspond to different QRNG schemes discussed in this work.
• Figure 2: Impact of atomic coherence on intrinsic randomness, for temporal measurement and an adversary with no access to the atomic system. The curves are plotted with different numbers of time bin and coherence is quantified using the $l_1$ norm of coherence. When $n=1$, temporal measurement becomes the single-photon detection. The diagonal terms of the state $\rho_A$ is set to be both 1/2 and its possible $l_1$ norm of coherence ranges from 0 to 1. The randomness is expressed in terms of number of extractable bits.

Theorems & Definitions (1)

• Proposition 1