Private Weakly-Random Sequences from Human Heart Rate for Quantum Amplification

• Main Authors: Maciej Stankiewicz, Karol Horodecki, Omer Sakarya, Danuta Makowiec
• Format: Article
• Language: English
• Published: MDPI AG 2021-09-01
• Series: Entropy
• Subjects: quantum randomness amplification; weak randomness test; heart rate
• Online Access: https://www.mdpi.com/1099-4300/23/9/1182

We investigate whether the heart rate can be treated as a semi-random source with the aim of amplification by quantum devices. We use a semi-random source model called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ε</mi></semantics></math></inline-formula>-Santha–Vazirani source, which can be amplified via quantum protocols to obtain a fully private random sequence. We analyze time intervals between consecutive heartbeats obtained from Holter electrocardiogram (ECG) recordings of people of different sex and age. We propose several transformations of the original time series into binary sequences. We have performed different statistical randomness tests and estimated quality parameters. We find that the heart can be treated as a good enough, and private by its nature, source of randomness that every human possesses. As such, in principle, it can be used as input to quantum device-independent randomness amplification protocols. The properly interpreted <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ε</mi></semantics></math></inline-formula> parameter can potentially serve as a new characteristic of the human heart from the perspective of medicine.