Algorithmic Randomness and Quantum Mechanics: the title alone should make clear that this is, by some margin, the most technical presentation I have ever attempted.
I shall be discussing it with people who actually know what they are doing. On my side: a couple of years of GenAI red teaming, a reasonably quick tongue, and the increasingly fragile hope that forty minutes will somehow pass before anyone notices.
The Q&A, I fear, is where they get me.
Back home, or
into the footnotes?
The Event
- Conference
- Algorithmic Randomness and Quantum Mechanics
- Hosted by
- * Uniwersytet Jagielloński;
- Where & when
- Uniwersytet Jagielloński — 31 August - 1 September, 2026
- Official Links
-
* Philevents Page
* Jagiellonian University
Research summary - Certifying the Unpredictable: Quantum Randomness Between Physics, Computation, and Security
What kind of randomness does security actually require? Quantum random number generators (QRNGs) bring together three distinct ideas that are often treated as interchangeable. In mathematics and computer science, algorithmic randomness describes sequences with no effectively detectable pattern – often formalised through Martin-Löf tests and linked to the idea that a sequence cannot be compressed. In quantum physics, quantum randomness concerns the status of measurement outcomes, which can depend on how quantum mechanics is interpreted. In cryptography, however, randomness means something more practical: values must remain unpredictable, or indistinguishable from random, to an adversary with specified capabilities. These three concepts overlap, but they do not provide the same guarantees.
The differences matter whenever a quantum device is promoted as a source of ‘true randomness.’ Statistical tests can examine its output, but no finite string can prove the strong, infinite-sequence property described by algorithmic randomness. Nor does quantum indeterminacy automatically provide cryptographic security. Even genuinely quantum outcomes may be compromised by defective hardware, side channels, poor calibration, or careless integration into a security protocol. Security therefore does not reside in the output alone. It depends on assumptions about the source, the device, the adversary, and the wider system in which the random values are used.
Device-independent QRNGs make this problem especially visible. Instead of relying on a detailed model of a trusted device, they use violations of Bell inequalities to certify quantum behaviour, then apply a randomness extractor to produce secure random bits – even when an adversary may possess quantum information about the system. This process translates a physical claim about quantum behaviour into an operational security guarantee. Randomness consequently becomes a trust object: something made credible through theory, experiment, engineering, testing, standards, certification, and institutional authority. In line with Theodore Porter’s work on trust in numbers and post-Kuhnian accounts of scientific objectivity, the central question is not simply whether quantum processes are random. It is what randomness becomes when it must carry the burden of security and trust.