Entropy test results

Test run: 27 July 2026 · Published: 10 August 2026

This page publishes the statistical test results behind the randomness claim on our homepage, plus enough method to let you re-run them against the live API yourself.

What was tested

One million bits pulled from the live QuantumRand API in 245 sequential calls (business-tier key, 4,096 bits per call), while the service reported real_quantum_seeded=true — that is, while its generator was seeded from real IBM quantum hardware. The same battery was then run on one million bits from /dev/urandom as a control, to check the test harness itself.

Seven tests from the NIST SP 800-22 suite, at a significance level of α = 0.01. This is a seven-test subset, not the complete fifteen-test suite — see what this is not.

What this shows — and what it does not

Both sources pass all seven tests. That is the expected and correct result, and we want to be precise about what it means.

• It shows that QuantumRand's output is statistically indistinguishable from ideal randomness on these tests. Nothing in the delivery path — the generator, the entropy pool, the API — is introducing detectable structure.
• It does not show that our output is "more random" than a good classical generator. It isn't, and no statistical test could show that: /dev/urandom passes too. Any vendor claiming otherwise is misreading their own results.
• It is not the complete SP 800-22 suite. Seven of the fifteen tests are implemented. It is also not a NIST certification, an accredited lab result, or a validation of any kind — it is our own test run, published so you can check it.

What the quantum seed actually buys you is provenance: the seed originates in quantum hardware rather than a formula, and every API response is labelled with the source that produced it. That is a supply-chain property, not a per-bit statistical one.

Re-running it yourself

The battery is deliberately reproducible. With an API key, pull a million bits and run any SP 800-22 implementation over them — ours, NIST's reference suite, or dieharder. Bits arrive as hex; n is the number of bits (a multiple of 4, at most 4096 per call):

curl -H "X-API-Key: $QR_KEY" \
  "https://quantumrand.dev/generate/hex?n=4096"

Repeat to your sample size, concatenate, convert hex to a bitstream, and test. Check the source field on each response so you know what you measured, and /health for the seed state at the time of your run — seed_source and real_quantum_seeded tell you whether the generator was on a real hardware seed or a labelled fallback.

Expect p-values to differ from ours. They should: each run is a fresh sample, and a p-value is not a score. A single test falling below α on one run is ordinary sampling behaviour, not a defect — that is what α = 0.01 means.