Quantifying randomness with measurement incompatibility

• URL: http://arxiv.org/abs/2607.08697v1
• Date: Thu, 09 Jul 2026 16:54:26 GMT
• Title: Quantifying randomness with measurement incompatibility
• Abstract summary: We present a trade-off between the amount of observed measurement incompatibility and the capabilities of a classical Eavesdropper.<n>We find a tight connection between steerability and randomness generation in a setting using any finite number of measurement inputs.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a trade-off between the amount of observed measurement incompatibility and the capabilities of a classical Eavesdropper in a prepare-and-measure scenario. The result is based on a qualitative connection between measurement incompatibility and randomness generation together with the utilization of incompatibility witnesses as randomness certificates. This allows one to use a geometric measure of incompatibility, the generalised robustness, to bound Eve's strategies through a semi-definite program, while providing an explicit protocol for generating randomness from any set of incompatible measurements. By translating the result to quantum steering, we find a tight connection between steerability and randomness generation in a setting using any finite number of measurement inputs. We further show how our techniques can be generalised to scenarios where Eve has a quantum memory by using a dimensional generalisation of joint measurability.

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