Secure uniform random number extraction via incoherent strategies

Abstract

To guarantee the security of uniform random numbers generated by a quantum random number generator, we study secure extraction of uniform random numbers when the environment of a given quantum state is controlled by the third party, the eavesdropper. Here we restrict our operations to incoherent strategies that are composed of the measurement on the computational basis and incoherent operations (or incoherence-preserving operations). We show that the maximum secure extraction rate is equal to the relative entropy of coherence. By contrast, the coherence of formation gives the extraction rate when a certain constraint is imposed on eavesdropper's operations. The condition under which the two extraction rates coincide is then determined. Furthermore, we find that the exponential decreasing rate of the leaked information is characterized by Rényi relative entropies of coherence. These results clarify the power of incoherent strategies in random number generation, and can be applied to guarantee the quality of random numbers generated by a quantum random number generator.

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Cited by in corpus (12)

• Operational Resource Theory of Quantum Channels
• One-Shot Coherence Distillation: Towards Completing the Picture
• Quantum Coherence and Intrinsic Randomness
• Two-Way Physical Layer Security Protocol for Gaussian Channels
• Secure Network Code for Adaptive and Active Attacks with No-Randomness in Intermediate Nodes
• Distributed Private Randomness Distillation
• One-shot Coherence Distillation with Catalysts
• Efficient estimation of multipartite quantum coherence
• Quantum coherence via conditional entropy
• Secure network code over one-hop relay network
• Unification of quantum resources in distributed scenarios
• Finite Block Length Analysis on Quantum Coherence Distillation and Incoherent Randomness Extraction