Infinite randomness expansion with a constant number of devices

We present a device-independent randomness expansion protocol, involving only a constant number of non-signaling quantum devices, that achieves infinite expansion : starting with m bits of uniform private randomness, the protocol can produce an unbounded amount of certified randomness that is exp(--Ω( m 1/3 ))-close to uniform and secure against a quantum adversary. The only parameters which depend on the size of the input are the soundness of the protocol and the security of the output (both are inverse exponential in m ). This settles a long-standing open problem in the area of randomness expansion and device-independence. The analysis of our protocols involves overcoming fundamental challenges in the study of adaptive device-independent protocols. Our primary technical contribution is the design and analysis of device-independent protocols which are Input Secure ; that is, their output is guaranteed to be secure against a quantum eavesdropper, even if the input randomness was generated by that same eavesdropper ! The notion of Input Security may be of independent interest to other areas such as device-independent quantum key distribution.

Authors

• Matthew Coudron
• Henry Yuen

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