Robust Quantum Random Number Generation
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Quantum measurements are believed to be inherently unpredictable, and therefore quantum devices offer the promise of true random number generation. In 2006 R. Colbeck proposed (without proof) a protocol for expanding a random seed using 3 quantum devices. Remarkably, this approach does not rely on any prior trust in the quantum devices used–the protocol includes a certification test which, if passed, is supposed to guarantee that the output is uniformly random.
Yaoyun Shi and I (arXiv:1402.0489) recently gave the first robust proof of security for Colbeck's protocol. (This follows partial security proofs that were given by several authors, and the non-robust full security proof given by Vazirani and Vidick in 2012.) The proof establishes other features which were not known before, including cryptographic security, constant quantum memory, and positive bit rate. The goal of my talk is to outline our new results and to show some of the techniques that we created. I will discuss the Schatten matrix norms, which offer an interesting geometric interpretation of the security proof.