Device-independent quantum cryptography

This section needs expansion with: unbounded expansion. You can help by adding missing information. (February 2015)

The goal of randomness expansion is to generate a longer private random string starting from a uniform input string and using untrusted quantum devices. The idea of using Bell test to achieve this goal was first proposed by Colbeck.^[2] Subsequent works have aimed to prove unconditional security with robustness and the increase the rate of expansion. ^{[citation needed]} Vazrani and Vidick were the first to prove full quantum security for an exponentially expanding protocol.^[7] Miller and Shi^[4] achieved several additional features, including cryptographic level security, robustness, and a single-qubit requirement on the quantum memory. The approach was subsequently extended by the same authors to show that the noise level can approach the obvious upper bound, when the output may become deterministic.^[5]

This section needs expansion with: physical interpretations. You can help by adding missing information. (February 2015)

The goal of randomness amplification is to generate near-perfect randomness (approximating a fair coin toss) starting from a single source of weak randomness (a coin each of whose tosses is somewhat unpredictable, though it may be biased and correlated with previous tosses). This is known to be impossible classically.^[8] However, by using quantum devices, it becomes possible even if the devices are untrusted. Roger Colbeck and Renato Renner were motivated by physics considerations to ask the question first.^[9] Their construction and the subsequent improvement by Rodrigo Gallego et al.^[10] are secure against a non-signalling adversary, and have significant physical interpretations. The first construction that does not require any structural assumptions on the weak source is due to Kai-Min Chung, Yaoyun Shi, and Xiaodi Wu.^[6] Since then, research has focused on making constructions that are suitable for implementation.^[11][12]