Classical physics cannot guarantee the security of a procedure for distributing a cryptographic key between two parties. In a quantum world, any attempt by Eve to eavesdrop on communications between Alice and Bob can be revealed. The chapter shows how Alice and Bob can share secrets with unconditional security in Bananaworld by exploiting the “monogamous” correlations of Popescu–Rohrlich bananas, and discusses a protocol by Ekert that exploits the monogamy of entanglement in our quantum world to allow Alice and Bob to share a secret key. Finally, the chapter shows how this can be extended to a device-independent scenario, where Alice and Bob can share a secret key even if they suspect that the devices they use to prepare and measure entangled quantum states are insecure and might have been supplied by an adversary.
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