In quantum cryptography, device-independent (DI) protocols can be certified secure without requiring assumptions about the inner workings of the devices used to perform the protocol. In order to display nonlocality, which is an essential feature in DI protocols, the device must consist of at least two separate components sharing entanglement. This raises a fundamental question: how much entanglement is needed to run such DI protocols? We present a two-device protocol for DI random number generation (DIRNG) which produces approximately $n$ bits of randomness starting from $n$ pairs of arbitrarily weakly entangled qubits. We also consider a variant of the protocol where $m$ singlet states are diluted into $n$ partially entangled states before performing the first protocol, and show that the number $m$ of singlet states need only scale sublinearly with the number $n$ of random bits produced. Operationally, this leads to a DIRNG protocol between distant laboratories that requires only a sublinear amount of quantum communication to prepare the devices.
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机译：在量子密码术中，可以独立于设备（DI）协议进行安全认证，而无需假设用于执行该协议的设备的内部工作情况。为了显示非局部性（这是DI协议的一项基本功能），设备必须至少包含两个共享缠结的独立组件。这就提出了一个基本的问题：运行这种DI协议需要多少纠缠？我们提出了一种用于DI随机数生成（DIRNG）的两设备协议，该协议从$ n $对任意弱纠缠的量子位开始，产生大约$ n $位的随机性。我们还考虑了该协议的一种变体，其中在执行第一个协议之前，$ m $个单重态被稀释为$ n $个部分纠缠的状态，并且表明，单价态的数量$ m $只需要与数字$ n $线性变化即可。产生的随机位。在操作上，这导致了遥远实验室之间的DIRNG协议，该协议仅需要亚线性量的量子通信即可制备设备。
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