Abstract
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 approximatelynbits of randomness starting fromnpairs of arbitrarily weakly entangled qubits. We also consider a variant of the protocol wheremsinglet states are diluted intonpartially entangled states before performing the first protocol, and show that the numbermof singlet states need only scale sublinearly with the numbernof 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.
Highlights
A quantum random number generation (RNG) protocol is device-independent (DI) if its output can be guaranteed to be random with respect to any adversary on the sole basis of certain minimal assumptions, such as the validity of quantum physics and the existence of secure physical locations [1]
DI random number generation (DIRNG) protocols necessarily consume two fundamental resources: entangled states shared across separated devices and an initial public random seed that is uncorrelated to the devices and used to determine the random measurements performed on the entangled states
Even ideal devices are not expected to achieve the quantum maximum when they are used a finite number n of times because of inherent statistical noise. We address this by introducing an explicit DIRNG protocol based on the tilted-CHSH inequalities and a robust security analysis based on the entropy accumulation theorem (EAT) [12,13,14] and the self-testing properties of the tilted-CHSH inequalities introduced in [15]
Summary
A quantum random number generation (RNG) protocol is device-independent (DI) if its output can be guaranteed to be random with respect to any adversary on the sole basis of certain minimal assumptions, such as the validity of quantum physics and the existence of secure physical locations [1]. From the relation (4) between the tilted-CHSH game and the tilted-CHSH expression, it follows from the results of [9] that the winning probability ω goes up to 1/2 + (2 + β)/(8 + 2β) for classical devices, and 1/2 + 8 + 2β2/(8 + 2β) = ωq for quantum devices This quantum value ωq is uniquely achieved (up to local transformations and up to Bob’s measurement operator for y = 2) by a pair of devices implementing certain local measurements on a two-qubit partially entangled state |ψθ = cos θ |00 +sin θ |11 with tan(2θ) = 2/β2 − 1/2 [9]. A larger fraction of game rounds (i.e., a larger γ) makes the success criterion fluctuate less, which allows for a higher threshold (i.e., a smaller ξ)
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