Device- and semi–device-independent random numbers based on noninequality paradox

Abstract

In this work, we propose device independent true random numbers generation protocols based on non-inequality paradoxes such as Hardy's and Cabello's non-locality argument. The efficiency of generating randomness in our protocols are far better than any other proposed protocols certified by CHSH inequality or other non-locality test involving inequalities. Thus, highlighting non-inequality paradox as an important resource for device independent quantum information processing in particular generating true randomness. As a byproduct, we find that the non-local bound of the Cabello's argument with arbitrary dimension is the same as the one achieved in the qubits system. More interestingly, we propose a new dimension witness paradox based on the Cabello's argument, which can be used for constructing semi-device-independent true random numbers generation protocol.

Device-independent bounds from Cabello's nonlocality argument

“…To summarize, in this paper, for the simplest Bell scenario, we studied a generalized Hardy-type nonlocality argument known as the Cabello's nonlocality argument [30,35]. We derived the device independent bound for the degree of success of Cabello's test of nonlocality and proved that it can be achieved with a pure two qubit state and projective measurements.…”

“…The Hardy type demonstrations of nonlocality are simple (often referred as the simplest demonstration of Bell nonlocality [21]) and yet it can reveal rich structures in the quantum set of correlations [22-25, 27, 28]. Recently, such results derived for Hardy and Hardy-type correlation has been shown to be useful for witnessing postquantum correlations [28], constructing device-independent dimension witness [29], and devising quantum random number generators [30][31][32]. One of the characteristic features of Hardy-type nonlocality arguments is that, unlike standard Bell-inequalities, they follow from certain prior constraints placed on some of the outcome probabilities.…”

Practical No-Signalling proof Randomness Amplification using Hardy paradoxes and its experimental implementation

“…One of them is the application of the simplest Hardy paradox, following Ref. [7] where it was shown that the Hardy paradox is a natural tool for generating randomness -namely, if the correlations exhibit Hardy paradox, then for a quantum adversary the probability of the so-called Hardy output is often bounded both from both below and from above (however it must be noted that the important problem of randomness amplification was not considered in this context). The power of using Hardy paradoxes as opposed to the pseudo-telepathy games considered so far, is illustrated in Fig.…”

“…The constraints (i)-(iv) are satisfied for any value 0 < θ < π/2, and the optimal value of P A,B|X,Y (0, 0|0, 0) (= Bell scenario, the paradoxes have been intensively studied and various extensions have been proposed [9,33,36], especially with a view to boost the probability of the Hardy output. In [7] it was noted that the Hardy paradox is especially suited to reveal intrinsic randomness of quantum statistics. Namely, the authors show (in the case of quantum adversary) that the Hardy output is a source of so-called min-entropy, identifying thereby a natural source of Bell inequalities dedicated for randomness generation.…”

“…Remark. The linear programming part is replacing the semidefinite programming used in works such as [7] for a quantum adversary.…”