Entangled systems are unbounded sources of nonlocal correlations and of certified random numbers

Abstract

The outcomes of local measurements made on entangled systems can be certified to be random provided that the generated statistics violate a Bell inequality. This way of producing randomness relies only on a minimal set of assumptions because it is independent of the internal functioning of the devices generating the random outcomes. In this context it is crucial to understand both qualitatively and quantitatively how the three fundamental quantities -entanglement, non-locality and randomness -relate to each other. To explore these relationships, we consider the case where repeated (non projective) measurements are made on the physical systems, each measurement being made on the post-measurement state of the previous measurement. In this work, we focus on the following questions: For systems in a given entangled state, how many nonlocal correlations in a sequence can we obtain by measuring them repeatedly? And from this generated sequence of non-local correlations, how many random numbers is it possible to certify? In the standard scenario with a single measurement in the sequence, it is possible to generate non-local correlations between two distant observers only and the amount of random numbers is very limited. Here we show that we can overcome these limitations and obtain any amount of certified random numbers from an entangled pair of qubit in a pure state by making sequences of measurements on it. Moreover, the state can be arbitrarily weakly entangled. In addition, this certification is achieved by near-maximal violation of a particular Bell inequality for each measurement in the sequence. We also present numerical results giving insight on the resistance to imperfections and on the importance of the strength of the measurements in our scheme.Digital Object Identifier 10.4230/LIPIcs...

Experimental realization of sequential weak measurements of non-commuting Pauli observables

“…testing quantum contextuality [28,29], macroscopic realism [20,30,31], uncertainty relation [32,33], verifying measurement induced geometric phase [34] and so on [35,36]. Moreover, our results have important applications in the areas such as realization of counterfactual computation [13,22,23], direct measurement of matrix density [8,9], direct process tomography [15,24] and unbounded randomness certification [25,26].…”

“…Contrary to previous methods, the use of discrete pointer in our case makes the proposal here more feasible practically. The results presented here are not only helpful in understanding measurement of non-commuting observables but also useful in realizing counterfactual computation experimentally [13,22,23], direct process tomography [15,24], direct measurement of density matrix [9] and unbounded randomness certification [25,26].…”

Device-independent characterization of quantum instruments

“…are associated to quantum instruments which tend to be projective in the limit θ → 0, and the identity in the weak limit when θ → π/4. Such an instrument is sufficient to implement the scheme proposed in [33,34,35] to produce more randomness than possible with von Neumann measurements.…”

“…for generating randomness. Whereas randomness generation based on projective measurements requires at least as many maximally-entangled states as the number of certified random bits, an arbitrary number of random bits can in principle be extracted from a single maximally-entangled state by applying successive quantum instruments which do not break entanglement [32,33,34,35]. The certification of such measurements is thus not only of fundamental interest but could be used in practice to characterise the potential of an actual quantum instrument for producing large amounts of device-independent randomness with a single entangled state.…”