Maximal Randomness Generation from Steering Inequality Violations Using Qudits

Abstract

We consider the generation of randomness based upon the observed violation of an Einstein-Podolsky-Rosen (EPR) steering inequality, known as one-sided device-independent randomness generation. We show that in the simplest scenario-involving only two parties and two measurements for the uncharacterised party with d outcomes-that there exist EPR steering inequalities whose maximal violation certifies maximal randomness generation, equal to log(d) bits. We further show that all pure partially entangled full-Schmidt-rank states in all dimensions can achieve maximal violation of these inequalities, and thus lead to maximal randomness generation in the one-sided device-independent setting. More generally, the amount of randomness that can be generated is given by a semidefinite program, which we use to study the behavior for nonmaximal violations of the inequalities.

Experimental Measurement-Device-Independent Quantum Steering and Randomness Generation Beyond Qubits

“…5, we investigate the amount of randomness H min generated from Alice's measurements (for either setting x) with p ∈ [0.6, 1] by using the semidefinite program from Ref. [10]. It was proven in Ref.…”

“…However, in the measurement-device-independent (MDI) scenario, Charlie does not trust Bob to perform this positive-operator-valued measure (POVM) {E B b|j } b,j in the inequality (10…”

“…The steering inequality and maximal randomness generation.-Next, we study the amount of randomness that can be certified from our results, in terms of the optimal probability P guess (x * ) for an eavesdropper, Eve, to guess the outcome of Alice's result for a given measurement setting x = x * . It was shown in [10] that the maximal amount of randomness that can be certified via quantum steering, as quantified by the min-entropy…”

Certified Randomness From Steering Using Sequential Measurements

“…In Table 1 we compare our work with that of [7], showing how, by trusting one party's measurements, we exponentially reduce the number of measurements required. In work by Skrzypczyk and Cavalcanti, it was shown how, by increasing the local Hilbert space dimension of the quantum state held by Alice and Bob, more randomness can be certified in the one-sided device-independent scenario [10]. In particular, for a local dimension d, then Ω(log d) bits can be certified.…”

Experimental demonstration of measurement-device-independent measure of quantum steering

“…Later, Kocsis et al 60 experimentally proposed a QRSG and verified the steerability for the family of two-qubit Werner states in such a scenario, which is also referred to as an MDI scenario. Moreover, such a QRSG scenario can be used to generate the private random number by maximal violation of the higher dimensional steering inequality under the MDI framework 61,62 .…”