Optimal randomness certification in the quantum steering and prepare-and-measure scenarios

Abstract

Quantum mechanics predicts the existence of intrinsically random processes. Contrary to classical randomness, this lack of predictability can not be attributed to ignorance or lack of control. Here we find the optimal method to quantify the amount of local or global randomness that can be extracted in two scenarios: (i) the quantum steering scenario, where two parties measure a bipartite system in an unknown state but one of them does not trust his measurement apparatus, and (ii) the prepare-andmeasure scenario, where additionally the quantum state is known. We use our methods to compute the maximal amount of local and global randomness that can be certified by measuring systems subject to noise and losses and show that local randomness can be certified from a single measurement if and only if the detectors used in the test have detection efficiency higher than 50%.One of the most distinct features of quantum mechanics is its intrinsically random character. While in classical mechanics lack of predictability can always be associated to ignorance or lack of control of the probed systems, the rules of quantum physics say that one can not predict the outcome of a measurement even if all the variables of a system are known. This inherent unpredictability has been exploited in different applications such as quantum random number generation [1] and quantum key distribution [2].Recent results have shown that the randomness observed in quantum mechanics can be certified even without relying on any modelling of the quantum devices used for the generation of the random data. In fact, by analysing the data obtained in experiments involving local measurements on bipartite entangled systems one can prove that no one could have predicted this data in advance whenever a Bell inequality violation is observed [3,4]. This is called device-independent (DI) randomness certification [5,6]. The DI approach has the practical advantage that it does not rely on the exact description of the experimental set-up. This is crucial when implementing cryptographic protocols as an adversary can use a mismatch between the theoretical description and the actual implementation of the set-up to fake its performance [7][8][9]. However, DI protocols require low levels of noise [4], which make them very demanding experimentally.An intermediate scenario is that of quantum steering [10,11]. It refers to the case where two parties, say Alice and Bob, apply local measurements on an unknown bipartite system. While one of them, Bob, has complete knowledge of his measurement apparatuses, Alice does not, and treats her measuring device as a black box with classical inputs and outputs. Quantum steering has been receiving lot of attention recently due to the fact that it allows for entanglement detection which is more robust to noise and experimental imperfections than Bell nonlocality [11,12]. Moreover, quantum steering was shown to be useful for one-sided device independent quantum key distribution (1SDIQKD) [13] and randomness certification [14]. Several expe...

Experimental multipartite entanglement and randomness certification of the W state in the quantum steering scenario

“…where we had to use the finite set of non-signalling strategies {D N S µ (a|x)} µ to decompose the quantum probability distribution p(ab|xyλ) in terms of a finite number of distributions [5] (25) and the corresponding semi-device independent witnesŝ w is obtained from duality theory and has the same structure as (16).…”

“…2. The predictability of the outcome s when a given measurement m * is chosen is quantified by the guessing probability G σ (m * ): the probability that E guesses correctly the value of s, optimized over all of E's possible strategies, and conditioned on the observation of the assemblage σ C s|m by the party C [16,24]. Formally: …”

“…a linear functionalŵ) acting on the set of assemblages of C, having the same structure as (16), and such thatŵ (σ) = G σ (m * ). Finally, assuming Independent and Identically Distributed (IID) rounds in the experiment, the amount of genuine random bits certified is given by R = − log 2 (G σ (m * )), the min-entropy of the semi-device independent guessing probability [24].…”

Rigidity of quantum steering and one-sided device-independent verifiable quantum computation

“…The existing research involves the characterisation of steering correlations both analytically and geometrically [18][19][20], their relationship to other types of correlations [21,22] and their application to cryptographic tasks such as QKD and QRNG [23,24]. Experiments testing quantum steering inequalities [25] (loophole-free) and testing local but steerable states [26] have also been performed.…”

A channel-based framework for steering, non-locality and beyond

“…A modern approach to steering describes it as a way to certify entanglement in cryptographic situations where some devices in the protocol are not characterized [8]. Steering hence allows for a 'one-sided device-independent' implementation of several information-theoretic tasks, such as quantum key distribution [9], randomness certification [10,11], measurement incompatibility certification [12][13][14], and self-testing of quantum states [15,16].Even though these phenomena arise naturally within quantum mechanics, they are not restricted to it. Non-local correlations and steering beyond what quantum theory allows are conceivable while still complying with natural physical assumptions, such as relativistic causality [17,18].…”