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Experimental Device-Independent Certified Randomness Generation

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Experimental Device-Independent Certified Randomness Generation ARTICLE https://doi.org/10.1038/s42005-020-0375-6 OPEN Experimental device-independent certified randomness generation with an instrumental causal structure Iris Agresti1, Davide Poderini1, Leonardo Guerini 2, Michele Mancusi 1, Gonzalo Carvacho1, Leandro Aolita3, ✉ 1234567890():,; Daniel Cavalcanti4, Rafael Chaves5,6 & Fabio Sciarrino 1 The intrinsic random nature of quantum physics offers novel tools for the generation of random numbers, a central challenge for a plethora of fields. Bell non-local correlations obtained by measurements on entangled states allow for the generation of bit strings whose randomness is guaranteed in a device-independent manner, i.e. without assumptions on the measurement and state-generation devices. Here, we generate this strong form of certified randomness on a new platform: the so-called instrumental scenario, which is central to the field of causal inference. First, we theoretically show that certified random bits, private against general quantum adversaries, can be extracted exploiting device-independent quantum instrumental-inequality violations. Then, we experimentally implement the corre- sponding randomness-generation protocol using entangled photons and active feed-forward of information. Moreover, we show that, for low levels of noise, our protocol offers an advantage over the simplest Bell-nonlocality protocol based on the Clauser-Horn-Shimony- Holt inequality. 1 Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy. 2 International Center of Theoretical Physics - South American Institute for Fundamental Research, Instituto de Física Teórica - UNESP, R. Dr. Bento T. Ferraz 271, 01140-070 São Paulo, Brazil. 3 Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ 21941-972, Brazil. 4 ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, E-08860 Castelldefels, Barcelona, Spain. 5 International Institute of Physics, Federal University of Rio Grande do Norte, 59078-970P. O. Box 1613, Natal, Brazil. 6 School of Science and Technology, Federal University of Rio Grande do Norte, 59078-970 Natal, Brazil. ✉ email: [email protected] COMMUNICATIONS PHYSICS | (2020) 3:110 | https://doi.org/10.1038/s42005-020-0375-6 | www.nature.com/commsphys 1 ARTICLE COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-020-0375-6 he generation of random numbers has applications in a their dimension. Furthermore, in our case, the causal assumption wide range of fields, from scientific research—e.g. to consists in the requirement that A’s measurement choice does T — — fl simulate physical systems to military scopes e.g. for not have a direct in uence over B. In practical applications, this effective cryptographic protocols—and every-day concerns—like premise can be enforced, by shielding A’s measurement station, ensuring privacy and gambling. From a classical point of view, the in order to allow only for the communication of its outcome bit concept of randomness is tightly bound to the incomplete to B and prevent any other unwanted communication. To knowledge of a system; indeed, classical randomness has a sub- implement the protocol in all of its parts, we have set up a jective and epistemological nature and is erased when the system classical extractor following the theoretical design by Trevisan34. is completely known1. Hence, classical algorithms can only gen- Moreover, we prove that DI randomness generation protocols erate pseudo-random numbers2, whose unpredictability relies on implemented in this scenario, for high state visibilities, can bring the complexity of the device generating them. Besides, the certi- an advantage in the gain of random bits when compared to those fication of randomness is an elusive task, since the available tests based on the simplest two-input-two-output Bell scenario, the can only verify the absence of specific patterns, while others may Clauser–Horn–Shimony–Holt (CHSH)35. Therefore, this work go undetected but still be known to an adversary3. paves the way to further applications of the instrumental sce- On the other hand, randomness is intrinsic to quantum sys- nario in the field of DI protocols, which, until now, have relied tems, which do not possess definite properties until these are primarily on Bell-like tests. measured. In real experiments, however, this intrinsic quantum randomness comes embedded with noise and lack of complete Results control over the device, compromising the security of a quantum Randomness certification via instrumental violations. Let us random-number generator. A solution to that is to devise first briefly review some previous results obtained in the context quantum protocols whose correctness can be certified in a device- of Bell inequalities4. In a CHSH scenario35, two parties, A and B, independent (DI) manner. In such a framework, properties of the share a bipartite system and, without communicating to each considered system can be inferred under some causal assump- other, perform local measurements on their subsystems. If A and tions, not requiring a precise knowledge of the devices adopted in B choose between two given operators each, i.e. (A1, A2) and (B1, the implementation. For instance, from the violation of a Bell B2) respectively, and then combine their data, the mean value of 4,5 ¼jhiÀ; hiþ; hiþ; hij; inequality , under the assumption of measurement indepen- the operator S A1 B1 A1 B2 A2 B1 A2 B2 dence and locality, one can ensure that the statistics of certain should be upper-bounded by 2, for any deterministic model quantum experiments cannot be described in the classical terms respecting a natural notion of locality. However, as proved in of local deterministic models, hence being impossible to be ref. 35,ifA and B share an entangled state, they can get a value deterministically predicted by any local observer. Moreover, the exceeding this bound, whose explanation requires the presence of extent of such a violation can provide a lower bound on the non-classical correlations between the two parties. Hence, Bell certified randomness characterizing the measurement outputs of inequalities have been adopted in ref. 7 to guarantee the intrinsic the two parties performing the Bell test, as introduced and random nature of A’s and B’s measurements’ outcomes, within a developed in refs. 6–8. Several other seminal works based on Bell fi – DI randomness generation and certi cation protocol. inequalities have been developed9 22, advancing the topics of In the instrumental causal model, which is depicted in Fig. 1a, randomness amplification (the generation of near-perfect ran- the two parties (Alice and Bob) still share a bipartite state. Alice domness from a weaker source), randomness expansion (the 1 can choose among l possible d-outcome measurements (OA, ..., expansion of a short initial random seed), and quantum key l OA), according to the instrument variable x, which is independent distribution (sharing a common secret string through commu- of the shared correlations between Alice and Bob (Λ) and can nication over public channels). In particular, loophole-free Bell assume l different values. On the other hand, Bob’s choice y is tests based on randomness generation protocol have been among d observables (O1 , ..., Od ) and depends on Alice’s outcome implemented7,20,23 and more advanced techniques have been B B a, specifically y = a. In other words, as opposed to the spatially- developed to provide security against general adversarial separated correlations in a Bell-like scenario, the instrumental attacks19,21,24,25. process constitutes a temporal scenario, with one-way commu- From a causal perspective, the non-classical behavior revealed nication of Alice’s outcomes to select Bob’s measurement. This by a Bell test lies in the incompatibility of quantum predictions – implies, first, that Alice and Bob are not space-like separated, to with our intuitive notion of cause and effect26 28. Given that ensure that the causal structure’s constraints are fulfilled, unlike the causal structure underlying a Bell-like scenario involves five in Bell-like scenarios. Secondly, due to the communication of variables (the measurement choices and outcomes for each of Alice’s outcome a to Bob, Bob’s outcome b is not independent of the two observers and a fifth variable representing the common x; however, the instrumental network specifies this influence to be cause of their correlations), it is natural to wonder whether a indirect, formalized by the constraint p(b∣x, a, λ) = p(b∣a, λ) and different, and simpler, causal structure could give rise to an justifying the absence of an arrow from X to B in Fig. 1a. This is analogous discrepancy between quantum and classical causal the aforementioned causal assumption within our protocol. predictions29,30. The instrumental causal structure31,32, where the Similarly to Bell-like scenarios, the causal structure underlying two parties (A and B) are linked by a classical channel of com- an instrumental process imposes some constraints on the classical munication, is the simplest model (in terms of the number of joint probabilities {p(a, b∣x)} that are compatible with it31,32 involved nodes) achieving this result33. This scenario has fun- a,b,x (the so-called instrumental inequalities). In the particular case damental importance in causal inference, since it allows the where the instrument x can assume three different values (1,2,3), estimation of causal influences even in the presence of unknown while a and b
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