Nonlocal correlations are useful for device-independent (DI) randomness certification (P ironio S. et al. , Nature (London) , 464 (2010) 1021). The advantage of this DI protocol over the conventional quantum protocol is that randomness can be certified even when experimental apparatuses are not trusted. Quantum entanglement is the necessary physical source for the nonlocal correlation required for such DI task. However, nonlocality and entanglement are distinct concepts. There exist entangled states which produce no nonlocal correlation and hence are not useful for the DI randomness certification task. Here we introduce the measurement-device–independent randomness certification task where one has trusted quantum state preparation devices but the mesurement devices are completely unspecified. Interestingly we show that there exist entangled states, with local description, that are a useful resource in such task but are useless in the corresponding DI scenario.
Nonlocal correlations are useful for device-independent (DI) randomness certification (P ironio S. et al. , Nature (London) , 464 (2010) 1021). The advantage of this DI protocol over the conventional quantum protocol is that randomness can be certified even when experimental apparatuses are not trusted. Quantum entanglement is the necessary physical source for the nonlocal correlation required for such DI task. However, nonlocality and entanglement are distinct concepts. There exist entangled states which produce no nonlocal correlation and hence are not useful for the DI randomness certification task. Here we introduce the measurement-device–independent randomness certification task where one has trusted quantum state preparation devices but the mesurement devices are completely unspecified. Interestingly we show that there exist entangled states, with local description, that are a useful resource in such task but are useless in the corresponding DI scenario.
Nonlocal correlations obtained from entangled quantum states are useful for device independent (DI) randomness certification [Nature (London) 464, 1021 (2010)]. The advantage of this DI protocol over the conventional quantum protocol is that even with untrusted experimental apparatus randomness can be certified. Although quantum entanglement is the necessary physical source for nonlocal correlation, these two are different concepts. There exist entangled states which produce no nonlocal correlation and hence are not useful for the DI randomness certification task. In this work we introduce measurement-device-independent randomness certification task and show that entangled states, having local description, can be useful resource in such task which otherwise are useless in corresponding DI scenario.
Recently it has been found that there exist maximally nonlocal quantum correlations that fail to certify randomness for any fixed input pair, rendering them useless for device-independent spot-checking randomness expansion schemes. Here we show that conversely, in DI randomness amplification protocols where all input pairs are used for randomness generation, any amount of quantum nonlocality is sufficient to certify randomness. This shows that no bound randomness exists in quantum nonlocality - any quantum nonlocal behavior is useful in a DI randomness generation task with appropriate modification of protocol structure. Secondly, we show that in contrast to the hitherto considered fixed-input guessing probability, the average guessing probability over all inputs is a faithful and monotonic measure of nonlocality. We use the average guessing probability to show that in contrast to findings in PRL 134, 090201, the detection efficiency threshold for randomness generation is never lower than that for nonlocality detection. Finally, we analytically compute the average guessing probability by a quantum adversary of a single player's measurement outputs in a standard CHSH Bell test, and use it to demonstrate an improvement in the generation rate in state-of-art amplification protocols.
The generation of certifiable randomness is one of the most promising applications of quantum technologies. Furthermore, the intrinsic non-locality of quantum correlations allow us to certify randomness in a device-independent way, i.e., we do not need to make assumptions about the devices used. Due to the work of Curchod et al. a single entangled two-qubit pure state can be used to produce arbitrary amounts of certified randomness. However, the obtaining of this randomness is experimentally challenging as it requires a large number of measurements, both projective and general. Motivated by these difficulties in the device-independent setting, we instead consider the scenario of one-sided device independence where certain devices are trusted, and others are not; a scenario motivated by asymmetric experimental set-ups such as ion-photon networks. We show how certain aspects of previous works can be adapted to this scenario and provide theoretical bounds on the amount of randomness that can be certified. Furthermore, we give a protocol for unbounded randomness certification in this scenario, and provide numerical results demonstrating the protocol in the ideal case. Finally, we numerically test the possibility of implementing this scheme on near-term quantum technologies, by considering the performance of the protocol on several physical platforms.
The generation of certifiable randomness is one of the most promising applications of quantum technologies. Furthermore, the intrinsic non-locality of quantum correlations allow us to certify randomness in a device-independent way, ie, we do not need to make assumptions about the devices used. Due to the work of Curchod et al. a single entangled two-qubit pure state can be used to produce arbitrary amounts of certified randomness. However, the obtaining of this randomness is experimentally challenging as it requires a large number of measurements, both projective and general. Motivated by these difficulties in the device-independent setting, we instead consider the scenario of one-sided device independence where certain devices are trusted, and others are not; a scenario motivated by asymmetric experimental set-ups such as ion-photon networks. We show how certain aspects of previous works can be adapted to this scenario and provide theoretical bounds on the amount of randomness that can be certified. Furthermore, we give a protocol for unbounded randomness certification in this scenario, and provide numerical results demonstrating the protocol in the ideal case. Finally, we numerically test the possibility of implementing this scheme on near-term quantum technologies, by considering the performance of the protocol on several physical platforms.
Abstract 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 corresponding 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.
The question of certifying quantum nonlocality under a relaxation of the assumptions in the Bell theorem has gained traction, with potential for device-independent applications under weak seeds and cross-talk. Recently, it was shown that quantum nonlocality can be certified even under a simultaneous arbitrary (but not full) relaxation of the assumptions of Measurement Independence (MI) and Parameter Independence (PI), using states of local dimension d=poly((1−ε)−1) for an ε∈[0,1)-relaxation. Here, we derive three results strengthening the state-of-art. Firstly, we show that states of constant local dimension d are already sufficient to certify quantum nonlocality under arbitrary MI and PI relaxation, albeit in a non-robust manner. Secondly, and as a theoretical paradigm to derive the above, we introduce the notion of \textit{measurement-dependent parameter-dependent locality} as the set of input-output behaviors under simultaneous relaxations of measurement and parameter independence. We provide a rigorous characterisation of the vertices of the polytope of joint input-output behaviors that obey a μ-relaxation of MI and ε-relaxation of PI. We highlight a relation between nonlocality certification under PI relaxation and that under detection inefficiencies by pointing out alternative extremal correlations to the Eberhard correlations that also allow to achieve detection efficiency of η=2/3 in the two-input scenario. Finally, we study the implication of the relaxed assumptions for device-independent randomness certification. We analytically derive the quantum guessing probability for one player's outcomes in the CHSH Bell test, as a function of the noise in the test as well as of a leakage of an average amount of I(X:B)<1 bits of input information per measurement round.