Device-independent randomness certification using multiple copies of entangled states

Mahato, Shyam Sundar; Pan, A. K.

doi:10.1016/j.physleta.2022.128534

Cited by 4 publications

(3 citation statements)

References 31 publications

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“…On the other hand, the incommensurability between randomness and entanglement has also been shown [5] by achieving maximum amount of certifiable randomness from a pure non-maximally entangled state, but by going beyond the 2-2-2 scenario. Thus, beyond the 2-2-2 scenario, a line of study has been developed for demonstrating maximum amount of certifiable randomness by using different methods, such as increasing the number of measurement settings [7][8][9], introducing higher outcome POVM [10].…”

Section: Introductionmentioning

confidence: 99%

“… in quantum theory by using the CLL relations Similar to the Hardy relations, here we characterise the joint probability distributions exhibiting CLL nonlocality. The constraints on joint probabilities given by equation (9)(10)(11) imply that 〈ψ|u 1 ⊗ 0〉 = 〈ψ|0 ⊗ v 1 〉 = 0. This, in turn, specifies two of the independent state parameters appearing in equation (21) in terms of the two measurement parameters α and β.…”

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confidence: 99%

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Revealing incommensurability between device-independent randomness, nonlocality, and entanglement using Hardy and Hardy-type relations

Sasmal,

Rai,

Gangopadhyay

et al. 2024

Phys. Scr.

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A comprehensive treatment of the quantification of randomness certified device-independently by using the Hardy and Cabello-Liang-Li (CLL) nonlocality relations is provided in the two parties – two measurements per party – two outcomes per measurement (2-2-2) scenario. For the Hardy nonlocality, it is revealed that for a given amount of nonlocality signified by a particular non-zero value of the Hardy parameter, the amount of Hardy-certifiable randomness is not unique, unlike the way the amount of certifiable randomness is related to the CHSH nonlocality. This is because any specified non-maximal value of Hardy nonlocality parameter characterises a set of quantum extremal distributions. Then this leads to a range of certifiable amounts of randomness corresponding to a given Hardy parameter. On the other hand, for a given amount of CLL-nonlocality, the certifiable randomness is unique, similar to that for the CHSH nonlocality. Furthermore, the tightness of our analytical treatment evaluating the respective guaranteed bounds for the Hardy and CLL relations is demonstrated by their exact agreement with the Semi-Definite-Programming based computed bounds. Interestingly, the analytically evaluated maximum achievable bounds of both Hardy and CLL-certified randomness have been found to be realisable for non-maximal values of the Hardy and CLL nonlocality parameters. In particular, we have shown that even close to the maximum 2 bits of CLL-certified randomness can be realised from non-maximally entangled pure two-qubit states corresponding to small values of the CLL nonlocal parameter. This, therefore, clearly illustrates the quantitative incommensurability between randomness, nonlocality and entanglement.

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Revealing incommensurability between device-independent randomness, nonlocality, and entanglement using Hardy and Hardy-type relations

Sasmal,

Rai,

Gangopadhyay

et al. 2024

Phys. Scr.

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“…Such tests have recently been realized [25][26][27][28][29] enabling experimental demonstrations of DI certification of randomness [30,31]. Of late, the DI certification is used as a resource for secure quantum key distribution [32][33][34][35], randomness certification [36][37][38][39], witnessing Hilbert space dimension [40][41][42][43][44][45][46] and for achieving advantages in communication complexity tasks [47].…”

Section: Introductionmentioning

confidence: 99%

Device-independent self-testing of unsharp measurements

Roy

Pan

2023

New J. Phys.

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Semi-device-independent certification of an unsharp instrument has recently been demonstrated [New J. Phys. 21, 083034 (2019)] based on the sequential sharing of quantum advantages in a prepare-measure communication game by assuming the system to be qubit. In this work, we provide device-independent (DI) self-testing of the unsharp instrument through the quantum violation of two Bell inequalities where the devices are uncharacterized and the dimension of the system remains unspecified. We introduce an elegant sum-of-squares approach to derive the dimension-independent optimal quantum violation of Bell inequalities which plays a crucial role. Note that the standard Bell test cannot self-test the post-measurement states and consequently cannot self-test unsharp instruments. The sequential Bell test possesses the potential to self-test an unsharp instrument. We demonstrate that there exists a trade-off between the maximum sequential quantum violations of the Clauser-Horne-Shimony-Halt inequality, and they form an optimal pair that enables the DI self-testing of the entangled state, the observables, and the unsharpness parameter. Further, we extend our study to the case of elegant Bell inequality, and we argue that it has two classical bounds - the local bound and the non-trivial preparation non-contextual bound, lower than the local bound. Based on the sharing of preparation contextuality by three independent sequential observers, we demonstrate the DI self-testing of two unsharpness parameters. Since an experimental scenario involves losses and imperfection, we demonstrate the robustness of our certification to noise.

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