Experimental nonlocality-based randomness generation with nonprojective measurements

Gómez, Santiago; Máttar, Alejandro; Gómez, Esteban S.; Cavalcanti, Daniel; Farías, Osvaldo Jiménez; Acín, Antonio; Lima, G.

doi:10.1103/physreva.97.040102

Cited by 34 publications

(25 citation statements)

References 23 publications

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“…Finding an expression I p¢ also requires methods of inference of the behavior of the device from a finite sample: indeed, the estimated behavior (18) cannot be used directly to find a candidate I p , as p almost always violates the no-signaling conditions. There exist different approaches to this inference (see for instance [20,[34][35][36][37]), so a nontrivial choice must be made.…”

Section: Bounding Randomness From Several Bell Expressions (T1)mentioning

confidence: 99%

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Device-independent randomness generation from several Bell estimators

et al. 2018

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Device-independent randomness generation and quantum key distribution protocols rely on a fundamental relation between the non-locality of quantum theory and its random character. This relation is usually expressed in terms of a trade-off between the probability of guessing correctly the outcomes of measurements performed on quantum systems and the amount of violation of a given Bell inequality. However, a more accurate assessment of the randomness produced in Bell experiments can be obtained if the value of several Bell expressions is simultaneously taken into account, or if the full set of probabilities characterizing the behavior of the device is considered. We introduce protocols for device-independent randomness generation secure against classical side information, that rely on the estimation of an arbitrary number of Bell expressions or even directly on the experimental frequencies of measurement outcomes. Asymptotically, this results in an optimal generation of randomness from experimental data (as measured by the min-entropy), without having to assume beforehand that the devices violate a specific Bell inequality.

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Section: Bounding Randomness From Several Bell Expressions (T1)mentioning

confidence: 99%

“…). But since the probabilities p a x ( | ) satisfy normalization and no-signaling, they are uniquely specified by the 8 correlators of equation (37), which constitute 8 Bell expressions g g , ,…”

Section: Bounding Randomness From Several Bell Expressions (T1)mentioning

confidence: 99%

Device-independent randomness generation from several Bell estimators

et al. 2018

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“…Finally, we have also self-tested the trine-POVM in a different prepare-and-measure scenario (see Appendix C). In Appendix D, we use this prepare-and-measure scenario to derive a tight bound on projective measurements by evaluating the right-hand-side of (12).…”

Section: B Example Ii: the Qubit Trine-povmmentioning

confidence: 99%

“…A possible way to circumvent this problem is to consider a Bell scenario with quantum systems of bounded Hilbert space dimension. In particular, Refs [12,22] recently reported the experimental certification of a non-projective measurement in a Bell experiment assuming qubits. However, these experiments do not represent selftests, as they certify the non-projective character of a measurement, but not how it relates to a specific target POVM.…”

Section: Introductionmentioning

confidence: 99%

Self-testing nonprojective quantum measurements in prepare-and-measure experiments

et al. 2020

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Self-testing represents the strongest form of certification of a quantum system. Here we investigate theoretically and experimentally the question of self-testing non-projective quantum measurements. That is, how can one certify, from observed data only, that an uncharacterised measurement device implements a desired non-projective positive-operator-valued-measure (POVM). We consider a prepare-and-measure scenario with a bound on the Hilbert space dimension, which we argue is natural for this problem since any measurement can be made projective by artificially increasing the Hilbert space dimension. We develop methods for (i) robustly self-testing extremal qubit POVMs (which feature either three or four outcomes), and (ii) certify that an uncharacterised qubit measurement is non-projective, or even a genuine four-outcome POVM. Our methods are robust to noise and thus applicable in practice, as we demonstrate in a photonic experiment. Specifically, we show that our experimental data implies that the implemented measurements are very close to certain ideal three and four outcome qubit POVMs, and hence non-projective. In the latter case, the data certifies a genuine four-outcome qubit POVM. Our results open interesting perspective for strong "black-box" certification of quantum devices.

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“…Most actual experiments do not correspond to projective measurements, but to some more general POVMs. The influence of POVMs on Bell nonlocality has been investigated both theoretically [18][19][20][21][22][23] and experimentally [24,25]. At the same time, theoretical [26][27][28] and experimental [29,30] studies of violations of the Leggett-Garg inequality with generalized measurements have been performed.…”

Section: Introductionmentioning

confidence: 99%

Quantum witness of a damped qubit with generalized measurements

2019

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We evaluate the quantum witness based on the no-signaling-in-time condition of a damped two-level system for nonselective generalized measurements of varying strength. We explicitly compute its dependence on the measurement strength for a generic example. We find a vanishing derivative for weak measurements and an infinite derivative in the limit of projective measurements. The quantum witness is hence mostly insensitive to the strength of the measurement in the weak measurement regime and displays a singular, extremely sensitive dependence for strong measurements. We finally relate this behavior to that of the measurement disturbance defined in terms of the fidelity between pre-measurement and post-measurement states.

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Experimental nonlocality-based randomness generation with nonprojective measurements

Cited by 34 publications

References 23 publications

Device-independent randomness generation from several Bell estimators

Device-independent randomness generation from several Bell estimators

Self-testing nonprojective quantum measurements in prepare-and-measure experiments

Quantum witness of a damped qubit with generalized measurements

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