Device-independent point estimation from finite data and its application to device-independent property estimation

Lin, Pei Sheng; Rosset, Denis; Zhang, Yanbao; Bancal, Jean-Daniel; Liang, Yeong-Cherng

doi:10.1103/physreva.97.032309

Cited by 31 publications

(32 citation statements)

References 94 publications

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“…As the objective function in Equation ( 5 ) is strictly convex in

and the feasible set

is convex, the minimizer of the above optimization problem—which we shall denote by

—is unique (see, e.g., Ref. [ 27 ]). It follows from the results presented in Ref.…”

Section: Methodsmentioning

confidence: 99%

“…For example, using the observed relative frequencies as a naïve estimator of the underlying correlations would generically (see, e.g., Refs. [ 26 , 27 ]) lead to a violation of the nonsignaling conditions [ 28 , 29 ]. Since the assumption of nonsignaling is a prerequisite for any Bell tests, it is only natural that a Bell test of LHV theories must also be accompanied by the corresponding test of this assumption [ 22 , 23 , 24 , 25 , 30 ] (see also Refs.…”

Section: Introductionmentioning

confidence: 99%

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Bounding the Plausibility of Physical Theories in a Device-Independent Setting via Hypothesis Testing

Liang

Zhang

2019

Entropy

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The device-independent approach to physics is one where conclusions about physical systems (and hence of Nature) are drawn directly and solely from the observed correlations between measurement outcomes. This operational approach to physics arose as a byproduct of Bell's seminal work to distinguish, via a Bell test, quantum correlations from the set of correlations allowed by local-hidden-variable theories. In practice, since one can only perform a finite number of experimental trials, deciding whether an empirical observation is compatible with some class of physical theories will have to be carried out via the task of hypothesis testing. In this paper, we show that the prediction-based-ratio method-initially developed for performing a hypothesis test of localhidden-variable theories-can equally well be applied to test many other classes of physical theories, such as those constrained only by the nonsignaling principle, and those that are constrained to produce any of the outer approximation to the quantum set of correlations due to Navascués-Pironio-Acín. We numerically simulate Bell tests using hypothetical nonlocal sources of correlations to illustrate the applicability of the method in both the independent and identically distributed (i.i.d.) scenario and the non-i.i.d. scenario. As a further application, we demonstrate how this method allows us to unveil an apparent violation of the nonsignaling conditions in certain experimental data collected in a Bell test. This, in turn, highlights the importance of the randomization of measurement settings, as well as a consistency check of the nonsignaling conditions in a Bell test.

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“…As the objective function in Equation ( 5 ) is strictly convex in

and the feasible set

is convex, the minimizer of the above optimization problem—which we shall denote by

—is unique (see, e.g., Ref. [ 27 ]). It follows from the results presented in Ref.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bounding the Plausibility of Physical Theories in a Device-Independent Setting via Hypothesis Testing

Liang

Zhang

2019

Entropy

Self Cite

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“…It is important to note that both these minimisations can be efficiently solved (see [21] for details), thus making this approach operationally relevant. A detailed study of these regularisation methods, and, in particular, of their convergence to the underlying distribution, is beyond the scope of this article; we refer the readers to [21] for information on that subject. We can now define the following regularisation-based protocol for generating randomness from uncharacterised devices:…”

Section: A Optimising the Bell Expression Via Regularisationmentioning

confidence: 99%

Regularising data for practical randomness generation

Bourdoncle

Lin

Rosset

et al. 2019

Quantum Sci. Technol.

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Assuming that the no-signalling principle holds, non-local correlations contain intrinsic randomness. In particular, for a specific Bell experiment, one can derive relations between the amount of randomness produced, as quantified by the min-entropy of the output data, and its associated violation of a Bell inequality. In practice, due to finite sampling, certifying randomness requires the development of statistical tools to lower-bound the min-entropy of the data as a function of the estimated Bell violation. The quality of such bounds relies on the choice of certificate, i.e., the Bell inequality whose violation is estimated. In this work, we propose a method for choosing efficiently such a certificate and analyse, by means of extensive numerical simulations (with various choices of parameters), the extent to which it works. The method requires sacrificing a part of the output data in order to estimate the underlying correlations. Regularising this estimate then allows one to find a Bell inequality that is well suited for certifying practical randomness from these specific correlations. We then study the effects of various parameters on the obtained min-entropy bound and explain how to tune them in a favourable way. Lastly, we carry out several numerical simulations of a Bell experiment to show the efficiency of our method: we nearly always obtain higher min-entropy rates than when we use a pre-established Bell inequality, namely the Clauser-Horne-Shimony-Holt inequality.

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“…These results are well within the limits of experimental feasibility (see Figure 2 in Appendix C for a plot of our results). Additionally, the number of copies required by our finite analysis is sufficiently high so as to provide a good enough estimate of the quantum distribution, meaning that we do not need to employ regularisation methods as in [47]. Our scheme is thus the first authenticated teleportation protocol that is practical in its robustness, implementable with existing experimental setups, and further, tolerates untrusted devices.We now comment on possible extensions of this work.…”

mentioning

confidence: 99%

Authenticated teleportation with one-sided trust

Unnikrishnan

Markham²

2019

Phys. Rev. A

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We introduce a protocol for authenticated teleportation, which can be proven secure even when the receiver does not trust their measurement devices, and is experimentally accessible. We use the technique of self-testing from the device-independent approach to quantum information, where we can characterise quantum states and measurements from the exhibited classical correlations alone. First, we derive self-testing bounds for the Bell state and Pauli σX , σZ measurements, that are robust enough to be implemented in the lab. Then, we use these to determine a lower bound on the fidelity of an untested entangled state to be used for teleportation. Finally, we apply our results to propose an experimentally feasible protocol for one-sided device-independent authenticated teleportation. This can be interpreted as a first practical authentication of a quantum channel, with additional one-sided device-independence.Quantum teleportation is well-established as a cornerstone of the field of quantum information, allowing the transfer of a qubit from one party to another using an entangled pair and a classical communication channel [1]. While interesting in its own right, it is also a key ingredient in many protocols, such as secret sharing [2,3], anonymous transmission [4] and multiparty computation [5], and is an important tool across quantum information.From a cryptographic point of view, it is then vital to study the security of teleportation. We consider authenticated teleportation, where we wish to verify that the teleportation has succeeded even when we do not trust the entangled pair being used. This authenticates its application as a quantum channel between the two parties. Previous schemes for authentication of a quantum channel, such as [6], rely on generating large entangled states or performing entangling measurements. In order to guarantee high security of such protocols, one would need levels of entanglement that are, in practice, unfeasible. We solve this problem and go one step further: allowing Alice and Bob to authenticate their quantum channel even when their devices may not be trusted.Device-independence has become a highly desirable feature of quantum communication and computation protocols, from its early applications to quantum key distribution [7-9] and quantum random number generation [10,11]. This approach addresses the situation where the untrusted components may have been obtained from, or be in the control of, an adversary. In the two party setting, one can consider two trust settings: one-sided device-independent (1sDI), where Alice trusts her device but Bob does not (or vice versa), and fully deviceindependent (DI), where neither party trusts their devices. One-sided trust should allow for a much simpler experimental implementation as in [12][13][14]. This scenario is particularly relevant when one party is naturally trusted, for example, a trusted client but untrusted server, or simply if the channel and local measurement device are untrusted when one may wish to receive a resource (for example...

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Device-independent point estimation from finite data and its application to device-independent property estimation

Cited by 31 publications

References 94 publications

Bounding the Plausibility of Physical Theories in a Device-Independent Setting via Hypothesis Testing

Bounding the Plausibility of Physical Theories in a Device-Independent Setting via Hypothesis Testing

Regularising data for practical randomness generation

Authenticated teleportation with one-sided trust

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