Optimality of entropic uncertainty relations

Abdelkhalek, Kais; Schwonnek, René; Maassen, Hans; Furrer, Fabian; Duhme, Jörg; Raynal, Philippe; Englert, Berthold-Georg; Werner, Reinhard

doi:10.48550/arxiv.1509.00398

Cited by 4 publications

(8 citation statements)

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“…holds for all possible combinations of states and measurements (in any dimension) that are consistent with the observed CHSH value S. An inequality like equation ( 9) is commonly referred to as an entropic uncertainty relation, and in our case, we are interested in relations with quantum side-information [22,37,38]. There is a vast amount of literature [23,39,40] in which relations of this form [22,37,38,41] or similar [42][43][44][45][46][47][48] have been studied and several types of uncertainty relations have been discovered. A typical family of entropic uncertainty relation, which is close to our problem, is that proposed by Berta et al [22] and the weighted generalisation of it from Gao et al [38].…”

Section: Device Independent Entropic Uncertainty Relationmentioning

confidence: 99%

Device-Independent Quantum Key Distribution with Random Key Basis

Schwonnek,

Goh,

Primaatmaja

et al. 2020

Preprint

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Device-independent quantum key distribution (DIQKD) is the art of using untrusted devices to distribute secret keys in an insecure network. It thus represents the ultimate form of cryptography, offering not only information-theoretic security against channel attacks, but also against attacks exploiting implementation loopholes. In recent years, much progress has been made towards realising the first DIQKD experiments, but current proposals are just out of reach of today's loophole-free Bell experiments. In this Letter, we close the gap between the theory and practice of DIQKD with a simple variant of the original protocol based on the celebrated Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. In using two randomly chosen key generating bases instead of one, we show that the noise tolerance of DIQKD can be significantly improved. In particular, the extended feasibility region now covers some of the most recent loophole-free CHSH experiments, hence indicating that the first realisation of DIQKD already lies within the range of these experiments.

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Section: Device Independent Entropic Uncertainty Relationmentioning

confidence: 99%

Device-Independent Quantum Key Distribution with Random Key Basis

Schwonnek,

Goh,

Primaatmaja

et al. 2020

Preprint

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“…In order to fully characterise the obtainable uncertainties, it is thus necessary to consider functions of H(A) and H(B) beyond their sum; indeed, there is no a priori reason why one should only consider entropic uncertainty relations based on the sum H(A) + H(B). Much more recent work [22] has made progress in this direction working with more general Rényi entropies, and presents several conjectures and numerical results beyond two dimensions.…”

Section: A Entropic Uncertainty Relationsmentioning

confidence: 99%

“…Often, one is interested only in the monotone closure of the uncertainty region (as in Refs. [22,26]); that is, the closure under increasing either coordinate of the set of realisable pairs (∆A, ∆B). .…”

Section: Uncertainty Relations In Terms Of Standard Deviationsmentioning

confidence: 99%

Tight State-Independent Uncertainty Relations for Qubits

et al. 2016

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Abstract:The well-known Robertson-Schrödinger uncertainty relations have state-dependent lower bounds, which are trivial for certain states. We present a general approach to deriving tight state-independent uncertainty relations for qubit measurements that completely characterise the obtainable uncertainty values. This approach can give such relations for any number of observables, and we do so explicitly for arbitrary pairs and triples of qubit measurements. We show how these relations can be transformed into equivalent tight entropic uncertainty relations. More generally, they can be expressed in terms of any measure of uncertainty that can be written as a function of the expectation value of the observable for a given state.

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“…Entropic uncertainty relations are currently the subject of active research (see the reviews [11][12][13] and references therein). Questions of their optimality are addressed in [14]. Other approaches are based on the sum of variances [15,16] and on majorization relations [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Entropic uncertainty relations for successive measurements of canonically conjugate observables

Rastegin

2016

Annalen der Physik

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Uncertainties in successive measurements of general canonically conjugate variables are examined. Such operators are approached within a limiting procedure of the Pegg-Barnett type. Dealing with unbounded observables, we should take into account a finiteness of detector resolution. An appropriate reformulation of two scenarios of successive measurements is proposed and motivated. Uncertainties are characterized by means of generalized entropies of both the Rényi and Tsallis types. The Rényi and Tsallis formulations of uncertainty relations are obtained for both the scenarios of successive measurements of canonically conjugate operators. Entropic uncertainty relations for the case of position and momentum are separately discussed.

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Optimality of entropic uncertainty relations

Cited by 4 publications

References 0 publications

Device-Independent Quantum Key Distribution with Random Key Basis

Device-Independent Quantum Key Distribution with Random Key Basis

Tight State-Independent Uncertainty Relations for Qubits

Entropic uncertainty relations for successive measurements of canonically conjugate observables

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