Robust protocols for securely expanding randomness and distributing keys using untrusted quantum devices

Miller, Carl A.; Shi, Yuanming

doi:10.48550/arxiv.1402.0489

Cited by 18 publications

(59 citation statements)

References 46 publications

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“…The following lemma generalises a classical result originally proposed in [43]. It follows rather directly from similar statements proved in [52,50,35,33].…”

Section: Necessity Of the Markov Chain Conditionssupporting

confidence: 74%

“…For these entropies, we derive a novel chain rule, which forms the core technical part of our proof. In addition, some of the concepts used in this work generalise techniques proposed in the recent security proofs for device-independent cryptography presented in [33,34]. In particular, the dominant terms of the lower bound on the amount of randomness obtained in [34], called rate curves, are similar to the tradeoff functions considered here (cf.…”

Section: Introductionmentioning

confidence: 95%

See 1 more Smart Citation

Entropy accumulation

Dupuis,

Fawzi,

Renner

2016

Preprint

133

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We ask the question whether entropy accumulates, in the sense that the operationally relevant total uncertainty about an n-partite system A = (A1, . . . An) corresponds to the sum of the entropies of its parts Ai. The Asymptotic Equipartition Property implies that this is indeed the case to first order in n -under the assumption that the parts Ai are identical and independent of each other. Here we show that entropy accumulation occurs more generally, i.e., without an independence assumption, provided one quantifies the uncertainty about the individual systems Ai by the von Neumann entropy of suitably chosen conditional states. The analysis of a large system can hence be reduced to the study of its parts. This is relevant for applications. In device-independent cryptography, for instance, the approach yields essentially optimal security bounds valid for general attacks, as shown by .

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“…The following lemma generalises a classical result originally proposed in [43]. It follows rather directly from similar statements proved in [52,50,35,33].…”

Section: Necessity Of the Markov Chain Conditionssupporting

confidence: 74%

Section: Introductionmentioning

confidence: 95%

Entropy accumulation

Dupuis,

Fawzi,

Renner

2016

Preprint

133

View full text Add to dashboard Cite

show abstract

“…We learn from the above that the considered bound entangled state and measurements, which can produce randomness, cannot produce a key using a one-way DIQKD protocol. 10 This does not mean that other more complex protocols cannot use this state to produce a key in a DI way. Yet, as bound entangled states are a useful resource also for one-way device-dependent QKD protocols [30,36], considering one-way DIQKD as above is an interesting starting point.…”

Section: B First Evidencementioning

confidence: 99%

“…The focus of the previous works so far was to lower -bound the key rate, i.e., to find the minimal length of a key that can be created, in terms of the relevant parameters of the protocol. With improved lower bounds over the years [8][9][10], a tight lower bound was recently provided [11,12]. 2 These lower bounds can be seen as a statement regarding the minimal amount of key that can be extracted from an entangled state, winning the CHSH game with a certain probability, using the standard DIQKD protocol.…”

Section: Introductionmentioning

confidence: 99%

Upper bounds on device-independent quantum key distribution rates and a revised Peres conjecture

Arnon-Friedman,

Leditzky

2020

Preprint

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Device-independent quantum key distribution (DIQKD) is one of the most challenging tasks in quantum cryptography. The protocols and their security are based on the existence of Bell inequalities and the ability to violate them by measuring entangled states. We study the entanglement needed for DIQKD protocols in two different ways. Our first contribution is the derivation of upper bounds on the key rates of CHSH-based DIQKD protocols in terms of the violation of the inequality; this sets an upper limit on the possible DI key extraction rate from states with a given violation. Our upper bound improves on the previously known bound of Kaur et al. Our second contribution is the initiation of the study of the role of bound entangled states in DIQKD. We present a revised Peres conjecture stating that such states cannot be used as a resource for DIQKD. We give a first piece of evidence for the conjecture by showing that the bound entangled state found by Vertesi and Brunner, even though it can certify DI randomness, cannot be used to produce a key using protocols analogous to the well-studied CHSH-based DIQKD protocol.

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“…To design a device independent random number generator, one can use the fact that states exhibiting super-classical correlation properties exhibit intrinsic randomness if measured locally. A line of research was devoted to expansion of free randomness using quantum devices (see e. g. [8,9,10,11,12]), which, in the spirit of seeded randomness extractors, expands the length of preexisting independent random seed. Recently several researchers attempted to solve the problem of perfect randomness production, suggesting ways to amplify existing weak randomness with the use of untrusted quantum devices (characterized either as Santha-Vazirani source [13,14,15,16,17] or min-entropy source [18,19]).…”

Section: Introductionmentioning

confidence: 99%

Device-independent randomness amplification with a single device

Plesch

Pivoluska

2014

Physics Letters A

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Expansion and amplification of weak randomness with untrusted quantum devices has recently become a very fruitful topic of research. Here we contribute with a procedure for amplifying a single weak random source using tri-partite GHZ-type entangled states. If the quality of the source reaches a fixed threshold $R=\frac{1}{4}\log_{2}(10)$, perfect random bits can be produced. This technique can be used to extract randomness from sources that can't be extracted neither classically, nor by existing procedures developed for Santha-Vazirani sources. Our protocol works with a single fault-free device decomposable into three non-communicating parts, that is repeatedly reused throughout the amplification process.Comment: 23 pages, 4 figures, accepted in PL

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Robust protocols for securely expanding randomness and distributing keys using untrusted quantum devices

Cited by 18 publications

References 46 publications

Entropy accumulation

Entropy accumulation

Upper bounds on device-independent quantum key distribution rates and a revised Peres conjecture

Device-independent randomness amplification with a single device

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