Min-entropy uncertainty relation for finite-size cryptography

Ng, Nelly Huei Ying; Berta, Mario; Wehner, Stephanie

doi:10.1103/physreva.86.042315

Cited by 57 publications

(73 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Even though, the topic of entropic uncertainty relations (EURs) has a long history (for a detailed review see [4,5]), one can observe a recent increase of interest within the quantum information community leading to several improvements [6][7][8][9][10][11][12][13][14][15][16][17] or even a deep asymptotic analysis of different bounds [18]. This is quite understandable, because the entropic uncertainty relations have various applications, for example in entanglement detection [19][20][21][22][23], security of quantum protocols [24,25], quantum memory [26,27] or as an ingredient of Einstein-Podolsky-Rosen steering criteria [28,29]. Moreover, the recent discussion [30] about the original Heisenberg idea of uncertainty, led to the entropic counterparts of the noise-disturbance uncertainty relation [31,32] (also obtained with quantum memory [33]).…”

Section: Introductionmentioning

confidence: 99%

Majorization approach to entropic uncertainty relations for coarse-grained observables

Rudnicki

2015

Phys. Rev. A

View full text Add to dashboard Cite

We improve the entropic uncertainty relations for position and momentum coarse-grained measurements. We derive the continuous, coarse-grained counterparts of the discrete uncertainty relations based on the concept of majorization. The obtained entropic inequalities involve two Rényi entropies of the same order, and thus go beyond the standard scenario with conjugated parameters. In a special case describing the sum of two Shannon entropies the majorization-based bounds significantly outperform the currently known results in the regime of larger coarse graining, and might thus be useful for entanglement detection in continuous variables.

show abstract

Section: Introductionmentioning

confidence: 99%

Majorization approach to entropic uncertainty relations for coarse-grained observables

Rudnicki

2015

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…However, for many operators the right hand side of (1) depends on a state |ψ and can equal to 0, although both variances on the left hand side of (1) cannot simultaneously equal to 0. Several authors recognized that one can express uncertainty relations in terms of entropies (see [2,3] for review and [4][5][6][7][8][9][10][11] for recent developments). In particular Maassen and Uffink [12] inspired by the work of Deutsch [13] derived the following entropic uncertainty relation [17] S(B (1) ) + S(B (2) ) ≥ − log a.…”

Section: Introductionmentioning

confidence: 99%

Conjectured strong complementary-correlations tradeoff

Grudka

Horodecki

et al. 2013

Phys. Rev. A

View full text Add to dashboard Cite

We conjecture new uncertainty relations which restrict correlations between results of measurements performed by two separated parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when one party measures a single observable and the other party measures one of two observables. The uncertainty relation does not follow from MaassenUffink uncertainty relation and is much stronger than Hall uncertainty relation derived from the latter. The second uncertainty relation bounds the sum of two mutual informations when each party measures one of two observables. We provide numerical evidence for validity of conjectured uncertainty relations and prove them for large classes of states and observables.

show abstract

“…Even at short distances with the new min-entropy relation [29] requiring us to detect as few as 6.65×10…”

Section: Discussionmentioning

confidence: 99%

“…Finally, we can explore the ROT rate formula [19,29] which tells Alice and Bob how many secure ROT bits they can keep from the privacy amplification operation. It is given by…”

Section: Securitymentioning

confidence: 99%

Experimental Implementation of Oblivious Transfer in the Noisy Storage Model

Erven

Wehner

Laflamme

et al. 2012

Conference on Lasers and Electro-Optics 2012

View full text Add to dashboard Cite

Cryptography's importance in our everyday lives continues to grow in our increasingly digital world. Oblivious transfer (OT) has long been a fundamental and important cryptographic primitive since it is known that general two-party cryptographic tasks can be built from this basic building block. Here we show the experimental implementation of a 1-2 random oblivious transfer (ROT) protocol by performing measurements on polarization-entangled photon pairs in a modified entangled quantum key distribution system, followed by all of the necessary classical post-processing including one-way error correction. We successfully exchange a 1,366 bits ROT string in ∼3 min and include a full security analysis under the noisy storage model, accounting for all experimental error rates and finite size effects. This demonstrates the feasibility of using today's quantum technologies to implement secure two-party protocols.Cryptography, prior to the modern computing age, was synonymous with the protection of private communications using a variety of encryption techniques, such as a wax seal or substitution cypher. However, with the advent of modern digital computing and an increasingly internet-driven society, important new cryptographic challenges have arisen. People now wish to do business and interact with others they neither know nor trust. In the field of cryptography this is known as secure two-party computation. Here we have two users, Alice and Bob, who wish to perform a computation on their private inputs in such a way that they obtain the correct output but without revealing any additional information about their inputs.A particularly important and familiar example is the task of secure identification, which we perform any time we use a bank's ATM to withdraw money. Here honest Alice (the bank) and honest Bob (the legitimate customer) share a password. When authenticating a new session, Alice checks to make sure she is really interacting with Bob by validating his password before dispensing any money. However, we do not want Bob to simply announce his password since a malicious Alice could steal his password and impersonate him in the future. What we require is a method for checking whether Bob's password is valid without revealing any additional information. While protocols for general two-party cryptographic tasks such as this one may be very involved, it is known that they can be built from a basic cryptographic building block called oblivious transfer (OT) [1].Many classical cryptography techniques currently in use have their security based on conjectured mathematical assumptions such as the hardness of finding the prime factors of a large number, assumptions which no longer hold once a sufficiently large quantum computer is built [2]. Alternatively, quantum cryptography offers means to accomplish cryptographic tasks which are provably secure using fewer assumptions that are ideally much more stringent than those employed classically. However, until now almost all of the experimental work has focused exclusively on q...

show abstract

Min-entropy uncertainty relation for finite-size cryptography

Cited by 57 publications

References 24 publications

Majorization approach to entropic uncertainty relations for coarse-grained observables

Majorization approach to entropic uncertainty relations for coarse-grained observables

Conjectured strong complementary-correlations tradeoff

Experimental Implementation of Oblivious Transfer in the Noisy Storage Model

Contact Info

Product

Resources

About