Robustness of a quantum key distribution with two and three mutually unbiased bases

Caruso, Filippo; Bechmann-Pasquinucci, H.; Macchiavello, Chiara

doi:10.1103/physreva.72.032340

Cited by 15 publications

(9 citation statements)

References 13 publications

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“…For example, under certain postselection strategies, the restriction p(x) = q(x) in theorem 1 may be violated. We will show later that for sifting on orthogonal basis states, the convexity property (22) holds.…”

Section: Properties Of the Mutual Information And The Holevo Quanmentioning

confidence: 94%

“…The proof of this theorem is in appendix C. Since we use postselection in our protocols, we need to extend these theorems to hold for the key rater(E(ρ AB )) in the following sensē r(E(ρ AB )) ≤ λr(E(ρ AB )) + (1 − λ)r(E(σ AB )). (22) This property (22) does not hold in general. For example, under certain postselection strategies, the restriction p(x) = q(x) in theorem 1 may be violated.…”

Section: Properties Of the Mutual Information And The Holevo Quanmentioning

confidence: 99%

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Symmetries in quantum key distribution and the connection between optimal attacks and optimal cloning

2012

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We investigate the connection between the optimal collective eavesdropping attack and the optimal cloning attack where the eavesdropper employs an optimal cloner to attack the quantum key distribution (QKD) protocol. The analysis is done in the context of the security proof in Refs. [1,2] for discrete variable protocols in d-dimensional Hilbert spaces. We consider a scenario in which the protocols and cloners are equipped with symmetries. These symmetries are used to define a quantum cloning scenario. We find that, in general, it does not hold that the optimal attack is an optimal cloner. However, there are classes of protocols, where we can identify an optimal attack by an optimal cloner. We analyze protocols with 2, d and d + 1 mutually unbiased bases where d is a prime, and show that for the protocols with 2 and d + 1 MUBs the optimal attack is an optimal cloner, but for the protocols with d MUBs, it is not 1 . Finally, we give criteria to identify protocols which have different signal states, but the same optimal attack. Using these criteria, we present qubit protocols which have the same optimal attack as the BB84 protocol or the 6-state protocol. arXiv:1112.3396v1 [quant-ph]

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Section: Properties Of the Mutual Information And The Holevo Quanmentioning

confidence: 94%

Section: Properties Of the Mutual Information And The Holevo Quanmentioning

confidence: 99%

Symmetries in quantum key distribution and the connection between optimal attacks and optimal cloning

2012

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“…In high-dimensional systems, complementary observables and the corresponding MUBs have been exploited to enhance the security in quantum cryptograpy [7], perform fundamental tests of quantum mechanics, such as quantum contextuality [8][9][10], explore logical indetermi-nacy [11], and several other tasks in quantum information. For instance, new quantum key distribution protocols were conceived in which a larger error rate can be tolerated while preserving security [12,13]. Moreover a different protocol extending Ekert91 [14] by using entangled qutrits has been experimentally realized [15].…”

Section: Introductionmentioning

confidence: 99%

“…For instance, new quantum key distribution protocols were conceived in which a larger error rate can be tolerated while preserving security1213. Moreover a different protocol extending Ekert9114 by using entangled qutrits has been experimentally realized15.…”

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confidence: 99%

Test of mutually unbiased bases for six-dimensional photonic quantum systems

D’Ambrosio

Cardano

Karimi

et al. 2013

Sci Rep

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In quantum information, complementarity of quantum mechanical observables plays a key role. The eigenstates of two complementary observables form a pair of mutually unbiased bases (MUBs). More generally, a set of MUBs consists of bases that are all pairwise unbiased. Except for specific dimensions of the Hilbert space, the maximal sets of MUBs are unknown in general. Even for a dimension as low as six, the identification of a maximal set of MUBs remains an open problem, although there is strong numerical evidence that no more than three simultaneous MUBs do exist. Here, by exploiting a newly developed holographic technique, we implement and test different sets of three MUBs for a single photon six-dimensional quantum state (a “qusix”), encoded exploiting polarization and orbital angular momentum of photons. A close agreement is observed between theory and experiments. Our results can find applications in state tomography, quantitative wave-particle duality, quantum key distribution.

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“…In particular, it has been shown that an increase in the dimension leads to a better performance of various quantum information protocols, such as for example quantum cryptography [4][5][6] and some problems in distributed quantum computing [7]. Moreover, a relevant experimental effort has been recently spent in the generation, manipulation and detection of quantum systems with higher dimension [8,9].…”

Section: Introductionmentioning

confidence: 99%