Modified Wigner inequality for secure quantum-key distribution

Castelletto, Stefania; Degiovanni, I. P.; Rastello, María Luisa

doi:10.1103/physreva.67.044303

Cited by 15 publications

(37 citation statements)

References 21 publications

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“…, W ≥ 0 for local realistic theories and W = −0.125 for the singlet state, but allows secure QKD, because W contains the additional term accounting for the anticorrelation. In our experiment we also measure W and we observe that the minimum of W is well above the limit for local-realistic theories in agreement with the theory [16], ensuring a secure QKD.…”

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confidence: 86%

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confidence: 99%

“…Unfortunately this is not the case. In fact, only when Eve adopts an interceptresend strategy and detects one photon of the pair, the inequality becomes W ≥ 0.0625, but, as we will show, this is not for eavesdropping on both channels, because in this case there is no limit [16].In this letter we perform an experiment proving the weakness of the Wigner inequality as a security test for QKD, under the condition of Eve gaining total control of the source of photon pairs. Under this condition, she prepares each particle of the pair separately in a well defined polarization direction, in other words she prepares the photon in Alice's channel in the state |φ A , and the photon in Bob's channel in the state |φ B , respectively…”

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confidence: 99%

“…[16] presented a modified version of the Wigner's parameter W which maintains the same limits, i.e. , W ≥ 0 for local realistic theories and W = −0.125 for the singlet state, but allows secure QKD, because W contains the additional term accounting for the anticorrelation.…”

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confidence: 99%

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Experimental eavesdropping attack against Ekert’s protocol based on Wigner’s inequality

Bovino¹,

Colla²,

Castagnoli³

et al. 2003

Phys. Rev. A

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We experimentally implemented an eavesdropping attack against the Ekert protocol for quantum key distribution based on the Wigner inequality. We demonstrate a serious lack of security of this protocol when the eavesdropper gains total control of the source. In addition we tested a modified Wigner inequality which should guarantee a secure quantum key distribution.Quantum key distribution (QKD) provides a method for distributing a secret key for unconditional secret communications based on the "one time pad" because it guarantees that the presence of any eavesdropper compromising the security of the key is revealed. For a review on this topic see [1].The first protocol for QKD has been proposed in 1984 by Bennett and Brassard [2], the worldwide famous BB84 protocol. In 1991 A. Ekert proposed a new QKD protocol whose security relies on the non-local behavior of quantum mechanics, i.e., on Bell's inequalities [3].Several groups around the world implemented and tested QKD systems based on variants of the BB84 protocol using either faint laser [4,5,6,7,8,9] or entangled photons [10,11,12,13,14], while, to our knowledge, only recently two groups implemented the Ekert's protocol [12,13]. In particular Naik et al.[13] implemented a variant of the Ekert's protocol based on Clauser-HorneShimony-Holt (CHSH) inequality as proposed in Ekert's paper [3], and Jennewein et al. [12] implemented the Ekert's protocol based on the Wigner inequality.In ref.[12] the Wigner inequality was first proposed to provide an easier and equally reliable eavesdropping test as the CHSH when the Ekert protocol is implemented. The necessary security proof of the Ekert protocol based on the Wigner inequality consists in verifying the violation of W ≥ 0.To obtain the Wigner inequality (W ≥ 0) it is necessary to review the Wigner argument [15]. Two main assumptions are stipulated in the proofs of the Wigner inequality: locality and realism. Locality means that Alice's measurements do not influence Bob's measurements, and vice versa. Realism means that, given any physical property, its value exists independently of its observation or measurement. The counterpart of the local-realistic theories is the non-locality behavior of quantum mechanics, a signature of quantum entanglement. In particular Wigner considered a quantum system prepared in the singlet state, and he obtained the violation of the inequality W ≥ 0, i.e. , W = −0.125. Furthermore, in the derivation of his inequality, Wigner assumed perfect anticorrelation in the measurement results. This assumption is obviously reasonable in the test of realism and locality of a physical theory (it reflects the classical counterpart of a quantum system prepared in the singlet state). Nevertheless, in terms of QKD this assumption corresponds to a lack of security.In fact, when the eavesdropper, Eve, measures photons on either one or both of Alice and Bob channels, her presence should be revealed by a higher value of W than the local-realistic theories limit W = 0, as it happens for the CHSH inequality [3]....

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confidence: 86%

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confidence: 99%

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confidence: 99%

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confidence: 99%

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Experimental eavesdropping attack against Ekert’s protocol based on Wigner’s inequality

Bovino¹,

Colla²,

Castagnoli³

et al. 2003

Phys. Rev. A

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“…The probabilities Pr i are nonnegative, and therefore Pr 3 + Pr 4 ≤ Pr 3 + Pr 4 + Pr 2 +Pr 7 within the framework conceived by Wigner [3,4,5], as described in detail in [6, p. 227-228]. (If we assume, with Wigner, the existence of these probabilities, his inequality must be true, because the existence of these probabilities corresponds in essence to Kolmogorov's consistency conditions).…”

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Controlled NOT function can provoke biased interpretation from Bell’s test experiments

Castro

2017

Preprint

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Abstract. Recently, we showed that the controlled-N OT function is a permutation that cannot be inverted in subexponential time in the worst case [Quantum Information Processing. 16:149 (2017)]. Here, we show that such a condition can provoke biased interpretations from Bell's test experiments.Let CN OT be the canonical two-qubit entangling gate in quantum key distribution (QKD) cryptographic protocols, where CN OT |a, x = |a, a + x , so that the control parameter a and the target variable x ∈ F 2 = {0, 1}.For x = a, CN OT |a, x = |a, x 2 + x , since x ∧ x = x = x 2 , and for x = a, CN OT |a, x = |a,(i) The permutation x 2 +x = x⊕x is a factorable polynomial (reducible) over a finite field of two elements, whose Hamming distance between its even inputs is equal to 0 (local model), and (ii) The permutation x 2 + x + 1 = x ⊕ N OT (x) is a nonfactorable polynomial (irreducible) over a finite field of two elements, whose Hamming distance between its odd inputs is not equal to 0 (nonlocal model). However, these models are deducible from each other because x 2 + x (+1) = 0 (+1) = x 2 + x + 1 andConsider the Hadamard basis {|+ , |− } of a one-qubit register given by:The circuit below takes computational basis F 2 = {0, 1} to Bell states:

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Bipartite qutrit local realist inequalities and the robustness of their quantum mechanical violation

et al. 2017

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Distinct from the type of local realist inequality (known as the Collins-Gisin-Linden-MassarPopescu or CGLMP inequality) usually used for bipartite qutrit systems, we formulate a new set of local realist inequalities for bipartite qutrits by generalizing Wigner's argument that was originally formulated for the bipartite qubit singlet state. This treatment assumes existence of the overall joint probability distributions in the underlying stochastic hidden variable space for the measurement outcomes pertaining to the relevant trichotomic observables, satisfying the locality condition and yielding the measurable marginal probabilities. Such generalized Wigner inequalities (GWI) do not reduce to Bell-CHSH type inequalities by clubbing any two outcomes, and are violated by quantum mechanics (QM) for both the bipartite qutrit isotropic and singlet states using trichotomic observables defined by six-port beam splitter as well as by the spin-1 component observables. The efficacy of GWI is then probed in these cases by comparing the QM violation of GWI with that obtained for the CGLMP inequality. This comparison is done by incorporating white noise in the singlet and isotropic qutrit states. It is found that for the six-port beam splitter observables, QM violation of GWI is more robust than that of the CGLMP inequality for singlet qutrit states, while for isotropic qutrit states, QM violation of the CGLMP inequality is more robust. On the other hand, for the spin-1 component observables, QM violation of GWI is more robust for both the type of states considered.

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Modified Wigner inequality for secure quantum-key distribution

Cited by 15 publications

References 21 publications

Experimental eavesdropping attack against Ekert’s protocol based on Wigner’s inequality

Experimental eavesdropping attack against Ekert’s protocol based on Wigner’s inequality

Controlled NOT function can provoke biased interpretation from Bell’s test experiments

Bipartite qutrit local realist inequalities and the robustness of their quantum mechanical violation

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