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arXiv:1004.1242 · QP-PQ, quantum probability and white noise analysis

A FAIR SAMPLING TEST FOR EKERT PROTOCOL

GUILLAUME ADENIER, NOBORU WATANABE, Andrei Yu. Khrennikov

Published Jan 1, 2011• 1 citation
arXivHTMLPDF

Abstract

We propose a local scheme to enhance the security of quantum key distribution in Ekert protocol (E91). Our proposal is a fair sampling test meant to detect an eavesdropping attempt that would use a biased sample to mimic an apparent violation of Bell inequalities. The test is local and non disruptive: it can be unilaterally performed at any time by either Alice or Bob during the production of the key, and together with the Bell inequality test.

DOI
10.1142/9789814343763_0031

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We propose a local scheme to enhance the security of quantum key distribution in Ekert protocol (E91). Our proposal is a fair sampling test meant to detect an eavesdropping attempt that would use a biased sample to mimic an apparent violation of Bell inequalities. The test is local and non disruptive: it can be unilaterally performed at any time by either Alice or Bob during the production of the key, and together with the Bell inequality test.
In 1991 Ekert proposed to use Bell inequalities in the so called E91 quantum key distribution protocol. This was the first alternative to the well known BB84 protocol of Bennett and Brassard. In 1992, Bennett, Brassard and Mermin explained that the E91 protocol is no more secure than the original BB84 protocol which do not use Bell inequalities at all. So, apparently, violation of locality was not useful in quantum cryptography. In 1998 Mayers and Yao restored back violation of locality in quantum cryptography with the concept of a self-checking source , a source of Bell states which is provided together with testing devices. The test is designed such that, if passed, the source and the testing devices are guaranteed to be identical modulo some isomorphism to the original specification. We discuss the self-checking source of Mayers and Yao, how it is related to the E91 protocol and the fair sampling assumption which was first used to address the detection loophole in Bell inequalities experiments.
The Ekert 1991 quantum key distribution (QKD) protocol appears to be secure regardless of whatever devices legitimate users adopt for the protocol, as long as the devices give a result that violates Bell's inequality. However, this is not the case if they ignore nondetection events because Eve can make use of the detection loophole, as Larrson showed [Quantum Inf. Comput. 2, 434 (2002)]. We show that even when legitimate users take into account nondetection events Eve can successfully eavesdrop if the QKD system has been appropriately designed by the manufacturer. A loophole utilized here is that of ``free choice'' (or ``real randomness''). Local QKD devices with a pseudorandom sequence generator installed in them can apparently violate Bell's inequality.
In elaborating on the multiple-photon absorption attack on Ekert protocol proposed in arXiv:1011.4740, we show that it can be used in other entanglement-based protocols, in particular the BBM92 protocol. In this attack, the eavesdropper (Eve) is assumed to be in control of the source, and she sends pulses correlated in polarization (but not entangled) containing several photons at frequencies for which only multiple-photon absorptions are possible in Alice's and Bob's detectors. Whenever the photons stemming from one pulse are dispatched in such a way that the number of photons is insufficient to trigger a multiple-photon absorption in either channel, the pulse remains undetected. We show that this simple feature is enough to reproduce the type of statistics on the detected pulses that are considered as indicating a secure quantum key distribution, even though the source is actually a mixture of separable states. The violation of Bell inequalities measured by Alice and Bob increases with the order of the multiple-photon absorption that Eve can drive into their detectors, while the measured quantum bit error rate decreases as a function of the same variable. We show that the attack can be successful even in the simplest case of a two-photon absorption or three-photon absorption attack, and we discuss possible countermeasures, in particular the use of a fair sampling test.
We use the Qiskit quantum computing framework to simulate the E91 Quantum Key Distribution (QKD) protocol. By measuring entangled photon pairs, the E91 protocol uses quantum entanglement to safely transfer cryptographic keys between Alice and Bob. In order to investigate the key generation rates, Bell’s inequality violation, and the protocol’s resilience to eavesdropping, we simulate the protocol in this work using IBM’s quantum simulator. The findings demonstrate that the E91 protocol may effectively create a secure key by taking advantage of quantum entanglement and identifying any eavesdropping attempts by breaking Bell’s inequality, with a calculated Bell’s parameter of S = 2.47, exceeding the classical limit which is 2. Additionally, key extraction is shown to be possible by the analysis of measurement results, where the key creation rate improves with the number of entangled particles, achieving a key generation rate of 1.59 bps for 25 singlet states, 5.37 bps for 100 singlet states, 10.52 bps for 250 singlet states, and 12.24 bps for 500 singlet states, with corresponding key lengths of 7, 25, 57, and 106 bits, respectively.