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Kluwer Academic Publishers eBooks

Violation of Locality and Self-Checking Source: A Brief Account

Dominic Mayers, Christian J. Tourenne

Published Feb 24, 2006• 1 citation
Publisher

Abstract

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.

DOI
10.1007/0-306-47114-0_43

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The concept of nonlocality, whereby a local operation on one state can instantaneously affect the properties of another spatially-separated state, has been investigated through the violation of Bell inequalities. Realisations of such violations in the laboratory paved the way for not only experimental justification of quantum theory, but also one of the subject's first significant applications in cryptography. The violation of Bell inequalities can be used as an indicator for security in the task of key distribution. Furthermore, it has more recently been shown that such security is guaranteed by the violations alone, regardless of assumptions about the workings and trustworthiness of the devices provided for the task. We provide a brief history of Bell inequalities and their use in the development of device-independent key distribution, which is less reliant on the validity of quantum theory than previously thought.

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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.
Quantum key distribution, first proposed by C.H. Bennett and G. Brassard (1984), provides a possible key distribution scheme whose security depends only on the quantum laws of physics. So far the protocol has been proved secure even under channel noise and detector faults of the receiver but is vulnerable if the photon source used is imperfect. In this paper we propose and give a concrete design for a new concept, self-checking source, which requires the manufacturer of the photon source to provide certain tests; these tests are designed such that, if passed, the source is guaranteed to be adequate for the security of the quantum key distribution protocol, even though the testing devices may not be built to the original specification. The main mathematical result is a structural theorem which states that, for any state in a Hilbert space, if certain EPR-type equations are satisfied, the state must be essentially the orthogonal sum of EPR pairs.
We study, in the context of quantum information and quantum communication, a configuration of devices that includes (1) a source of some unknown bipartite quantum state that is claimed to be the Bell state Φ+\Phi^+Φ+ and (2) two spatially separated but otherwise unknown measurement apparatus, one on each side, that are each claimed to execute an orthogonal measurement at an angle θ∈{−π/8,0,π/8}\theta \in \{-\pi/8, 0, \pi/8\}θ∈{−π/8,0,π/8} that is chosen by the user. We show that, if the nine distinct probability distributions that are generated by the self checking configuration, one for each pair of angles, are consistent with the specifications, the source and the two measurement apparatus are guaranteed to be identical to the claimed specifications up to a local change of basis on each side. We discuss the connection with quantum cryptography. testing quantum apparatus (pp273-286) D. Mayers and A. Yao We study, in the context of quantum information and quantum communication, a configuration of devices that includes (1) a source of some unknown bipartite quantum state that is claimed to be the Bell state Φ+\Phi^+Φ+ and (2) two spatially separated but otherwise unknown measurement apparatus, one on each side, that are each claimed to execute an orthogonal measurement at an angle θ∈{−π/8,0,π/8}\theta \in \{-\pi/8, 0, \pi/8\}θ∈{−π/8,0,π/8} that is chosen by the user. We show that, if the nine distinct probability distributions that are generated by the self checking configuration, one for each pair of angles, are consistent with the specifications, the source and the two measurement apparatus are guaranteed to be identical to the claimed specifications up to a local change of basis on each side. We discuss the connection with quantum cryptography.
Summary form only given. In a Bell experiment, one prepares pairs of entangled particles and sends them to two observers, Alice and Bob, for measurement and detection [1]. For some choices of their measurement settings, Alice and Bob may observe strong correlations between their results in accordance with the predictions of quantum mechanical theory. Conversely, any physical theory that assumes no physical influence can be faster than the speed of light and that properties of physical systems are elements of reality [2] - a local realistic theory - can predict only a limited amount of correlation between Alice's and Bob's measurement outcomes. Upon observing correlations sufficient to violate Bell's inequality, Alice and Bob must abandon local realism.It is common that in an experiment, some particles emitted by the source will not be detected. Then the subset of detected particles might display correlations that violate the Bell inequality although the entire ensemble can be described by a local realistic theory [3]. To achieve a conclusive Bell violation without assuming that the detected particles are a “fair” sample, a highly efficient setup is necessary. Due to experimental limitations, fair sampling has been assumed in most Bell experiments performed to date, and it has never been possible to avoid this assumption with photons due to the absence of efficient sources and detectors. Here we report the first Bell experiment with photons that does not rely on any fair-sampling assumption. In our experiment we employ the Eberhard inequality, a Bell inequality that by construction does not rely on the fair-sampling assumption [4]. Our source of entangled photon pairs utilizes bulk-crystal spontaneous parametric downconversion in a Sagnac configuration, which has shown to be very efficient [5, 6]. For photon detection, we employ superconducting transition-edge sensors, which not only offer high efficiency but also are intrinsically free of dark counts [7]. This combination of features is imperative for an experiment in which no correction of count rates can be tolerated. We achieve uncorrected coupling efficiencies over 73% in each arm of our source, facilitating a violation of the inequality by nearly 70 standard deviations after five minutes of measurement. Since the first experimental Bell test, a satisfactory laboratory realization of the motivating gedankenexperiment has remained an outstanding challenge. The two other main assumptions include “locality” [8, 9] and “freedom of choice” [10]. Invoking any of these renders an experiment vulnerable to explanation by a local realistic theory. The realization of an experiment that is free of all three assumptions-a so-called loopholefree Bell test-remains an important outstanding goal for the physics community with strong implications for quantum technologies. We note that with our experiment, photons are the first physical system for which each of these three assumptions has been successfully addressed, albeit in different experiments. This represents promise for practical applications like one-sided device-independent quantum key distribution [11], and in an additional test, we also demonstrate that our experimental apparatus is capable of implementing this protocol on both sides.
We present a source of entangled photons that violates a Bell inequality free of the "fair-sampling" assumption, by over 7 standard deviations. This violation is the first reported experiment with photons to close the detection loophole, and we demonstrate enough "efficiency" overhead to eventually perform a fully loophole-free test of local realism. The entanglement quality is verified by maximally violating additional Bell tests, testing the upper limit of quantum correlations. Finally, we use the source to generate "device-independent" private quantum random numbers at rates over 4 orders of magnitude beyond previous experiments.
The concept of nonlocality, whereby a local operation on one state can instantaneously affect the properties of another spatially-separated state, has been investigated through the violation of Bell inequalities. Realisations of such violations in the laboratory paved the way for not only experimental justification of quantum theory, but also one of the subject's first significant applications in cryptography. The violation of Bell inequalities can be used as an indicator for security in the task of key distribution. Furthermore, it has more recently been shown that such security is guaranteed by the violations alone, regardless of assumptions about the workings and trustworthiness of the devices provided for the task. We provide a brief history of Bell inequalities and their use in the development of device-independent key distribution, which is less reliant on the validity of quantum theory than previously thought.