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08 SECURITY PROOF OF QUANTUM KEY DISTRIBUTION WITH DETECTION EFFICIENCY MISMATCH

Chi‐Hang Fred Fung, Kiyoshi Tamaki, Bing Qi, Hoi-kwong Lo, Xiongfeng Ma

Published Aug 16, 2016• 66 citations
OpenAlex

Abstract

In theory, quantum key distribution (QKD) offers unconditional security based on the laws of physics. However, as demonstrated in recent quantum hacking theory and experimental papers, detection efficiency loophole can be fatal to the security of practical QKD systems. Here, we describe the physical origin of detection efficiency mismatch in various domains including spatial, spectral, and time domains and in various experimental set-ups. More importantly, we prove the unconditional security of QKD even with detection efficiency mismatch. We explicitly show how the key generation rate is characterized by the maximal detection efficiency ratio between the two detectors. Furthermore, we prove that by randomly switching the bit assignments of the detectors, the effect of detection efficiency mismatch can be completely eliminated.

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Security proof of quantum key distribution with detection efficiency mismatch

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In theory, quantum key distribution (QKD) offers unconditional security based on the laws of physics. However, as demonstrated in recent quantum hacking theory and experimental papers, detection efficiency loophole can be fatal to the security of practical QKD systems. Here, we describe the physical origin of detection efficiency mismatch in various domains including spatial, spectral, and time domains and in various experimental set-ups. More importantly, we prove the unconditional security of QKD even with detection efficiency mismatch. We explicitly show how the key generation rate is characterized by the maximal detection efficiency ratio between the two detectors. Furthermore, we prove that by randomly switching the bit assignments of the detectors, the effect of detection efficiency mismatch can be completely eliminated.

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The rules of quantum mechanics makes it possible to exchange a secret key at a distance. This is called quantum key distribution (QKD). In theory the key exchange can be made completely secure. Real QKD implementations however, has numerous imperfections. Luckily one has also been able to prove the security of QKD with a large variety of imperfections. The field of QKD has matured over the recent years, and it has now reached commercial applications with photons as the quantum bits, and optical fibers as the quantum channel. Today there are at least three commercial vendors of QKD-systems. We live in the times of quantum hacking. Researchers has begun the task of breaking the security of QKD-systems. Many new imperfections has been discovered, some of which might be used to break the security of QKD. This thesis is a study of the detector efficiency mismatch loophole. Most QKD-systems require two detectors, and it is virtually impossible to make two identical detectors with the exact same efficiency. What is worse, it turns out that the eavesdropper can often control the relative efficiencies of the two detectors trough some domain, for instance by controlling the timing, the frequency or the spacial mode of the photons. This can in turn be used by the eavesdropper to gain information about the secret key. Previously the best known attack would compromise security if the detector efficiency mismatch of about 1:15. Here the current attacks on systems with detector efficiency mismatch are improved to compromise security for a mismatch of about 1:4. This is less than the mismatch found in a commercial QKD-system, so the attack could in principle be used to eavesdrop on this QKD-system. One might try to close the loophole by modifying the implementation. One suggestion is the four state Bob. The problem is that this patch will in turn open other loopholes, and one of these loopholes reopen the detector efficiency mismatch loophole. One can remove Eves information about the key by doing a sufficient amount of extra privacy amplification. Here a general security bound is presented, quantifying the required amount of extra privacy amplification to remove Eve's information about the key. The proof is more general than the previous security proof, and is valid for any basis dependent, possibly lossy, linear optical imperfections in the channel and receiver/detectors. Since this is more realistic assumptions for a QKD-implementation, the proof represents a major step of closing the loophole in real devices.

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In theory, quantum key distribution (QKD) offers unconditional security based on the laws of physics. However, as demonstrated in recent quantum hacking theory and experimental papers, detection efficiency loophole can be fatal to the security of practical QKD systems. Here, we describe the physical origin of detection efficiency mismatch in various domains including spatial, spectral, and time domains and in various experimental set-ups. More importantly, we prove the unconditional security of QKD even with detection efficiency mismatch. We explicitly show how the key generation rate is characterized by the maximal detection efficiency ratio between the two detectors. Furthermore, we prove that by randomly switching the bit assignments of the detectors, the effect of detection efficiency mismatch can be completely eliminated.
In theory, quantum key distribution (QKD) offers unconditional security based on the laws of physics. However, as demonstrated in recent quantum hacking theory and experimental papers, detection efficiency loophole can be fatal to the security of practical QKD systems. Here, we describe the physical origin of detection efficiency mismatch in various domains including spatial, spectral, and time domains and in various experimental set-ups. More importantly, we prove the unconditional security of QKD even with detection efficiency mismatch. We explicitly show how the key generation rate is characterized by the maximal detection efficiency ratio between the two detectors. Furthermore, we prove that by randomly switching the bit assignments of the detectors, the effect of detection efficiency mismatch can be completely eliminated.
In theory, quantum key distribution (QKD) offers unconditional security based on the laws of physics. However, as demonstrated in recent quantum hacking theory and experimental papers, detection efficiency loophole can be fatal to the security of practical QKD systems. Here, we describe the physical origin of detection efficiency mismatch in various domains including spatial, spectral, and time domains and in various experimental set-ups. More importantly, we prove the unconditional security of QKD even with detection efficiency mismatch. We explicitly show how the key generation rate is characterized by the maximal detection efficiency ratio between the two detectors. Furthermore, we prove that by randomly switching the bit assignments of the detectors, the effect of detection efficiency mismatch can be completely eliminated.
Quantum key distribution (QKD) protocols with threshold detectors are driving high-performance QKD demonstrations.The corresponding security proofs usually assume that all physical detectors have the same detection efficiency.However, the efficiencies of the detectors used in practice might show a mismatch depending on the manufacturing and setup of these detectors.A mismatch can also be induced as the different spatialtemporal modes of an incoming signal might couple differently to a detector.Here we develop a method that allows to provide security proofs without the usual assumption.Our method can take the detection-efficiency mismatch into account without having to restrict the attack strategy of the adversary.Especially, we do not rely on any photon-number cutoff of incoming signals such that our security proof is directly applicable to practical situations.We illustrate our method for a receiver that is designed for polarization encoding and is sensitive to a number of spatial-temporal modes.In our detector model, the absence of quantum interference between any pair of spatial-temporal modes is assumed.For a QKD protocol with this detector model, we can perform a security proof with characterized efficiency mismatch and without photon-number cutoff assumption.Our method also shows that in the absence of efficiency mismatch in our detector model, the key rate increases if the loss due to detection inefficiency is assumed to be outside of the adversary's control, as compared to the view where for a security proof this loss is attributed to the action of the adversary.
The rules of quantum mechanics makes it possible to exchange a secret key at a distance. This is called quantum key distribution (QKD). In theory the key exchange can be made completely secure. Real QKD implementations however, has numerous imperfections. Luckily one has also been able to prove the security of QKD with a large variety of imperfections. The field of QKD has matured over the recent years, and it has now reached commercial applications with photons as the quantum bits, and optical fibers as the quantum channel. Today there are at least three commercial vendors of QKD-systems. We live in the times of quantum hacking. Researchers has begun the task of breaking the security of QKD-systems. Many new imperfections has been discovered, some of which might be used to break the security of QKD. This thesis is a study of the detector efficiency mismatch loophole. Most QKD-systems require two detectors, and it is virtually impossible to make two identical detectors with the exact same efficiency. What is worse, it turns out that the eavesdropper can often control the relative efficiencies of the two detectors trough some domain, for instance by controlling the timing, the frequency or the spacial mode of the photons. This can in turn be used by the eavesdropper to gain information about the secret key. Previously the best known attack would compromise security if the detector efficiency mismatch of about 1:15. Here the current attacks on systems with detector efficiency mismatch are improved to compromise security for a mismatch of about 1:4. This is less than the mismatch found in a commercial QKD-system, so the attack could in principle be used to eavesdrop on this QKD-system. One might try to close the loophole by modifying the implementation. One suggestion is the four state Bob. The problem is that this patch will in turn open other loopholes, and one of these loopholes reopen the detector efficiency mismatch loophole. One can remove Eves information about the key by doing a sufficient amount of extra privacy amplification. Here a general security bound is presented, quantifying the required amount of extra privacy amplification to remove Eve's information about the key. The proof is more general than the previous security proof, and is valid for any basis dependent, possibly lossy, linear optical imperfections in the channel and receiver/detectors. Since this is more realistic assumptions for a QKD-implementation, the proof represents a major step of closing the loophole in real devices.
Quantum key distribution (QKD) is poised to be the first widespread implementation of quantum communication. In principle, it offers unconditional security: an eavesdropper introduces errors and thus cannot remain concealed from the legitimate parties. However, in practical implementations the actual security depends on a host of technological and protocol-operational components. We propose and experimentally demonstrate a hack to induce a large and deterministic temporal efficiency mismatch between the two detectors of Clavis2, a commercial QKD system from ID Quantique.
Detection-efficiency mismatch is a common problem in practical quantum key distribution (QKD) systems. Current security proofs of QKD with detection-efficiency mismatch rely either on the assumption of the single-photon light source on the sender side or on the assumption of the single-photon input of the receiver side. These assumptions impose restrictions on the class of possible eavesdropping strategies. Here we present a rigorous security proof without these assumptions and, thus, solve this important problem and prove the security of QKD with detection-efficiency mismatch against general attacks (in the asymptotic regime). In particular, we adapt the decoy state method to the case of detection-efficiency mismatch.