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Modern Physics Letters A

Amplitude damping error on QKD: Effect and a probable bypass

Munsi Afif Aziz, Bishwajit Prasad Gond, Srijita Nandi, Soujanya Ray, Debasmita Bhoumik, Ritajit Majumdar

Published Apr 10, 2023• 3 citations
Publisher

Abstract

Quantum cryptography was proposed as a counter to the capacity of quantum computers to break classical cryptosystems. A broad subclass of quantum cryptography, called quantum key distribution (QKD), relies on quantum mechanical process for secure distribution of the keys. Quantum channels are inherently noisy, and therefore these protocols will be susceptible to noise as well. In this paper, we study the performance of two QKD protocols — BB84 and E91 under amplitude damping error. We show that while E91 protocol loses its security immediately due to loss of entanglement, the performance of BB84 protocol reduces to random guessing with increasing time. Next, we consider the action of an Eve on the BB84 protocol under amplitude damping noise, who is restricted to guessing the outcome of the protocol only. Under this restriction, we show that Eve can still do better than random guessing when equipped with the characteristics of the noisy channel. Finally, we propose a modification of the BB84 protocol which retains the security of the original protocol, but ensures that Eve cannot get any advantage in guessing the outcome, even with complete channel information.

DOI
10.1142/s021773232350058x

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IEEE International Conference on Information Theory and Information Security•Dec 1, 2010•1 citation
Quantum cryptography was proposed as a counter to the capacity of quantum computers to break classical cryptosystems. A broad subclass of quantum cryptography, called quantum key distribution (QKD), relies on quantum mechanical process for secure distribution of the keys. Quantum channels are inherently noisy, and therefore these protocols will be susceptible to noise as well. In this paper, we study the performance of two QKD protocols — BB84 and E91 under amplitude damping error. We show that while E91 protocol loses its security immediately due to loss of entanglement, the performance of BB84 protocol reduces to random guessing with increasing time. Next, we consider the action of an Eve on the BB84 protocol under amplitude damping noise, who is restricted to guessing the outcome of the protocol only. Under this restriction, we show that Eve can still do better than random guessing when equipped with the characteristics of the noisy channel. Finally, we propose a modification of the BB84 protocol which retains the security of the original protocol, but ensures that Eve cannot get any advantage in guessing the outcome, even with complete channel information.
Error mitigation is one of the key challenges in realising the full potential of quantum cryptographic protocols. Consequently, there is a lot of interest in adapting techniques from quantum error correction (QEC) to improve the robustness of quantum cryptographic protocols. In this work, we benchmark the performance of different QKD protocols on noisy quantum devices, with and without error correction. We obtain the secure key rates of BB84, B92 and BBM92 QKD protocols over a quantum channel that is subject to amplitude-damping noise. We demonstrate, theoretically and via implementations on the IBM quantum processors, that B92 is the optimal protocol under amplitude-damping and generalized amplitude-damping noise. We then show that the security of the noisy BBM92 protocol crucially depends on the type and the mode of distribution of an entangled pair. Finally, we implement an error-corrected BB84 protocol using dual-rail encoding on a noisy quantum processor, and show that the dual-rail BB84 implementation outperforms the conventional BB84 in the presence of noise. Our secure key rate calculation also takes into account the effects of CNOT imperfections on the error rates of the protocols.
Quantum cryptography is anticipated to drive substantial advancements in cybersecurity. The impending arrival of quantum cryptography compromises current encryption methods, possibly compromising the effectiveness of traditional key management-based security protocols. One fundamental Quantum Key Distribution (QKD) protocol, BB84, encounters challenges when operating with fewer Quantum bits (Qubits) and bases that only support up to 8 Qubits. This limitation weakens the system’s security, making brute force, intercept, and resend attacks less challenging. Consequently, this study proposes a method to enhance the security of the BB84 protocol, to reduce susceptibility to attacks and eavesdropping. The improved BB84 protocol utilizes 9, 12, and 16 quantum bits along with two, and three bases to significantly bolster security. This allows authorized parties to eliminate the use of compromised keys. Additionally, the study implements the E91 QKD protocol utilizing the Entanglement Pair Generation (EPR) method to produce secure keys. While the existing E91 protocol ensures security through Bell’s theorem and Bell’s inequality, it overlooks the impact of noise, leading to inaccuracies in eavesdropper detection. To address this, the study introduces an additional security measure. Whenever an eavesdropper attempts to measure the quantum state, the proposed E91 protocol collapses its state from$\vert 10\rangle tototo\vert 11\rangle ,settingthefirstQubitto, setting the first Qubit to,settingthefirstQubitto\vert 1\rangle andtheotherQubittoand the other Qubit toandtheotherQubitto\vert 0\rangle $, thus providing the eavesdropper with incorrect information, accompanied by a phase angle of$15\pi $/8. This leads to a misconception, preventing eavesdroppers from obtaining useful details about transferred quantum states. Additionally, considering that the proposed E91 protocol relies on entangled particles and utilizes double Qubit gates, which are inherently noisier than single Qubit gates and more susceptible to quantum decoherence, this study employs error mitigation techniques during the final measurement to predict outcomes more efficiently.
Practical quantum key distribution (QKD) systems operate under noise, but security of most protocols have been analyzed under ideal noiseless scenarios. In this work, we investigated security performance of BB84 protocol under effect of collective rotation noise. Using theoretical quantum information frameworks, we analyzed key security parameters including quantum bit error rate (QBER), mutual information and secret key rate (SKR). Security of protocol is studied under various eavesdropping scenarios based on intercept and resend attacks. Our results show that collective rotation noise has a significant impact on the information shared between the two parties. Particularly, we extended prior treatments by suggesting a noise engineering strategy where we identified a non-zero noise range where information accessed by Eve is minimized while corresponding SKR degradation remains relatively small. This analysis provide insights into robustness of BB84 protocol under realistic noisy channels and may contribute towards development of more resilient QKD systems.
Quantum Key Distribution is theoretically possible secure communication through the use of quantum-mechanical principles, such as superposition, measurement disturbance, and others. The BB84 and E91 protocols provide security by leveraging quantum principles against classical eavesdropping; nevertheless, the current implementation of QKD is vulnerable to photon-number-splitting attacks, imperfections in the devices used, and environmental quantum noise. Improving practical resistance to all of those is crucial for providing secure real-life use of QKD. Extending the current state-of-the-art through further development of research on eavesdropper detection and improvement of qubit-based security mechanisms, this research aims to develop the state-of-the art further by introducing a decoy-state BB84 framework and analyzing the behavior of such a system under realistic quantum noise. To find solutions to these problems, the current research will try to adopt the decoy-state BB84 model and analyze the system behavior under realistic quantum noise scenarios. So, the proposed approach, a standard BB84 protocol, will first be formulated and then further enhanced with decoy-state pulse generation to handle the vulnerabilities due to multi-photon pulses. Models like depolarizing noise, amplitude damping, and measurement errors will be used as real-world quantum channels. The model performance will be measured in terms of various performance metrics such as Key agreement ratio, Quantum Bit Error rate, and secure key rate for different qubit lengths. Scalability analysis and validation based on IBM quantum hardware will also be performed in order to measure the impact of real-world device noise on the reliability of generated keys.
Quantum cryptography, or, more precisely, quantum key distribution (QKD) allows two distant parties, Alice and Bob, to expand a previously shared secret key by sending quantum states through a quantum channel. The goal here is for Alice and Bob to communicate securely in the presence of an eavesdropper, Eve. The most well-known QKD protocol is the Bennett-Brassard 1984 (BB84) protocol, which has been proved unconditionally secure against any attacks allowed by quantum mechanics. The main advantage of QKD over conventional cryptography is its absolute security. Thus, it is imperative to evaluate the security and performance of QKD protocols and realistic QKD systems. In this thesis, we study the security and performance aspects of QKD in four parts. In the first part, we study the Scarani-Acin-Ribordy-Gisin 2004 (SARG04) protocol. This protocol differs from the BB84 protocol only in the classical post-processing step and uses the same four quantum states as the BB84 protocol. We compared these two protocols and showed that in typical situations, the classical post-processing software for BB84 should be used in order to have a higher performance. In the second part, we prove the security of a three-state protocol. This protocol is similar to the BB84 protocol in that they share the same three qubit states. In the third part, we consider a practical Trojan horse attack on practical QKD systems implementing the BB84 protocol. The attack works by taking advantage of the finite response time of practical phase modulators to remap the states sent out by the legitimate user, Alice. We showed that if Alice and Bob are unaware of our attack, the final key shared between them can be compromised in some situations. In the fourth part, we consider another type of Trojan horse attack, which is based on mismatch between detection efficiencies of detectors. Practical detectors in QKD systems usually do not have identical efficiencies and an eavesdropper Eve may be able to exploit this efficiency mismatch to steal information about the final secret key. We analyze the security of the attack and show that it is possible for Eve to acquire some information on the final secret key if Alice and Bob are unaware of this attack.