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arXiv:quant-ph/0111066 · Physical Review A

Security proof of quantum cryptography based entirely on entanglement purification

Hans Aschauer, Hans J. Briegel

Published Sep 4, 2002• 22 citations
arXivHTMLPDF

Abstract

We give a proof that entanglement purification, even with noisy apparatus, is sufficient to disentangle an eavesdropper (Eve) from the communication channel. In the security regime, the purification process factorizes the overall initial state into a tensor-product state of Alice and Bob, on one side, and Eve on the other side, thus establishing a completely private, albeit noisy, quantum communication channel between Alice and Bob. The security regime is found to coincide for all practical purposes with the purification regime of a two-way recurrence protocol. This makes two-way entanglement purification protocols, which constitute an important element in the quantum repeater, an efficient tool for secure long-distance quantum cryptography.

DOI
10.1103/physreva.66.032302

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We give a proof that entanglement purification, even with noisy apparatus, is sufficient to disentangle an eavesdropper (Eve) from the communication channel. In the security regime, the purification process factorizes the overall initial state into a tensor-product state of Alice and Bob, on one side, and Eve on the other side, thus establishing a completely private, albeit noisy, quantum communication channel between Alice and Bob. The security regime is found to coincide for all practical purposes with the purification regime of a two-way recurrence protocol. This makes two-way entanglement purification protocols, which constitute an important element in the quantum repeater, an efficient tool for secure long-distance quantum cryptography.
Complete security proofs for quantum communication protocols can be notoriously involved, which convolutes their verification, and obfuscates the key physical insights the security finally relies on. In such cases, for the majority of the community, the utility of such proofs may be restricted. Here, we provide a simple proof of confidentiality for parallel quantum channels established via entanglement distillation based on hashing, in the presence of noise, and a malicious eavesdropper who is restricted only by the laws of quantum mechanics. The direct contribution lies in improving the linear confidentiality levels of recurrence-type entanglement distillation protocols to exponential levels for hashing protocols. The proof directly exploits the security relevant physical properties: measurement-based quantum computation with resource states and the separation of Bell-pairs from an eavesdropper. The proof also holds for situations where Eve has full control over the input states, and obtains all information about the operations and noise applied by the parties. The resulting state after hashing is private, i.e. disentangled from the eavesdropper. Moreover, the noise regimes for entanglement distillation and confidentiality do not coincide: confidentiality can be guaranteed even in situations where entanglement distillation fails. We extend our results to multiparty situations which are of special interest for secure quantum networks.
Complete security proofs for quantum communication protocols can be notoriously involved, which convolutes their verification, and obfuscates the key physical insights the security finally relies on. In such cases, for the majority of the community, the utility of such proofs may be restricted. Here, we provide a simple proof of confidentiality for parallel quantum channels established via entanglement distillation based on hashing, in the presence of noise, and a malicious eavesdropper who is restricted only by the laws of quantum mechanics. The direct contribution lies in improving the linear confidentiality levels of recurrence-type entanglement distillation protocols to exponential levels for hashing protocols. The proof directly exploits the security relevant physical properties: measurement-based quantum computation with resource states and the separation of Bell-pairs from an eavesdropper. The proof also holds for situations where Eve has full control over the input states, and obtains all information about the operations and noise applied by the parties. The resulting state after hashing is private, i.e. disentangled from the eavesdropper. Moreover, the noise regimes for entanglement distillation and confidentiality do not coincide: confidentiality can be guaranteed even in situations where entanglement distillation fails. We extend our results to multiparty situations which are of special interest for secure quantum networks.
Entanglement purification protocols promise to play a critical role in the future of quantum networks by distributing entanglement across noisy channels. However, only the security of two-way purification protocols have been closely studied. To address this, we propose a one-way entanglement purification protocol which utilizes quantum sampling and prove its security against an adversary restricted to single qubit Pauli gates. This is done through leveraging the equivalence of one-way entanglement purification protocols with error-correcting codes. To prove the security of this protocol, we first use the quantum sampling framework introduced by Bouman and Fehr to estimate the Hamming weight of the qubits which passed through the channel and then use the estimated relative Hamming weight ωωω to determine the amount of interference that Eve has subjected to the quantum channel. Since Eve is restricted to single qubit Pauli gates, the number of applied gates can be directly estimated using the Hamming weight. Estimating the number of adversarial single qubit gates, allows us to perform error correction and disentangle the logical qubit from Eve with probability 1−εquδ1-ε_{qu}^δ1−εquδ​. Since this protocol allows communication only in one direction, the distance of the code must be decided before transmission, and therefore Bob will be forced to abort the protocol if he finds that Eve has applied more gates than the code can correct. One-way protocols may find use when communication is limited, or when we desire to decrease latency compared to the multiple rounds of communication needed in two-way protocols. Further research may investigate the security of this protocol against arbitrary single or multi-qubit gates to obtain security guarantees against a more general adversary.