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Entanglement purification with noisy apparatus can be used to factor out an eavesdropper

Aschauer, H, Briegel, H J

Published Aug 13, 2001• 1 citation
OpenAlex

Abstract

We give a proof that entanglement purification, even with noisy apparatus, is sufficient to disentangle an eavesdropper (Eve) from the communication channel. Our proof applies to all possible attacks (individual and coherent). Due to the quantum nature of the entanglement purification protocol, it is also possible to use the obtained quantum channel for secure transmission of quantum information.

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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 $ω$ 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 $1-ε_{qu}^δ$. 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.

arXiv:2306.10455•Jun 18, 2023•0 citations
We give a proof that entanglement purification, even with noisy apparatus, is sufficient to disentangle an eavesdropper (Eve) from the communication channel. Our proof applies to all possible attacks (individual and coherent). Due to the quantum nature of the entanglement purification protocol, it is also possible to use the obtained quantum channel for secure transmission of quantum information.
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.
In this thesis, we investigate how protocols in quantum communication theory are influenced by noise. Specifically, we take into account noise during the transmission of quantum information and noise during the processing of quantum information. We describe three novel quantum communication protocols which can be accomplished efficiently in a noisy environment: (1) Factorization of Eve: We show that it is possible to disentangle transmitted qubits a posteriori from the quantum channel's degrees of freedom. (2) Cluster state purification: We give multi-partite entanglement purification protocols for a large class of entangled quantum states. (3) Entanglement purification protocols from quantum codes: We describe a constructive method to create bipartite entanglement purification protocols form quantum error correcting codes, and investigate the properties of these protocols, which can be operated in two different modes, which are related to quantum communication and quantum computation protocols, respectively.
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.