Key Rate Available from Mismatched Measurements in the BB84 Protocol and the Uncertainty Principle

Ryutaroh Matsumoto, Shun Watanabe

Ryutaroh Matsumoto, Shun Watanabe

We consider the mismatched measurements in the BB84 quantum key distribution protocol, in which measuring bases are different from transmitting bases. We give a lower bound on the amount of a secret key that can be extracted from the mismatched measurements. Our lower bound shows that we can extract a secret key from the mismatched measurements with certain quantum channels, such as the channel over which the Hadamard matrix is applied to each qubit with high probability. Moreover, the entropic uncertainty principle implies that one cannot extract the secret key from both matched measurements and mismatched ones simultaneously, when we use the standard information reconciliation and privacy amplification procedure.

Kern, Oliver, Renes, Joseph M.

隆太郎 松本, Ryutaroh Matsumoto

Mohammed Th. Hassan, Omar Abouelazm

In this paper, we introduce a novel modification to the BB84 Quantum Key Distribution (QKD) protocol, aimed at enhancing its efficiency through the use of quantum memory and delayed measurement. In the standard BB84 protocol, the receiver immediately measures the qubits sent by the sender using randomly chosen bases. Due to mismatches between the sender and receiver's bases, a significant portion of the qubits are discarded, reducing the overall key generation rate. Our proposed protocol allows the receiver to store the received qubits in quantum memory and defer measurement until after the sender reveals her basis choices, effectively eliminating the need to discard mismatched qubits. This modification improves the key generation efficiency while maintaining the core security features of the standard BB84 protocol. By avoiding the unnecessary loss of qubits, our protocol achieves a higher secret key rate without introducing additional vulnerabilities. We present a detailed step-by-step explanation of the delayed measurement process. Although this approach does not alter the security guarantees of BB84, it represents a significant improvement in efficiency, making the protocol more viable for large-scale quantum communication networks.

峻 渡辺, Shun N. Watanabe, 隆太郎 松本 +3 more