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In some QKD phase-encoded schemes, a third party can perform a trojan-horse attack to observe the settings of Bob's phase modulator.

Does this compromise the established secret key in the BB84 protocol? Does it leak any information at all about the key?

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All trojan-horse attacks that I've heard about are useless against BB84 as long as some minimum mitigation is taken.

In a system where Alice produces the quantum states and sends them to Bob, these trojan-horse attacks allow an eavesdropper Eve to potentially determine the basis used to prepare or measure the quantum states.

For BB84, this attack is useless against Bob, because this basis is not secret anyway: Bob publishes the basis publicly immediately after the measurement.

The attack is potentially useful against Alice. However, it can be detected. The attack involves sending pulses of light to Alice and measuring the reflections. Since in BB84 Alice should not be receiving any signals, its fairly easy for Alice to detect these incoming pulses and abort the whole process.

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