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While studying the attack method of QKD, I found that intercept and resend attack is an example of an individual attack. What are the examples of collective attack and coherent attack? Specifically, what kind of attack is a Photon Number Splitting (PNS) attack?

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Different types of attacks can be explained by how Eve interacts with the quantum states Alice sends and how Eve processes the information she receives.

Individually, where the same unitary and the same POVM are applied to each state, collectively, where the same unitary is applied to each state but the measurement is given by a global POVM, or coherently, where a global ancilla system is attached to the tensor product of Alice’s states.

The photon number splitting attack (PNS) is an individual attack. It is applied on realistic photon sources emitting weak coherent pulses which generate single photons only with a certain probability. With a small probability, multi-photon pulses are emitted containing two or more photons having the same polarization. The strategy for Eve is to intercept these pulses coming from Alice, take one photon of the multi-photon pulse and send the remaining photon(s) along to Bob. Eve waits until Alice and Bob publicly compares their measurement bases and then measures the intercepted photon in the correct basis.

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