What happens to qubits if Swap Test fails?

[Dragonfall]

A swap-test is described here http://en.wikipedia.org/wiki/Quantu..._the_same_for_every_recipient_.28Swap_Test.29

Now if the target qubits are identical, then after the swap test they are not disturbed. But what happens to them if they weren't identical? What do they become after the test?

 

[Dragonfall]

Suppose the target qubits were |A> and |B>, and they are not equal. After the swap test do they both become the mixed state:

$$0.5\left| A\right>\left< A\right| + 0.5\left| B\right>\left< B\right|$$

??

 

[denian]

If the Swap Test fails, it means that the target qubits were not identical and did not pass the test. This could be due to errors in the qubits or external interference. As a result, the qubits will not be in the same state as they were before the test. They may have been disturbed or changed in some way, which could affect the overall outcome of the quantum digital signature.

In the context of quantum digital signature, this could potentially lead to a compromised public key, as the qubits are no longer identical and may not produce the expected results. This could make the signature vulnerable to attacks and compromise the security of the system.

In general, when a quantum system fails a test, it means that the state of the system has been altered in some way. This highlights the importance of maintaining the integrity and stability of qubits in quantum systems, as any external interference or errors can have significant consequences.

Further analysis and investigation would be needed to determine the exact state of the qubits after a failed Swap Test and how it may impact the overall system. This highlights the need for continual testing and monitoring of quantum systems to ensure their reliability and security.