1
$\begingroup$

Can a mixed state become pure due to its interaction with a vast environment? Certainly, a strange proposal, and yet let's take a diagonal matrix representing a mixed state, say $$\begin{pmatrix} p_{1} & \cdots & 0 \cr \vdots & \ddots & \vdots \cr 0 & \cdots & p_{n} \end{pmatrix}$$ And study its interaction with a large environment through the Lindblad equation. Let's set the system's Hamiltonian to zero for simplicity and take the Lindblad operators $L_{i}$ to be $\alpha\left|\psi_{k}\middle>\middle<\psi_{i}\right|$, allowing transitions to the k-th state to occur. Then the matrix would get closer and closer to a pure state matrix $diag(0,\cdots , 1,\cdots ,0)$ with a one on the k-th row.

Does this make any sense? Could this be implemented physically? And if so, what could the Hamiltonian of such an interaction look like? Ty!

$\endgroup$

1 Answer 1

1
$\begingroup$

A basic example of this is Amplitude Damping, where states decay into $|0\rangle$.

However, we would still consider this a type of decoherence, since regardless of the initial state, the final state is always the same so information about the input is being lost.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.