Entanglement/correlations in time

[WWCY]

From what I know about (bi-partite) entanglement, we write the combined Hilbert space as a tensor-product of Hilbert spaces for a particle at $A$ and a particle at $B$, ie $\mathcal{H} = \mathcal{H} ^{A} \otimes \mathcal{H} ^{B}$. If the particles share a non-separable state, they are considered to be "entangled".

Is it possible to do this in terms of a single particle but at two instances in time? So: $\mathcal{H} = \mathcal{H} ^{t_1} \otimes \mathcal{H} ^{t_2}$ for $t_1 < t_2$. If so, are there any published papers that expand on this idea?

Cheers.

 

[Heikki Tuuri]

If we have a free particle, then, obviously, its state at the time t_2 depends on the state at t_1. We may say that the states are entangled.

Can we completely erase the information in the particle after t_1? Then there would be no entanglement to the later state.

If we have two particles, they may be entangled before we prepare them to a quantum experiment. We assume that we can erase the entanglement, and we get two independent particles to the experiment.

The erasing is possible.