I Entanglement/correlations in time

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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.
 
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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.
 

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