The induction of NMDA receptor-dependent long-term potentiation (LTP) in chemical synapses in the brain occurs via a fairly straightforward mechanism.
[1][2] A substantial and rapid rise in calcium ion concentration inside the postsynaptic cell (or more specifically, within the dendritic spine) is most possibly all that is required to induce LTP.
The AMPAR, upon binding two glutamate molecules, undergoes a conformational change that resembles the opening of a clam shell.
The lifetime of the glutamate in the synaptic cleft is too short to allow more than a brief opening of the AMPAR channel, thus causing only a small depolarization.
The NMDA receptor (NMDAR) does not, in resting or near-resting membrane potential conditions, contribute significant current to the EPSP.
What makes this magnesium blockade of the NMDAR channel particularly significant in terms of LTP induction is that the block is membrane voltage-dependent.
However, when the cell is more hyperpolarized, the bound state of magnesium is stabilized and it leaves the channel less often and for a shorter period of time (on average).
More strictly speaking, inward cationic current (sodium or calcium) through the open unblocked NMDAR does decrease with depolarization (because of the decreased electrochemical "driving force"), but the voltage-dependent unblocking seems to outweigh this decrease in driving force, so the calcium influx into the spine caused by a pair of appropriately timed pre- and postsynaptic spikes significantly exceeds the sum of the influxes due to the individual spikes alone.