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Unfortunately one cannot (faithfuly) simulate a (fair) die using (sequences of) fair coin(s).

Simply because the die has a dimensiolity of $6$ and this cannot be a power of $2$ (which is what a fair coin provides).

But one can do this with a fair "tri-coin" (if such a term can be used). Meaning a coin with 3 outcomes. And a simple 2-coin, so the joint space of these 2 coins matches the event space of the die.

Rejection sampling (as mentioned in some answers) may provide an approximate simulation indeed. But it will still have an amount of error or mis-match of probabilities. So if one wants to actually match the event spaces of these 2 systems, it does not work.

In fact rejection sampling may take arbitrarily long to get an outcome in range (since sequences can be arbitrarily long with a specific outcome), so the statement about practicality is not rigorously correct.

Unfortunately one cannot (faithfuly) simulate a (fair) die using (sequences of) fair coin(s).

Simply because the event space of a die has a dimensionality of $6$ and this cannot be exactly matched by a power of $2$ (which is what the event space of a fair coin provides).

But one can do this with a fair "tri-coin" (if such a term can be used). Meaning a coin with 3 outcomes. And a simple 2-coin, so the joint space of these 2 coins matches exactly the event space of the die.

Rejection sampling (as mentioned in some answers) may provide an approximate simulation indeed. But it will still have an amount of error or mis-match of probabilities (in finite time). So if one wants to actually match the event spaces of these 2 systems, there will be cases it will not work.

In probabilistic simulation (of which rejection sampling is an example), generated typical sequences do indeed exhibit the relative elementary probabilities (in this case the event space of a die). However (as mentioned in comments) each of these typical sequences can contain arbitrarily long sub-sequences of exactly the same outcomes. This means that in order to use rejection sampling (in some cases) either it can take arbitrarily long or the generated distribution will be biased (i.e not fair die), due to over-representation or under-representation of some parts of its event space. if this was not the case, then a deterministic algorithm would be possible which would exactly match the event spaces of a die and a coin (which do not match by dimensionality).

Unfortunately one cannot (faithfuly) simulate a (fair) die using (sequences of) fair coin(s).

Simply because the die has a dimensiolity of $6$ and this cannot be a power of $2$ (which is what a fair coin provides).

But one can do this with a fair "tri-coin" (if such a term can be used). Meaning a coin with 3 outcomes.

Rejection sampling (as mentioned in some answers) may provide an approximate simulation indeed. But it will still have an amount of error or mis-match of probabilities. So if one wants to actually match the event spaces of these 2 systems, it does not work.

Unfortunately one cannot (faithfuly) simulate a (fair) die using (sequences of) fair coin(s).

Simply because the die has a dimensiolity of $6$ and this cannot be a power of $2$ (which is what a fair coin provides).

But one can do this with a fair "tri-coin" (if such a term can be used). Meaning a coin with 3 outcomes. And a simple 2-coin, so the joint space of these 2 coins matches the event space of the die.

Rejection sampling (as mentioned in some answers) may provide an approximate simulation indeed. But it will still have an amount of error or mis-match of probabilities. So if one wants to actually match the event spaces of these 2 systems, it does not work.

In fact rejection sampling may take arbitrarily long to get an outcome in range (since sequences can be arbitrarily long with a specific outcome), so the statement about practicality is not rigorously correct.

Unfortunately one cannot (faithfuly) simulate a (fair) die using (sequences of) fair coin(s).

Simply because the die has a dimensiolity of $6$ and this cannot be a power of $2$ (which is what a fair coin provides).

But one can do this with a fair "tri-coin" (if such a term can be used). Meaning a coin with 3 outcomes.

Rejection sampling (as mentioned in some answers) may provide an approximate simulation indeed. But it will still have an amount of error or mis-match of probabilities. So if one wants to actually match the event spaces of these 2 systems, it does not work.

Unfortunately one cannot (faithfuly) simulate a (fair) die using (sequences of) fair coin(s).

Simply because the die has a dimensiolity of $6$ and this cannot be a power of $2$ (which is what a fair coin provides).

But one can do this with a fair "tri-coin" (if such a term can be used). Meaning a coin with 3 outcomes.

Rejection sampling (as mentioned in some answers) may provide an approximate simulation indeed. But it will still have an amount of error or mis-match of probabilities. So if one wants to actually match the event spaces of these 2 systems, it does not work.