The Woman's Curse
3:16 To the woman He said, 'I will greatly increase your anguish and your pregnancy. It will be with anguish that you will give birth to children. Your passion will be to your husband, and he will dominate you.'
3:17 To Adam He said, 'You listened to your wife, and ate
from the tree regarding which I specifically gave you orders, saying,
'Do not eat from it.' The ground will therefore be cursed because of
you. You will derive food from it with anguish all the days of your
3:18 It will bring forth thorns and thistles for you, and you
will eat the grass of the field.
3:19 By the sweat of your brow you
will eat bread. Finally you will return to the ground, for it was from
[the ground] that you were taken. You are dust, and to dust you shall
— Kaplan's Translation, Genesis 3
Notice the last curse: "Finally you will return to the ground, …. You are dust, and to dust you shall return".
This is clearly describing a physical death.
This is stated as a consequence of their sin, which implies that had they not sinned, they would not return to dust. I.e. they would not have been subject to death, or at least would have had the potential to live forever.
Because of their sin, Adam and Eve were physically changed, as indirectly were all their descendants.
People were given a limited physical life span (though still much longer then than now), and as a result each of us will eventually experience a physical death and turn back into dust.
Since we, individually, did not exist then, it is perhaps not appropriate to think of this as a punishment on us for their sin. We are born with a limited life expectancy, so a short life is not something explicitly added to us personally, it is simply how we are created, what we are, and what we know to expect.
And certainly there is no implication, even if we are affected by their punishment, that we share any of the guilt or responsibility for their sin. (E.g. Catholic "original sin".)