We propose a new link between entropy and area: an eternal black hole with an ER bridge with cross-section A can carry quantum information, or be in a mixed state, with entropy S ≤ A/4GN . We provide evidence for our proposal in the context of AdS3 and JT gravity, by using the Island prescription and replica wormhole method for computing the Renyi entropy. We argue that a typical two sided black hole is described by a 'thermo-mixed double' state with only classical correlations between the two sides. Our reasoning suggests that an ER wormhole acts like a topological quantum memory, similar to the toric code.
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