Computational Entanglement Theory
Quantum entanglement is an important resource that contributes to the potential of quantum computers over classical computers. It turns out to be an interesting idea to quantify entanglement in states, and there are different approaches to this. We can, for example, consider the number of Bell states that are required to approximately produce a given state or the number of Bell states that can be produced from the state - these correspond to the 'entanglement cost’ and ‘distillable entanglement' respectively. Throughout this, we bear in mind a picture where Alice (A) and Bob (B) own a shared state, and are only able to perform LOCC operations on their respective systems. In practice, however, computational complexity must be taken into account. I will explain some recent developments towards taking computational complexity into account for these operational measures, as well as introducing pseudo-entanglement, and hopefully some quantum cryptography.
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