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On the Hardness of Disentanglers and Quantum de Finetti Theorems

Entanglement has a dual role in quantum computation and information. It is an important resource in protocols such as quantum teleportation and superdense coding. On the other hand, it can potentially reduce the soundness in quantum Multi-prover Merlin-Arthur proof systems. Thus, understanding and controlling entanglement is of primary importance. To achieve this goal a super-operator capable of breaking entanglement, called a disentangler, has been proposed, together with a variety of quantum de Finetti Theorems. In this work, we study some limits of these approaches using computational hardness notions. We rule out the existence of some disentanglers and de Finetti Theorems based on some plausible hardness assumptions.