The No-go Theorem of Purification
AI Breakdown
Get a structured breakdown of this paper — what it's about, the core idea, and key takeaways for the field.
Abstract
The Shannon's bound for compression is believed to be one of the key restrictions for compression of quantum information. Here we show that the unitarity of the compression operation imposes significant restrictions on the compression of the entropy of quantum states that are more limiting than the Shannon's compression bound. This translates to a no-go theorem for purification of quantum states. For a specific case of two-qubit system, our results indicates that it is not possible to distil purity beyond the initial purity of the two qubits. We also show that this no-go theorem results in the cooling limit of the heat-bath algorithmic cooling techniques.