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Scott Aaronson | On the Hardness of Detecting Macroscopic Superpositions

Abstract: When is decoherence "effectively irreversible"? We examine this question of quantum foundations using the tools of quantum computational complexity. We prove that, if one had a quantum circuit to determine if a system was in an equal superposition of two orthogonal states (for example, the |Alive⟩ and |Dead⟩ states of Schrödinger's cat), then with only a slightly larger circuit, one could also swap the two states (e.g., bring a dead cat back to life). In other words, observing interference between the |Alive⟩ and |Dead⟩ states is a "necromancy-hard" problem, technologically infeasible in any world where death is permanent. We also prove several related results, and we show that our results are quantitatively tight. Given the subject of the workshop, I'll also discuss some potential implications for how one should think about the Everett interpretation. See https://arxiv.org/abs/2009.07450. About the speaker: Scott Aaronson is David J. Bruton Jr. Centennial Professor of Computer Science at the University of Texas at Austin. He is well known for his research into quantum computation and computational complexity theory, as well as for his blog, Shtetl-Optimised.