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2020

On the Hardness of Detecting Macroscopic Superpositions

Aaronson, Scott, Atia, Yosi, Susskind, Leonard

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When is decoherence "effectively irreversible"? Here we examine this central 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$\rangle$ and $|$Dead$\rangle$ states of Schr\"{o}dinger's cat), then with only a slightly larger circuit, one could also $\mathit{swap}$ the two states (e.g., bring a dead cat back to life).
In other words, observing interference between the $|$Alive$\rangle$and $|$Dead$\rangle$ states is a "necromancy-hard" problem, technologically infeasible in any world where death is permanent.
As for the converse statement (i.e., ability to swap implies ability to detect interference), we show that it holds modulo a single exception, involving unitaries that (for example) map $|$Alive$\rangle$ to $|$Dead$\rangle$ but $|$Dead$\rangle$ to -$|$Alive$\rangle$.

On the Hardness of Detecting Macroscopic Superpositions · Around

Built on

The mind of wigner’s friend
Ludvik Bass · 1971
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Remarks on the mind-body question
Eugene P Wigner · 1995
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Classical and quantum computation
Alexei Yu Kitaev, Alexander Shen, and Mikhail N Vyalyi · 2002
Earlier work this paper cites.
Quantum versus classical proofs and advice
Scott Aaronson and Greg Kuperberg · 2007
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