# The Necromancy-Hardness of the Schrödinger's Cat Experiment

### APA

Aaronson, S. (2020). The Necromancy-Hardness of the Schrödinger's Cat Experiment. Perimeter Institute. https://pirsa.org/20010099

### MLA

Aaronson, Scott. The Necromancy-Hardness of the Schrödinger's Cat Experiment. Perimeter Institute, Jan. 29, 2020, https://pirsa.org/20010099

### BibTex

@misc{ pirsa_PIRSA:20010099, doi = {10.48660/20010099}, url = {https://pirsa.org/20010099}, author = {Aaronson, Scott}, keywords = {Other}, language = {en}, title = {The Necromancy-Hardness of the Schr{\"o}dinger{\textquoteright}s Cat Experiment}, publisher = {Perimeter Institute}, year = {2020}, month = {jan}, note = {PIRSA:20010099 see, \url{https://pirsa.org}} }

Scott Aaronson The University of Texas at Austin

## Abstract

Motivated by puzzles in quantum gravity AdS/CFT, Lenny Susskind posed the following question: supposing one had the technological ability to distinguish a macroscopic superposition of two given states |v> and |w> from incoherent mixture of those states, would one also have the technological ability to map |v> to |w> and vice versa? More precisely, how does the quantum circuit complexity of the one task relate to the quantum circuit complexity of the other? Here we resolve Susskind's question -- showing that the two complexities are essentially identical, even for approximate versions of these tasks, with the one caveat that a unitary transformation that maps |v> to |w> and |w> to -|v> need not imply any distinguishing ability. Informally, "if you had the ability to prove Schrödinger's cat was in superposition, you'd necessarily also have the ability to bring a dead cat back to life." I'll also discuss the optimality of this little result and some of its implications.

Paper (with Yosi Atia) in preparation