Information-theoretic Hardness of Out-of-time-order Correlators
- URL: http://arxiv.org/abs/2208.02256v1
- Date: Wed, 3 Aug 2022 18:00:00 GMT
- Title: Information-theoretic Hardness of Out-of-time-order Correlators
- Authors: Jordan Cotler, Thomas Schuster, Masoud Mohseni
- Abstract summary: We establish that there are properties of quantum many-body dynamics which are efficiently learnable if we are given access to out-of-time-order correlators.
This implies that any experimental protocol which reconstructs OTOCs solely from time-ordered correlators must be, in certain cases, exponentially inefficient.
- Score: 0.36832029288386126
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We establish that there are properties of quantum many-body dynamics which
are efficiently learnable if we are given access to out-of-time-order
correlators (OTOCs), but which require exponentially many operations in the
system size if we can only measure time-ordered correlators. This implies that
any experimental protocol which reconstructs OTOCs solely from time-ordered
correlators must be, in certain cases, exponentially inefficient. Our proofs
leverage and generalize recent techniques in quantum learning theory. Along the
way, we elucidate a general definition of time-ordered versus out-of-time-order
experimental measurement protocols, which can be considered as classes of
adaptive quantum learning algorithms. Moreover, our results provide a
theoretical foundation for novel applications of OTOCs in quantum simulations.
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