Quantum state restoration and single-copy tomography
Abstract
Given a single copy of an n qubit quantum state |psi>, the no-cloning theorem greatly limits the amount of information which can be extracted from it. Moreover, given only a procedure which verifies the state, for example a procedure which measures the operator |psi><psi|, we cannot prepare |psi> in time polynomial in n . In this paper, we consider the scenario in which we are given both a single copy of |psi> and the ability to verify it. We show that in this setting, we can do several novel things efficiently. We present a new algorithm that we call quantum state restoration which allows us to extend a large subsystem of |psi> to the full state, and in turn this allows us to copy small subsystems of |psi>. In addition, we present algorithms that can perform tomography on small subsystems of |psi>, and we show how to use these algorithms to estimate the statistics of any efficiently implementable POVM acting on |psi> in time polynomial in the number of outcomes of the POVM.
Cite
@article{arxiv.0912.3823,
title = {Quantum state restoration and single-copy tomography},
author = {Edward Farhi and David Gosset and Avinatan Hassidim and Andrew Lutomirski and Daniel Nagaj and Peter Shor},
journal= {arXiv preprint arXiv:0912.3823},
year = {2011}
}
Comments
edited for clarity; 13 pages, 1 figure