The Learnability of Quantum States

Details The Learnability of Quantum States The Learnability of Quantum States

2006-08-18

arxiv.org/abs/quant-ph/0608142v3

Physics

Quantum Physics

30 pages; added discussion of adaptive measurements, moved proofs to appendix, and corrected various minor errors

Scientific paper

10.1098/rspa.2007.0113

Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, we show that "for most practical purposes" one can learn a state using a number of measurements that grows only linearly with n. Besides possible implications for experimental physics, our learning theorem has two applications to quantum computing: first, a new simulation of quantum one-way communication protocols, and second, the use of trusted classical advice to verify untrusted quantum advice.

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