Journal
PHYSICAL REVIEW LETTERS
Volume 105, Issue 15, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.105.150401
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Funding
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Research Innovation
- NSF
- EU
- EURYI
- Direct For Mathematical & Physical Scien
- Division Of Physics [0803371] Funding Source: National Science Foundation
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We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In particular, they are able to reconstruct an unknown density matrix of dimension d and rank r using O(rdlog(2)d) measurement settings, compared to standard methods that require d(2) settings. Our methods have several features that make them amenable to experimental implementation: they require only simple Pauli measurements, use fast convex optimization, are stable against noise, and can be applied to states that are only approximately low rank. The acquired data can be used to certify that the state is indeed close to pure, so no a priori assumptions are needed.
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