{ "id": "0909.3304", "version": "v4", "published": "2009-09-18T01:43:05.000Z", "updated": "2010-08-16T19:01:03.000Z", "title": "Quantum state tomography via compressed sensing", "authors": [ "David Gross", "Yi-Kai Liu", "Steven T. Flammia", "Stephen Becker", "Jens Eisert" ], "comment": "4 pages, 1 figure; v3, v4: presentation improved", "journal": "Phys. Rev. Lett. 105, 150401 (2010)", "categories": [ "quant-ph" ], "abstract": "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(rd log^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. We present both theoretical bounds and numerical simulations.", "revisions": [ { "version": "v4", "updated": "2010-08-16T19:01:03.000Z" } ], "analyses": { "subjects": [ "03.65.Wj", "03.67.-a" ], "keywords": [ "quantum state tomography", "compressed sensing", "large quantum systems", "significant performance improvement", "unknown density matrix" ], "tags": [ "journal article" ], "publication": { "publisher": "APS", "journal": "Physical Review Letters", "doi": "10.1103/PhysRevLett.105.150401", "year": 2010, "month": "Oct", "volume": 105, "number": 15, "pages": 150401 }, "note": { "typesetting": "TeX", "pages": 4, "language": "en", "license": "arXiv", "status": "editable", "adsabs": "2010PhRvL.105o0401G" } } }