Efficient method for computing the maximum-likelihood quantum state from measurements with additive Gaussian noise
We provide an efficient method for computing the maximum-likelihood mixed quantum state (with density matrix ρ) given a set of measurement outcomes in a complete orthonormal operator basis subject to Gaussian noise. Our method works by first changing basis yielding a candidate density matrix μ which...
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| Published in | Physical review letters Vol. 108; no. 7; p. 070502 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
United States
17.02.2012
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| Online Access | Get more information |
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| Abstract | We provide an efficient method for computing the maximum-likelihood mixed quantum state (with density matrix ρ) given a set of measurement outcomes in a complete orthonormal operator basis subject to Gaussian noise. Our method works by first changing basis yielding a candidate density matrix μ which may have nonphysical (negative) eigenvalues, and then finding the nearest physical state under the 2-norm. Our algorithm takes at worst O(d(4)) for the basis change plus O(d(3)) for finding ρ where d is the dimension of the quantum state. In the special case where the measurement basis is strings of Pauli operators, the basis change takes only O(d(3)) as well. The workhorse of the algorithm is a new linear-time method for finding the closest probability distribution (in Euclidean distance) to a set of real numbers summing to one. |
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| AbstractList | We provide an efficient method for computing the maximum-likelihood mixed quantum state (with density matrix ρ) given a set of measurement outcomes in a complete orthonormal operator basis subject to Gaussian noise. Our method works by first changing basis yielding a candidate density matrix μ which may have nonphysical (negative) eigenvalues, and then finding the nearest physical state under the 2-norm. Our algorithm takes at worst O(d(4)) for the basis change plus O(d(3)) for finding ρ where d is the dimension of the quantum state. In the special case where the measurement basis is strings of Pauli operators, the basis change takes only O(d(3)) as well. The workhorse of the algorithm is a new linear-time method for finding the closest probability distribution (in Euclidean distance) to a set of real numbers summing to one. |
| Author | Smith, Graeme Gambetta, Jay M Smolin, John A |
| Author_xml | – sequence: 1 givenname: John A surname: Smolin fullname: Smolin, John A email: smolin@us.ibm.com organization: IBM TJ Watson Research Center, Yorktown Heights, New York 10598, USA. smolin@us.ibm.com – sequence: 2 givenname: Jay M surname: Gambetta fullname: Gambetta, Jay M – sequence: 3 givenname: Graeme surname: Smith fullname: Smith, Graeme |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/22401185$$D View this record in MEDLINE/PubMed |
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