Type of Publication:  Preprint 
Publication status:  Submitted 
Author:  IvanovaRohling, Violeta N.; Burkard, Guido; Rohling, Niklas 
Year of publication:  2020 
ArXivID:  arXiv:2012.14494 
Summary: 
We present a framework that formulates the quest for the most efficient quantum state tomography scheme as an optimization problem which can be solved numerically. This approach can be applied to a broad spectrum of relevant setups including measurements restricted to a subsystem. To illustrate the power of this method we present results for the sixdimensional Hilbert space constituted by a qubitqutrit system, which could be realized e.g. by the N14 nuclear spin1 and two electronic spin states of a nitrogenvacancy center in diamond. Measurements of the qubit subsystem are expressed by projectors of rank three, i.e., projectors on halfdimensional subspaces. For systems consisting only of qubits, it was shown analytically that a set of projectors on halfdimensional subspaces can be arranged in an informationally optimal fashion for quantum state tomography, thus forming socalled mutually unbiased subspaces. Our method goes beyond qubitsonly systems and we find that in dimension six such a set of mutuallyunbiased subspaces can be approximated with a deviation irrelevant for practical applications.

Subject (DDC):  530 Physics 
Keywords:  Quantum state tomography, numerical optimization problem 
Bibliography of Konstanz:  Yes 
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IVANOVAROHLING, Violeta N., Guido BURKARD, Niklas ROHLING, 2020. Quantum state tomography as a numerical optimization problem
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