# Regensburg 2019 – wissenschaftliches Programm

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# HL: Fachverband Halbleiterphysik

## HL 10: Quantum information systems

### HL 10.7: Vortrag

### Montag, 1. April 2019, 16:45–17:00, H36

**Optimal choice of state tomography quorum formed by projection operators** — Violeta N. Ivanova-Rohling^{1} and •Niklas Rohling^{2} — ^{1}Department of Mathematical Foundations of Computer Science, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Akad.G.Bonchev, block 8, 1113 Sofia, Bulgaria — ^{2}Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway

The density matrix of a *n*-dimensional quantum system, can be estimated by repeatedly performing projections on *n*+1 measurement operators. Ideally, the eigenbases of these operators form a set of mutually unbiased bases [1]. However, the situation is different if, due to restrictions in the experimental setup, only certain measurments are available. One example for this is the restriction to single-shot spin-to-charge conversion measurements for two spin qubits (*n*=4) in a double quantum dot where measuring the charge state is equivalent to projections on individual quantum states. In order to perform state tomography under this restriction for *n* dimensions, *n*^{2}−1 different quantum states need to be selected. While it is possible to use states from a set of mutually unbiased bases [2], we present here numerically optimized sets of quantum states which perform significantly better regarding the expected precision of the tomography scheme [3].

[1] W. K. Wootters and B. D. Fields, Ann. Phys. **191**, 363 (1989)

[2] N. Rohling and G. Burkard, Phys. Rev. B **88**, 085402 (2013)

[3] V. N. Ivanova-Rohling and N. Rohling, arXiv:1810.09484