Abstract
The techniques of low-rank matrix recovery were adapted for quantum state tomography (QST) previously by Gross et al. [Phys. Rev. Lett. 105, 150401 (2010)] where they consider the tomography of spin-1/2 systems. For the density matrix of dimension and rank with , it was shown that randomly chosen Pauli measurements of the order are enough to fully reconstruct the density matrix by running a specific convex optimization algorithm. The result utilized the low operator norm of the Pauli operator basis, which makes it “incoherent” to low-rank matrices. For quantum systems of dimension not a power of two, Pauli measurements are not available, and one may consider using measurements. Here, we point out that the operators, owing to their high operator norm, do not provide a significant savings in the number of measurement settings required for successful recovery of all rank- states. We propose an alternative strategy in which the quantum information is swapped into the subspace of a power-two system using only gates at most with QST being implemented, subsequently, by performing Pauli measurements. We show that, despite the increased dimensionality, this method is more efficient than the one using measurements.
- Received 9 March 2020
- Accepted 1 June 2020
DOI:https://doi.org/10.1103/PhysRevA.101.062328
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