&Bullet; physics 14, p34

Using a technique called self-directed tomography, researchers precisely measure the states of qudits – quantum systems like qubits, but with more than two dimensions.

M. Rambach / University of Queensland

In classic computing, a bit (binary digit) has two dimensions by definition. Quantum computers use qubits, the quantum equivalent of the classical bit, but could also use qudits, quantum systems with dpotential states or dimensions. Markus Rambach from the University of Queensland in Australia and colleagues have now brought such an approach one step closer to reality by showing that a certain technique for measuring quantum states works for higher-dimensional systems than previously tested [1] .

To use their full potential, researchers must be able to create them, control them, and measure their condition. Qudits states are measured using a class of techniques called quantum state tomography, but measurements become more difficult the more dimensions there are in a system. An approach called self-guided tomography could enable high accuracy and precision with fewer measurements compared to other quantum tomography techniques. However, until now, self-guided tomography has only been tested on low-dimensional systems, such as a system made up of two qubits that has a total number of dimensions



Rambach and colleagues tested the self-directed tomography on pure state qudits – states that can be written as individual vectors in a complex Hilbert space – with 3, 5 and 20 dimensions. They found that the technology is effective for such high-dimensional systems and achieves measurement accuracies of over 99% in all three cases. Although self-guided tomography was originally proposed for measuring pure states, the researchers expanded the method to treat mixed states and showed measurement accuracies of about 95% or more for mixed qudits of three dimensions. Such high-fidelity measurements will likely be necessary to read the mixed-state outputs expected from quantum computers based on high-dimensional qudits

–Erika K. Carlson

Erika K. Carlson is Corresponding Editor for physics based in New York City.


  1. M. Rambach et al., “Robust and efficient high-dimensional quantum state tomography”, Phys. Rev. Lett.126, 100402 (2021).

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