Dantong LiComputer Science / Yale
03

2023
Published

Quantum switch

Measuring incompatibility and clustering quantum observables with a quantum switch

Incompatibility,
measured.

Authors

Ning Gao, Dantong Li, Anchit Mishra, Junchen Yan, Kyrylo Simonov, Giulio Chiribella

Physical Review Letters 130, 170201 (2023) ↗

The example is described below.

A quantum switch can keep A → B and B → A coherent. The two order histories interfere. The control readout can then reveal how incompatible the operations are.

For this readout, the target qubit is an equal mixture of states 0 and 1. The two branches are order histories, not independent copies of the operations. The atlas below calculates MED for noiseless one-qubit measurement bases.

The contribution

From incompatibility to groups.

Measure incompatibility with a quantum switch and use the measure to group quantum observables.

Start with the idea

From the task to an example.

One quantum measurement can disturb the states associated with another. We need a way to compare this disturbance, including when the measurements are not fully known.

The paper defines mutual eigenspace disturbance, or MED. It then shows how a quantum switch can measure this quantity. The switch uses quantum control over the order of two measurements. The paper also uses MED to group measurements by their compatibility.

Try two axes in the one-qubit tool. Matching axes give MED 0. Axes 45° apart give MED 0.5. Moving the axes changes how much the measurement bases disturb each other. MED is a measure of disturbance, not the probability of an event.

The tool uses known axes in a noiseless one-qubit example. See the PRL paper for the quantum-switch protocol for unknown measurements, the clustering method and the noise analysis.

Try a small example

Compare measurements.
See the difference.

Select two measurements below. Change an axis and compare their incompatibility.

Two projective measurement bases at 45 degreesTwo undirected axes define unordered bases. Their angle is 45 degrees and their exact mutual eigenspace disturbance is 0.5.AB45°Exact value0.5Mutual eigenspacedisturbanceMED = sin(45°) / √2 = 0.5
One qubit, two noiseless projective measurements. The solid and dashed lines are axes, with no preferred direction. MED² is the average eigenstate-disturbance probability in this example.

About this example

A basis is a set of states that a measurement can distinguish. MED measures incompatibility; it is not a probability. Opposite axes describe the same unordered basis. Groups shown here use complete-link. The paper used k-medoids. This Atlas does not simulate the quantum switch.

Original work

Sources &
citation.

Physical Review Letters
2023 · Published

Read the paper ↗
arXiv ↗PDF ↗Supplement ↗Code ↗BibTeX ↓

Physical Review Letters 130, 170201 (2023)

View the citation
@article{prl-2023,
  title = {{Measuring incompatibility and clustering quantum observables with a quantum switch}},
  author = {Ning Gao and Dantong Li and Anchit Mishra and Junchen Yan and Kyrylo Simonov and Giulio Chiribella},
  year = {2023},
  journal = {Physical Review Letters},
  volume = {130},
  number = {17},
  pages = {170201},
  doi = {10.1103/PhysRevLett.130.170201},
  url = {https://doi.org/10.1103/PhysRevLett.130.170201}
}