Journal
PHYSICAL REVIEW LETTERS
Volume 123, Issue 26, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.123.260501
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Funding
- Czech Science Foundation [19-19002S, 0.0/0.0/16_019/0000754]
- Ministry of Education, Youth and Sports of the Czech Republic
- Palacky University [IGA-PrF-2019-008]
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We report on the experimental measurement of the Hilbert-Schmidt distance between two two-qubit states by many-particle interference. We demonstrate that our three-step method for measuring distances in the Hilbert space is far less complex than reconstructing density matrices and that it can be applied in quantum-enhanced machine learning to reduce the complexity of calculating Euclidean distances between multidimensional points, which can be especially interesting for near term quantum technologies and quantum artificial intelligence research. Our results are also a novel example of applying mixed states in quantum information processing. Usually working with mixed states is undesired, but here it gives the possibility of encoding extra information as the degree of coherence between the given two dimensions of the density matrix.
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