A note on Majorana representation of quantum states

Chi-Kwong Li () and Mikio Nakahara ()
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Chi-Kwong Li: College of William & Mary
Mikio Nakahara: IQM Quantum Computers

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 3, 1084-1088

Abstract: Abstract By the Majorana representation, for any $$d > 1$$ d > 1 there is a one-one correspondence between a quantum state of dimension d and $$d-1$$ d - 1 qubits represented as $$d-1$$ d - 1 points in the Bloch sphere. Using the theory of symmetry class of tensors, we present a simple scheme for constructing $$d-1$$ d - 1 points on the Bloch sphere and the corresponding $$d-1$$ d - 1 qubits representing a d-dimensional quantum state. Additionally, we demonstrate how the inner product of two d-dimensional quantum states can be expressed as a permanent of a matrix related to their $$(d-1)$$ ( d - 1 ) -qubit state representations. Extension of the result to mixed states is also considered.

Keywords: Quantum states; Majorana representation; Principal character; Permanent; 15A90; 15A60 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-024-00649-6

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