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A note on Majorana representation of quantum states

Author

Listed:
  • Chi-Kwong Li

    (College of William & Mary)

  • Mikio Nakahara

    (IQM Quantum Computers)

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.

Suggested Citation

  • Chi-Kwong Li & Mikio Nakahara, 2024. "A note on Majorana representation of quantum states," Indian Journal of Pure and Applied Mathematics, Springer, vol. 55(3), pages 1084-1088, September.
    • Handle: RePEc:spr:indpam:v:55:y:2024:i:3:d:10.1007_s13226-024-00649-6
    DOI: 10.1007/s13226-024-00649-6
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