Related papers: A note on Majorana representation of quantum states

A note on Majorana representation of quantum states

URL: http://arxiv.org/abs/2308.14765v4
Date: Tue, 2 Jul 2024 15:55:21 GMT
Title: A note on Majorana representation of quantum states
Authors: Chi-Kwong Li, Mikio Nakahara,
Abstract summary: For any $d > 1$ there is a one-one correspondence between a quantum state of dimension $d$ and $d-1$ qubits represented as $d-1$ points in the Bloch sphere. We present a simple scheme for constructing $d-1$ points on the Bloch sphere and the corresponding $d-1$ qubits representing a $d$-dimensional quantum state.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: By the Majorana representation, for any $d > 1$ there is a one-one correspondence between a quantum state of dimension $d$ and $d-1$ qubits represented as $d-1$ points in the Bloch sphere. Using the theory of symmetry class of tensors, we present a simple scheme for constructing $d-1$ points on the Bloch sphere and the corresponding $d-1$ 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 $(d-1)$-qubit state representations. Extension of the result to mixed states is also considered.

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