Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.14765 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929405184442368 |
|---|---|
| author | Li, Chi-Kwong Nakahara, Mikio |
| author_facet | Li, Chi-Kwong Nakahara, Mikio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_14765 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on Majorana representation of quantum states Li, Chi-Kwong Nakahara, Mikio Quantum Physics 15A90, 15A60 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. |
| title | A note on Majorana representation of quantum states |
| topic | Quantum Physics 15A90, 15A60 |
| url | https://arxiv.org/abs/2308.14765 |