Geometric multiaxial representation of N-qubit mixed symmetric separable states
Study of an N qubit mixed symmetric separable states is a long standing challenging problem as there exist no unique separability criterion. In this regard, we take up the N-qubit mixed symmetric separable states for a detailed study as these states are of experimental importance and offer elegant m...
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| Format: | Article |
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American Physical Society
2017
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| Online Access: | https://eprints.nottingham.ac.uk/45070/ |
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| author | Suma, S.P. Sirsi, Swarnamala Hegde, Subramanya Bharath, Karthik |
| author_facet | Suma, S.P. Sirsi, Swarnamala Hegde, Subramanya Bharath, Karthik |
| author_sort | Suma, S.P. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Study of an N qubit mixed symmetric separable states is a long standing challenging problem as there exist no unique separability criterion. In this regard, we take up the N-qubit mixed symmetric separable states for a detailed study as these states are of experimental importance and offer elegant mathematical analysis since the dimension of the Hilbert space reduces from 2N to N + 1. Since there exists a one to one correspondence between spin-j system and an N-qubit symmetric state, we employ Fano statistical tensor parameters for the parametrization of spin density matrix. Further, we use geometric multiaxial representation (MAR) of density matrix to characterize the mixed symmetric separable states. Since separability problem is NP hard, we choose to study it in the continuum limit where mixed symmetric separable states are characterized by the P-distribution function λ (ᶿ, Φ) We show that the N-qubit mixed symmetric separable state can be visualized as a uniaxial system if the distribution function is independent of ᶿ, and Φ. We further choose distribution function to be the most general positive function on a sphere and observe that the statistical tensor parameters characterizing the N-qubit symmetric system are the expansion coefficients of the distribution function. As an example for the discrete case, we investigate the MAR of a uniformly weighted two qubit mixed symmetric separable state. We also observe that there exists a correspondence between separability and classicality of states. |
| first_indexed | 2025-11-14T19:57:54Z |
| format | Article |
| id | nottingham-45070 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:57:54Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-450702020-05-04T19:02:54Z https://eprints.nottingham.ac.uk/45070/ Geometric multiaxial representation of N-qubit mixed symmetric separable states Suma, S.P. Sirsi, Swarnamala Hegde, Subramanya Bharath, Karthik Study of an N qubit mixed symmetric separable states is a long standing challenging problem as there exist no unique separability criterion. In this regard, we take up the N-qubit mixed symmetric separable states for a detailed study as these states are of experimental importance and offer elegant mathematical analysis since the dimension of the Hilbert space reduces from 2N to N + 1. Since there exists a one to one correspondence between spin-j system and an N-qubit symmetric state, we employ Fano statistical tensor parameters for the parametrization of spin density matrix. Further, we use geometric multiaxial representation (MAR) of density matrix to characterize the mixed symmetric separable states. Since separability problem is NP hard, we choose to study it in the continuum limit where mixed symmetric separable states are characterized by the P-distribution function λ (ᶿ, Φ) We show that the N-qubit mixed symmetric separable state can be visualized as a uniaxial system if the distribution function is independent of ᶿ, and Φ. We further choose distribution function to be the most general positive function on a sphere and observe that the statistical tensor parameters characterizing the N-qubit symmetric system are the expansion coefficients of the distribution function. As an example for the discrete case, we investigate the MAR of a uniformly weighted two qubit mixed symmetric separable state. We also observe that there exists a correspondence between separability and classicality of states. American Physical Society 2017-08-30 Article PeerReviewed Suma, S.P., Sirsi, Swarnamala, Hegde, Subramanya and Bharath, Karthik (2017) Geometric multiaxial representation of N-qubit mixed symmetric separable states. Physical Review A, 96 (2). 022328/1-022328/6. ISSN 2469-9934 https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.022328 doi:10.1103/PhysRevA.96.022328 doi:10.1103/PhysRevA.96.022328 |
| spellingShingle | Suma, S.P. Sirsi, Swarnamala Hegde, Subramanya Bharath, Karthik Geometric multiaxial representation of N-qubit mixed symmetric separable states |
| title | Geometric multiaxial representation of N-qubit mixed symmetric separable states |
| title_full | Geometric multiaxial representation of N-qubit mixed symmetric separable states |
| title_fullStr | Geometric multiaxial representation of N-qubit mixed symmetric separable states |
| title_full_unstemmed | Geometric multiaxial representation of N-qubit mixed symmetric separable states |
| title_short | Geometric multiaxial representation of N-qubit mixed symmetric separable states |
| title_sort | geometric multiaxial representation of n-qubit mixed symmetric separable states |
| url | https://eprints.nottingham.ac.uk/45070/ https://eprints.nottingham.ac.uk/45070/ https://eprints.nottingham.ac.uk/45070/ |