POVM construction: a simple recipe with applications to symmetric states
We propose a simple method for constructing POVMs using any set of matrices which form an orthonormal basis for the space of complex matrices. Considering the orthonormal set of irreducible spherical tensors, we examine the properties of the construction on the n+1-dimensional subspace of the 2n-dim...
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| Format: | Article |
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World Scientific Publishing
2017
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| Online Access: | https://eprints.nottingham.ac.uk/45067/ |
| _version_ | 1848797061879693312 |
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| author | Sirsi, Swarnamala Bharath, Karthik Shilpashree, S.P. Rao, H.S. Smitha |
| author_facet | Sirsi, Swarnamala Bharath, Karthik Shilpashree, S.P. Rao, H.S. Smitha |
| author_sort | Sirsi, Swarnamala |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We propose a simple method for constructing POVMs using any set of matrices which form an orthonormal basis for the space of complex matrices. Considering the orthonormal set of irreducible spherical tensors, we examine the properties of the construction on the n+1-dimensional subspace of the 2n-dimensional Hilbert space of n qubits comprising the permutationally symmetric states. Using the notion of vectorization, the constructed POVMs are interpretable as projection operators in a higher-dimensional space. We then describe a method to physically realize the constructed POVMs for symmetric states using the Clebsch-Gordan decomposition of the tensor product of irreducible representations of the rotation group. We illustrate the proposed construction on a spin-1 system, and show that it is possible to generate entangled states from separable ones. |
| first_indexed | 2025-11-14T19:57:54Z |
| format | Article |
| id | nottingham-45067 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:57:54Z |
| publishDate | 2017 |
| publisher | World Scientific Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-450672020-05-04T19:07:03Z https://eprints.nottingham.ac.uk/45067/ POVM construction: a simple recipe with applications to symmetric states Sirsi, Swarnamala Bharath, Karthik Shilpashree, S.P. Rao, H.S. Smitha We propose a simple method for constructing POVMs using any set of matrices which form an orthonormal basis for the space of complex matrices. Considering the orthonormal set of irreducible spherical tensors, we examine the properties of the construction on the n+1-dimensional subspace of the 2n-dimensional Hilbert space of n qubits comprising the permutationally symmetric states. Using the notion of vectorization, the constructed POVMs are interpretable as projection operators in a higher-dimensional space. We then describe a method to physically realize the constructed POVMs for symmetric states using the Clebsch-Gordan decomposition of the tensor product of irreducible representations of the rotation group. We illustrate the proposed construction on a spin-1 system, and show that it is possible to generate entangled states from separable ones. World Scientific Publishing 2017-09-14 Article PeerReviewed Sirsi, Swarnamala, Bharath, Karthik, Shilpashree, S.P. and Rao, H.S. Smitha (2017) POVM construction: a simple recipe with applications to symmetric states. International Journal of Quantum Information, 15 . p. 1750042. ISSN 1793-6918 Permutationally symmetric states; Projection operators; POVM http://www.worldscientific.com/doi/abs/10.1142/S0219749917500423 doi:10.1142/S0219749917500423 doi:10.1142/S0219749917500423 |
| spellingShingle | Permutationally symmetric states; Projection operators; POVM Sirsi, Swarnamala Bharath, Karthik Shilpashree, S.P. Rao, H.S. Smitha POVM construction: a simple recipe with applications to symmetric states |
| title | POVM construction: a simple recipe with applications to
symmetric states |
| title_full | POVM construction: a simple recipe with applications to
symmetric states |
| title_fullStr | POVM construction: a simple recipe with applications to
symmetric states |
| title_full_unstemmed | POVM construction: a simple recipe with applications to
symmetric states |
| title_short | POVM construction: a simple recipe with applications to
symmetric states |
| title_sort | povm construction: a simple recipe with applications to
symmetric states |
| topic | Permutationally symmetric states; Projection operators; POVM |
| url | https://eprints.nottingham.ac.uk/45067/ https://eprints.nottingham.ac.uk/45067/ https://eprints.nottingham.ac.uk/45067/ |