POVM construction: a simple recipe with applications to symmetric states

Sirsi, Swarnamala; Bharath, Karthik; Shilpashree, S.P.; Rao, H.S. Smitha

Abstract

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.

Citation

Sirsi, S., Bharath, K., Shilpashree, S., & Rao, H. S. (in press). POVM construction: a simple recipe with applications to symmetric states. International Journal of Quantum Information, 15, https://doi.org/10.1142/S0219749917500423

• Journal Article Type: Article
• Acceptance Date: Aug 11, 2017
• Online Publication Date: Sep 14, 2017
• Deposit Date: Aug 23, 2017
• Publicly Available Date: Sep 15, 2018
• Journal: International Journal of Quantum Information
• Print ISSN: 0219-7499
• Electronic ISSN: 1793-6918
• Publisher: World Scientific
• Peer Reviewed: Peer Reviewed
• Volume: 15
• DOI: https://doi.org/10.1142/S0219749917500423
• Keywords: Permutationally symmetric states; Projection operators; POVM
• Public URL: https://nottingham-repository.worktribe.com/output/883021
• Publisher URL: http://www.worldscientific.com/doi/abs/10.1142/S0219749917500423
• Additional Information: Electronic version of an article published as Swarnamala Sirsi et al, Int. J. Quantum Inform. 15, 1750042 (2017) [12 pages] https://doi.org/10.1142/S0219749917500423 copyright World Scientific Publishing Company http://www.worldscientific.com/doi/abs/10.1142/S0219749917500423