Geometric multiaxial representation of N-qubit mixed symmetric separable states

Suma, S.P. and Sirsi, Swarnamala and 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

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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.

Item Type: Article
Additional Information: ©2017 American Physical Society
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1103/PhysRevA.96.022328
Depositing User: Bharath, Karthik
Date Deposited: 23 Aug 2017 08:48
Last Modified: 20 Sep 2017 02:43

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