Geometric multiaxial representation of ℕ-qubit mixed symmetric separable states

Suma, S. P. and Swarnamala, Sirsi and Hegde, Subramanya and Bharath, Karthik (2017) Geometric multiaxial representation of ℕ-qubit mixed symmetric separable states. Physical Review A, 96 (2). ISSN 2469-9934

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The study of N-qubit mixed symmetric separable states is a longstanding challenging problem as no unique separability criterion exists. 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 an elegant mathematical analysis since the dimension of the Hilbert space is reduced from 2N to N+1. Since there exists a one-to-one correspondence between the spin-j system and an N-qubit symmetric state, we employ Fano statistical tensor parameters for the parametrization of the spin-density matrix. Further, we use a geometric multiaxial representation (MAR) of the density matrix to characterize the mixed symmetric separable states. Since the 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 states can be visualized as a uniaxial system if the distribution function is independent of θ and ϕ. We further choose a 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 the separability and classicality of states.

Item Type: Article
Subjects: D Physical Science > Physics
Divisions: Yuvaraj college > Physics
Depositing User: C Swapna Library Assistant
Date Deposited: 21 Jun 2019 05:18
Last Modified: 21 Jun 2019 05:18

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