Geometric multiaxial representation of Nqubit mixed symmetric separable statesTools Suma, S.P. and Sirsi, Swarnamala and Hegde, Subramanya and Bharath, Karthik (2017) Geometric multiaxial representation of Nqubit mixed symmetric separable states. Physical Review A, 96 (2). 022328/1022328/6. ISSN 24699934
AbstractStudy 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 Nqubit 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 spinj system and an Nqubit 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 Pdistribution function λ (ᶿ, Φ) We show that the Nqubit 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 Nqubit 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.
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