Wigner negativity in spin-$j$ systems

• URL: http://arxiv.org/abs/2008.10167v1
• Date: Mon, 24 Aug 2020 02:45:32 GMT
• Title: Wigner negativity in spin-$j$ systems
• Authors: Jack Davis, Meenu Kumari, Robert B. Mann, Shohini Ghose
• Abstract summary: The nonclassicality of simple spin systems as measured by Wigner negativity is studied on a spherical phase space. We derive a bound on the Wigner negativity of spin cat states that rapidly approaches the true value as spin increases beyond $j gtrsim 5$. Results underscore the influence that dynamical symmetry has on nonclassicality, and suggest a guiding perspective for finding novel quantum computational applications.
• Score: 1.1470070927586016
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The nonclassicality of simple spin systems as measured by Wigner negativity is studied on a spherical phase space. Several SU(2)-covariant states with common qubit representations are addressed: spin coherent, spin cat (GHZ/N00N), and Dicke ($\textsf{W}$). We derive a bound on the Wigner negativity of spin cat states that rapidly approaches the true value as spin increases beyond $j \gtrsim 5$. We find that spin cat states are not significantly Wigner-negative relative to their Dicke state counterparts of equal dimension. We also find, in contrast to several entanglement measures, that the most Wigner-negative Dicke basis element is spin-dependent, and not the equatorial state $| j,0 \rangle$ (or $|j,\pm 1/2 \rangle$ for half-integer spins). These results underscore the influence that dynamical symmetry has on nonclassicality, and suggest a guiding perspective for finding novel quantum computational applications.

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