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arXiv:2512.12504

Classical Second-Order Moments and Tensor Squeezing in Spin-1 Systems

K. S. Mallesh

quant-phSubmitted Dec 14, 2025• Announced Dec 16, 2025• 0 citations
v1 · Dec 14, 2025v2 · Jan 13, 2026v3 · Jan 15, 2026
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Abstract

We give a compact, frame-independent characterization of the set of classical second-order moments for a single spin-1 particle. Defining the moment matrix M = 2Q + (1/3) I, we show that a moment pair (s, Q) arises from a positive mixture of spin-coherent states if and only if M is positive semidefinite, M minus ss^T is positive semidefinite, and the trace of M equals one. These necessary and sufficient matrix conditions delimit the classical moment region and yield simple, basis-free witnesses of higher-order tensor nonclassicality, such as bounds on Tr(Q^2). A constructive proof of sufficiency is given in the appendix.

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7 pages

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We give a compact, frame-independent characterization of the set of classical second-order moments for a single spin-1 particle. Defining the moment matrix M = 2Q + (1/3) I, we show that a moment pair (s, Q) arises from a positive mixture of spin-coherent states if and only if M is positive semidefinite, M minus ss^T is positive semidefinite, and the trace of M equals one. These necessary and sufficient matrix conditions delimit the classical moment region and yield simple, basis-free witnesses of higher-order tensor nonclassicality, such as bounds on Tr(Q^2). A constructive proof of sufficiency is given in the appendix.
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