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For any quantum state representing a physical system of identical particles,the density operator must satisfy the symmetrisation principle (SP) and formassive particles also conform to super-selection rules (SSR) that prohibitcoherences between differing total particle numbers. Here we considerbi-partitite states for systems of massive bosons, where both the system andsubsystems are modes (or sets of modes), particles being associated withdiffering mode occupancies. To define non-entangled or separable states thesubsystem density operators are also required to satisfy the SP and conform toSSR, in contrast to some other approaches. Whilst in the presence of theseadditional constraints some of the known entanglement criteria are still valid,we present a detailed treatment to establish the validity of known criteria andderive new ones.

New Spin Squeezing and Other Entanglement Tests for Two Mode Systems of Identical Bosons