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These two accompanying papers treat two mode entanglement for systems ofidentical massive bosons and the relationship to spin squeezing and otherquantum correlation effects. Entanglement is a key quantum feature of compositesystems where the probabilities for joint measurements on the compositesub-systems are no longer determined from measurement probabilities on theseparate sub-systems. We focus on the meaning of entanglement, the quantumparadoxes associated with entangled states, and important tests that allow anexperimentalist to determine whether a quantum state - in particular, one formassive bosons is entangled. Our tests for entanglement fully utilise thesymmetrisation principle and super-selection rules for bosonic massiveparticles. These papers provides detailed arguments necessary for theconclusions of a recent paper which presented results for rigorouslydemonstrating the entanglement of a two-mode Bose-Einstein condensate (BEC).  In the first paper (I), we discuss the meaning of entanglement for systems ofidentical particles. For such systems, the relevant quantum density operatorsmust satisfy the symmetrisation principle and global and local super-selectionrules prohibiting states in which there are coherences between differingparticle numbers. We fully justify these requirements. In the secondquantisation approach, both the system and sub-systems are modes (or sets ofmodes) rather than particles, particles being associated with different modeoccupancies.  In the accompanying review paper (II), we consider spin squeezing and othertests for entanglement for two-mode bosonic systems. Starting from paper (I) wedetermine which tests are useful for detecting entanglement in massive bosonic(BEC), as opposed to photonic, systems. Several new inequalities are derived,and recent key experiments are analysed.

Quantum Entanglement for Systems of Identical Bosons. II Spin Squeezing and Other Entanglement Tests