2013/05/03 by B. J. Dalton, Libby Heaney, Dalton, Bryan +7
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Cold Atom Physics and Bose-Einstein Condensates #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.1305.0788
The concept of entangled quantum states is considered in the context of\nsystems of identical particles, based on the requirement that in order to\nrepresent physical states both for the overall system and the sub-systems which\nmay be entangled, the density operators must satisfy the symmetrisation\nprinciple and global and local super-selection rules that prohibit states in\nwhich there are coherences between differing particle numbers. These\nrequirements and their justification are fully discussed. In the second\nquantisation approach used, both the system and the sub-systems are modes (or\nsets of modes) rather than particles, particles being associated with different\noccupancies of the modes. The definition of entangled states is based on first\ndefining the non-entangled states - after specifying which modes constitute the\nsub-systems. This paper mainly focuses on two mode entanglement for massive\nbosons. Several inequalities involving variances and mean values of operators\ninvolving mode annihilation, creation operators have been proposed as tests for\ntwo mode entangled states, including the inequalities that define spin\nsqueezing. Spin squeezing criteria in two mode systems are examined, and spin\nsqueezing is best considered for principle spin operator components where the\ncovariance matrix is diagonal. It is shown that the presence of spin squeezing\nin at least one of the spin components requires entanglement of the relevant\npair of modes. Several of the other proposed tests for entanglement, including\nones based on the sum of the variances for two spin components are considered.\nAll of the tests are still valid when the present concept of entanglement based\non the symmetrisation and super-selection rule criteria is applied, but further\ntests have been obtained here. Sometimes the new tests are satisfied whilst\nthan those obtained in other papers are not.\n