Browsing by Subject "quantum entanglement"

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    Hyperdeterminants, entangled states, and invariant theory
    (2013) Şen, Emre
    In [1] and [2], A. Klyachko connects quantum entanglement and invariant theory so that entangled state of a quantum system can be explained by invariants of the system. After representing states in multidimensional matrices, this relation turns into finding multidimensional matrix invariants so called hyperdeterminants. Here we provide a necessary and sufficient condition for existence of a hyperdeterminant of a multidimensional matrix of an arbitrary format. The answer is given in terms of the so called castling transform that relates hyperdeterminants of different formats. Among castling equivalent formats there is a unique castling reduced one, that has minimal number of entries. We prove the following theorem: “Multidimensional matrices of a given format admit a non-constant hyperdeterminant if and only if logarithm of dimensions of the castling reduced format satisfy polygonal inequalities.”
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    Quantum entanglement and light propagation through Bose-Einstein condensate (BEC)
    (2009) Taşgın, Mehmet Emre
    We investigate the optical response of coherent media, a Bose-Einstein condensate (BEC), to intense laser pump stimulations and weak probe pulse propagation. First, we adopt the coherence in sequential superradiance (SR) as a tool for continuous-variable (CV) quantum entanglement of two counter-propagating pulses from the two end-fire modes. In the first-sequence the end-fire and side mode are CV entangled. In the second sequence of SR, this entanglement is swapped in between the two opposite end-fire modes. Second, we investigate the photonic bands of an atomic BEC with a triangular vortex lattice. Index contrast between the vortex cores and the bulk of the condensate is achieved through the enhancement of the index via atomic coherence. Frequency dependent dielectric function is used in the calculations of the bands. We adopt a Poynting vector method to distinguish the photonic band gaps from absorption/gain regimes.