7,882 research outputs found

    Infinite matrices may violate the associative law

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    The momentum operator for a particle in a box is represented by an infinite order Hermitian matrix PP. Its square P2P^2 is well defined (and diagonal), but its cube P3P^3 is ill defined, because PP2‚ȆP2PP P^2\neq P^2 P. Truncating these matrices to a finite order restores the associative law, but leads to other curious results.Comment: final version in J. Phys. A28 (1995) 1765-177

    Bell's inequality with Dirac particles

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    We study Bell's inequality using the Bell states constructed from four component Dirac spinors. Spin operator is related to the Pauli-Lubanski pseudo vector which is relativistic invariant operator. By using Lorentz transformation, in both Bell states and spin operator, we obtain an observer independent Bell's inequality, so that it is maximally violated as long as it is violated maximally in the rest frame.Comment: 7 pages. arXiv admin note: text overlap with arXiv:quant-ph/0308156 by other author

    Quantum mechanics explained

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    The physical motivation for the mathematical formalism of quantum mechanics is made clear and compelling by starting from an obvious fact - essentially, the stability of matter - and inquiring into its preconditions: what does it take to make this fact possible?Comment: 29 pages, 5 figures. v2: revised in response to referee comment

    Maximally-Disordered Distillable Quantum States

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    We explore classical to quantum transition of correlations by studying the quantum states located just outside of the classically-correlated-states-only neighborhood of the maximally mixed state (the largest separable ball (LSB)). We show that a natural candidate for such states raises the possibility of a layered transition, i.e., an annular region comprising only classical and the classical-like bound entangled states, followed by free or distillable entanglement. Surprisingly, we find the transition to be abrupt for bipartite systems: distillable states emerge arbitrarily close to the LSB. For multipartite systems, while the radius of the LSB remains unknown, we determine the radius of the largest undistillable ball. Our results also provide an upper bound on how noisy shared entangled states can be for executing quantum information processing protocols.Comment: Published Version, 7 pages, Late

    Minimal optimal generalized quantum measurements

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    Optimal and finite positive operator valued measurements on a finite number NN of identically prepared systems have been presented recently. With physical realization in mind we propose here optimal and minimal generalized quantum measurements for two-level systems. We explicitly construct them up to N=7 and verify that they are minimal up to N=5. We finally propose an expression which gives the size of the minimal optimal measurements for arbitrary NN.Comment: 9 pages, Late
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