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Entanglement Sharing in Real-Vector-Space Quantum Theory

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Abstract

The limitation on the sharing of entanglement is a basic feature of quantum theory. For example, if two qubits are completely entangled with each other, neither of them can be at all entangled with any other object. In this paper we show, at least for a certain standard definition of entanglement, that this feature is lost when one replaces the usual complex vector space of quantum states with a real vector space. Moreover, the difference between the two theories is extreme: in the real-vector-space theory, there exist states of arbitrarily many binary objects, “rebits,” in which every rebit in the system is maximally entangled with each of the other rebits.

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Authors and Affiliations

  1. Department of Physics, Williams College, Williamstown, MA 01267, USA

    William K. Wootters

  2. Department of Applied Physics, Kigali Institute of Science and Technology, B.P. 3900, Kigali, Rwanda

    William K. Wootters

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  1. William K. Wootters
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Correspondence to William K. Wootters.

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Wootters, W.K. Entanglement Sharing in Real-Vector-Space Quantum Theory. Found Phys 42, 19–28 (2012). https://doi.org/10.1007/s10701-010-9488-1

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  • DOI: https://doi.org/10.1007/s10701-010-9488-1

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