Abstract
In this paper we define a family of hermitian operators by which to extract what we call quantum-relative-phase properties of a pure or mixed multipartite quantum state, and we relate these properties to known measures of entanglement, namely the m-tangle and the invariant \({S_{(m)}^2}\) of the multi-local Lorentz-group \({SL(2, \mathbb{C})^{\otimes m}}\) . Our construction is based on the orthogonal complement of a positive operator valued measure on quantum phase.
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Heydari, H. Quantum relative phase, m-tangle, and multi-local Lorentz-group invariant. Quantum Inf Process 9, 233–238 (2010). https://doi.org/10.1007/s11128-009-0150-9
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DOI: https://doi.org/10.1007/s11128-009-0150-9