Five orthogonal three-qubit states exhibit strong nonlocality if and only if they contain imaginary components, forming the smallest unextendible biseparable basis of cardinality d² + d - 1 while spanning a locally indistinguishable subspace whose complement yields distillable genuine entanglement.
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Many-body chirality for Z_d^(k) stabilizer states equals mirror non-invariance of anyon data, is intrinsically four-partite, and states with d>2 also show intrinsic imaginarity not removable by local unitaries.
A real-valued framework based on Kähler space with a symplectic composition rule exactly reproduces all standard quantum mechanics predictions, including maximal CHSH violation.
Complex measurements in three-qubit entanglement protocols concentrate more bipartite entanglement and cut required bond occupation probability by 22.7% in honeycomb-lattice quantum network percolation.
The quotient-space real formulation of quantum mechanics is shown to be standard complex QM in real notation, not an independent real-amplitude theory, because it requires a hidden complex structure J, a superselection rule, and a balanced tensor product isomorphic to the complex tensor product.
The proposed postulate for choosing between real-number versions of quantum theory does not hold in Fermionic Information Theory and therefore is not general.
Real-number quantum theories with independent sources require nonlocal maps, implying complex numbers are necessary for entanglement between independent systems.
citing papers explorer
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Strong nonlocality with more imaginarity and less entanglement
Five orthogonal three-qubit states exhibit strong nonlocality if and only if they contain imaginary components, forming the smallest unextendible biseparable basis of cardinality d² + d - 1 while spanning a locally indistinguishable subspace whose complement yields distillable genuine entanglement.
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Many-body chirality of topological stabilizer states
Many-body chirality for Z_d^(k) stabilizer states equals mirror non-invariance of anyon data, is intrinsically four-partite, and states with d>2 also show intrinsic imaginarity not removable by local unitaries.
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Quantum mechanics over real numbers fully reproduces standard quantum theory
A real-valued framework based on Kähler space with a symplectic composition rule exactly reproduces all standard quantum mechanics predictions, including maximal CHSH violation.
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Entanglement concentration via measurement:- role of imaginarity
Complex measurements in three-qubit entanglement protocols concentrate more bipartite entanglement and cut required bond occupation probability by 22.7% in honeycomb-lattice quantum network percolation.
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Hidden Complex Structure in Quotient-Space Real Quantum Mechanics
The quotient-space real formulation of quantum mechanics is shown to be standard complex QM in real notation, not an independent real-amplitude theory, because it requires a hidden complex structure J, a superselection rule, and a balanced tensor product isomorphic to the complex tensor product.
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Comment on "Quantum theory based on real numbers cannot be experimentally falsified": On the compatibility of physical principles with information theory for fermions
The proposed postulate for choosing between real-number versions of quantum theory does not hold in Fermionic Information Theory and therefore is not general.
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Locality Implies Complex Numbers in Quantum Mechanics
Real-number quantum theories with independent sources require nonlocal maps, implying complex numbers are necessary for entanglement between independent systems.