Quantum / CONCEPT
The signed Pauli sum bound fails for three qubits
For three qubits, one choice of signs makes the signed sum of all 63 non-identity Pauli words an operator with eigenvalue 21, hence of norm at least 21, above (sqrt(3) + 1)^3 - 1 = 9 + 6 sqrt(3). This refutes the conjecture of O. Liabotro (arXiv:1607.02667, Eq. (78)) that every such signed sum on m qubits has norm at most (sqrt(3) + 1)^m - 1.
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DIRECT PREREQUISITES2
DIRECT CONSEQUENCES2
PROOF DEPTH5
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The conjectured bound fails for three qubits
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Proof dependencyStructural affinityDocument link
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RELATED KNOWLEDGE
Structural connections
- A SIC-compound from eight Hoggar SICsstructural-affinity · Closed
- A stabilizer code without universal logical Z supportstructural-affinity · Closed
- A stabilizer measurement beyond every maximally entangled onestructural-affinity · Closed
- Equal degree differences do not determine stored workstructural-affinity · Closed
- Local-unitary inequivalence of two weight-isometric pairs of stabilizer codesstructural-affinity · Closed
- Odd negative-line parity in linear doiliesstructural-affinity · Closed
- Pauli rotations with a hypersurface of critical valuesstructural-affinity · Closed
- Rank-One Born Reductionstructural-affinity · Closed
- Separable states outside every local-unitary stabilizer framestructural-affinity · Closed
- The sharp Hoggar-SIC sum negativitystructural-affinity · Closed
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