Quantum / CONCEPT
A property-T circulant with universal perfect state transfer
The circulant Circ(0, a, conj(a)) with a = (-4 sqrt(3) + i)/7 is a Hermitian circulant on three vertices whose nonzero entries have modulus 1 and whose continuous-time quantum walk has perfect state transfer between every pair of vertices, yet it is switching equivalent neither to K_2 nor to Circ(0, -i, i). This refutes the conjecture of E. Connelly, N. Grammel, M. Kraut, L. Serazo and C. Tamon (arXiv:1701.04145) that these two are the only circulants with property T and universal perfect state transfer.
A counterexample on three vertices
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Structural connections
- A 23-edge coupling realizes the ten-mode Fourier transformstructural-affinity · Closed
- Analytic Flow Generationstructural-affinity · Closed
- Conservation And Autonomy Are Distinctstructural-affinity · Closed
- CZX parent Lindbladian steady statestructural-affinity · Closed
- Hamiltonian Effect Completion Generatorstructural-affinity · Closed
- Infinitesimal Reducing Criterionstructural-affinity · Closed
- No perfect state transfer at time pi on rational paths with 2^k + 1 verticesstructural-affinity · Closed
- Projection Probability Flowstructural-affinity · Closed
- Song and Lin's parity conjecture for zero transfer is falsestructural-affinity · Closed
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