nt - p h / 03 06 14 4 v 1 2 2 Ju n 20 03 Operator - Schmidt decompositions and the Fourier transform , with applications to the operator - Schmidt numbers of unitaries

Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries

The operator-Schmidt decomposition is useful in quantum information theory for quantifying the nonlocality of bipartite unitary operations. We construct a family of unitary operators on C ⊗ C whose operatorSchmidt decompositions are computed using the discrete Fourier transform. As a corollary, we produce unitaries on C ⊗ C with operatorSchmidt number S for every S ∈ {1, ..., 9}. This corollary...

Operator-schmidt Decomposition of the Quantum Fourier Transform on C N 1 ⊗ C N 2

Operator-Schmidt decompositions of the quantum Fourier transform on C N1 ⊗ C N2 are computed for all N1,N2 ≥ 2. The decomposition is shown to be completely degenerate when N1 is a factor of N2 and when N1 > N2. The first known special case, N1 = N2 = 2 , was computed by Nielsen in his study of the communication cost of computing the quantum Fourier transform of a collection of qubits equally di...

ua nt - p h / 03 06 11 5 v 1 1 7 Ju n 20 03 THE GEOMETRY OF ENTANGLEMENT : METRICS , CONNECTIONS AND THE GEOMETRIC PHASE

Using the natural connection equivalent to the SU (2) Yang-Mills instanton on the quaternionic Hopf fibration of S 7 over the quaternionic projective space HP 1 ≃ S 4 with an SU (2) ≃ S 3 fiber the geometry of entanglement for two qubits is investigated. The relationship between base and fiber i.e. the twisting of the bundle corresponds to the entanglement of the qubits. The measure of entangle...

ua nt - p h / 03 06 19 6 v 1 2 9 Ju n 20 03 On Shor ’ s channel extension and constrained channels

ua nt - p h / 03 06 16 2 v 1 2 4 Ju n 20 03 Quasi exactly solvable ( QES ) equations with multiple algebraisations ∗

We review three examples of quasi exactly solvable (QES) Hamitonians which possess multiple algebraisations. This includes the most prominent example, the Lamé equation, as well as recently studied many-body Hamiltonians with Weierstrass interaction potential and finally, a 2× 2 coupled channel Hamiltonian.