Symplectic space and orthogonal space of n qubits

Details Symplectic space and orthogonal space of n qubits Symplectic space and orthogonal space of n qubits

2010-11-14

arxiv.org/abs/1011.3187v1

Physics

Quantum Physics

8 pages

Scientific paper

In the Hilbert space of n qubits, we introduce the symplectic space (n odd) and the orthogonal space (n even) via the spin-flip operator. Under this mathematical structure we discuss some properties of n qubits, including homomorphically mapping the local operations of n qubits into the symplectic group or orthogonal group, and prove that the generalized ``magic basis'' is just the bi-orthonormal basis (that is, the orthonormal basis of both Hilbert space and the orthogonal space ). Finally, an example is given to discuss the application in physics of this mathematical structure.

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