Canonical form of three-fermion pure-states with six single particle states
- Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3G1 (Canada)
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543 (Singapore)
- Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1 (Canada)
We construct a canonical form for pure states in Λ³(C⁶), the three-fermion system with six single particle states, under local unitary (LU) transformations, i.e., the unitary group U(6). We also construct a minimal set of generators of the algebra of polynomial U(6)-invariants on Λ³(C⁶). It turns out that this algebra is isomorphic to the algebra of polynomial LU-invariants of three-qubits which are additionally invariant under qubit permutations. As a consequence of this surprising fact, we deduce that there is a one-to-one correspondence between the U(6)-orbits of pure three-fermion states in Λ³(C⁶) and the LU orbits of pure three-qubit states when qubit permutations are allowed. As an important byproduct, we obtain a new canonical form for pure three-qubit states under LU transformations U(2) × U(2) × U(2) (no qubit permutations allowed)
- OSTI ID:
- 22306088
- Journal Information:
- Journal of Mathematical Physics, Vol. 55, Issue 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
Similar Records
Local unitary invariants for N-qubit pure states
On the oscillator realization of conformal U(2, 2) quantum particles and their particle-hole coherent states