Effective rationality for local unitary invariants of mixed states of two qubits
We calculate the field of rational local unitary invariants for mixed states of two qubits, by employing methods from algebraic geometry. We prove that this field is rational (i.e. purely transcendental), and that it is generated by nine algebraically independent polynomial invariants. We do so by constructing a relative section, in the sense of invariant theory, whose Weyl group is a finite abelian group. From this construction, we are able to give explicit expressions for the generating invariants in terms of the Bloch matrix representation of mixed states of two qubits. We also prove similar rationality results for the local unitary invariants of symmetrically mixed states of two qubits. We also provide a sketch of how to generalize our results to the case of an arbitrary number of qubits. Our results apply to both complex-valued and real-valued invariants.
- Research Organization:
- Wayne State Univ., Detroit, MI (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- Grant/Contract Number:
- SC0022134
- OSTI ID:
- 2578859
- Journal Information:
- Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 14 Vol. 57; ISSN 1751-8113
- Publisher:
- IOP PublishingCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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