How many invariant polynomials are needed to decide local unitary equivalence of qubit states?

Journal Article · Sun Sep 15 00:00:00 EDT 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4819499· OSTI ID:22217989

Maciążek, Tomasz ^[1]; Oszmaniec, Michał ^[1]; Sawicki, Adam ^[1]

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1. Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa (Poland)

Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for the minimal number of invariant polynomials needed for solving local unitary (LU) equivalence problem, that is, problem of deciding if two states can be connected by local unitary operations. Interestingly, this number is not the same for every collection of the spectra. Some spectra require less polynomials to solve LU equivalence problem than others. The result is obtained using geometric methods, i.e., by calculating the dimensions of reduced spaces, stemming from the symplectic reduction procedure.

• OSTI ID: 22217989
• Journal Information: Journal of Mathematical Physics, Vol. 54, Issue 9; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DENSITY MATRIX
GEOMETRY
POLYNOMIALS
QUANTUM COMPUTERS
QUANTUM ENTANGLEMENT
SPACE
SPECTRA