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arXiv · 1507.03350

A Complete Set of Invariants for LU-Equivalence of Density Operators

Jacob Turner·Jason Morton
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Abstract

We show that two density operators of mixed quantum states are in the same local unitary orbit if and only if they agree on polynomial invariants in a certain Noetherian ring for which degree bounds are known in the literature. This implicitly gives a finite complete set of invariants for local unitary equivalence. This is done by showing that local unitary equivalence of density operators is equivalent to local ${\rm GL}$ equivalence and then using techniques from algebraic geometry and geometric invariant theory. We also classify the SLOCC polynomial invariants and give a degree bound for generators of the invariant ring in the case of $n$-qubit pure states. Of course it is well known that polynomial invariants are not a complete set of invariants for SLOCC.

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BibTeXRIS

Jacob Turner, Jason Morton. 2015-07-13. A Complete Set of Invariants for LU-Equivalence of Density Operators. https://doi.org/10.3842/sigma.2017.028

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