8,427 research outputs found
Local unitary versus local Clifford equivalence of stabilizer states
We study the relation between local unitary (LU) equivalence and local
Clifford (LC) equivalence of stabilizer states. We introduce a large subclass
of stabilizer states, such that every two LU equivalent states in this class
are necessarily LC equivalent. Together with earlier results, this shows that
LC, LU and SLOCC equivalence are the same notions for this class of stabilizer
states. Moreover, recognizing whether two given stabilizer states in the
present subclass are locally equivalent only requires a polynomial number of
operations in the number of qubits.Comment: 8 pages, replaced with published versio
Some applications of differential topology in general relativity
Recently, there have been several applications of differential and algebraic
topology to problems concerned with the global structure of spacetimes. In this
paper, we derive obstructions to the existence of spin-Lorentz and pin-Lorentz
cobordisms and we show that for compact spacetimes with non-empty boundary
there is no relationship between the homotopy type of the Lorentz metric and
the causal structure. We also point out that spin-Lorentz and tetrad cobordism
are equivalent. Furthermore, because the original work [7] on metric homotopy
and causality may not be known to a wide audience, we present an overview of
the results here.Comment: 24 pages LaTeX, 8 xfig figures available from A. Chamblin at
[email protected], published in Jour. of Geometry and Physics, 13,
pages 357-377 (1994
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