[lemma=duality | word=that] [lemma=□]
[lemma=duality | word=that] [lemma=","]
[lemma=duality | word=that] [lemma=duality]
Finite dimensional vector space , inner-product , complex numbers , linear adjoints , unitary maps , projectors , trace , tensor product of Hilbert spaces , Dirac notation , bit , qubit , entanglement , map-state duality , no-cloning , quantum circuits , quantum gates , Shor 's algorithm , Grover 's algorithm , quantum teleportation , quantum key-exchange , teleportation and measurement based quantum computing , decoherence , mixed states , quantum information , quantum logic , quantum categorical semantics . In order to do that , one must understand who is going up , as well as the reasons why ( 1 ) the group going down is going down and ( 2 ) the group going up is going up . The optimality system follows from general results for convex state-constrained control problems by means of the theory of convex duality , using a suitable perturbation . Another is the fascination with the triplicity that issues from duality , an idea that has stimulated us from its handling by Nicholas Cusanus to its handling by Joyce in Finnegans Wake . He is operating on the serene assumption that , since it feels right to him , it will be right with the audience . One thing that is guaranteed about the order that rewrites are tried is that , for any given subformula , earlier rules in the rule set will be tried for that subformula before later ones . " It 's this duality , she says , that makes Shackleton such a compelling case , knocking him off a mythologized pedestal and into the messy stew of humanity , where good and bad , success and failure coexist . These comments asserted that , therefore , consumer complaints are not an appropriate monitoring tool . Lack of economic substance - - Professor Michael Graetz recently defined a tax shelter as " a deal done by very smart people that , absent tax considerations , would be very stupid .