(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 28579, 916] NotebookOptionsPosition[ 26156, 834] NotebookOutlinePosition[ 26627, 852] CellTagsIndexPosition[ 26584, 849] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"2", "-", "2"}]], "Input", CellChangeTimes->{{3.569613626184636*^9, 3.569613626781115*^9}}], Cell[BoxData["0"], "Output", CellChangeTimes->{3.569613628412166*^9, 3.5696143735896893`*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"p_", "\[CircleTimes]", "q_"}], ":=", RowBox[{"KroneckerProduct", "[", RowBox[{"p", ",", "q"}], "]"}]}]], "Input", CellChangeTimes->{{3.569614282694995*^9, 3.569614337789153*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"adj", "[", "x_", "]"}], ":=", RowBox[{"Conjugate", "[", RowBox[{"Transpose", "[", "x", "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.569616235906131*^9, 3.569616253227722*^9}}], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.569613640367957*^9}], Cell[CellGroupData[{ Cell["Partial Traces as Operations", "Title", CellChangeTimes->{{3.5696136733937073`*^9, 3.569613681951749*^9}}], Cell["\<\ Nicholas Wheeler 11 February 2013\ \>", "Text", CellChangeTimes->{{3.569613689032159*^9, 3.569613704030484*^9}}, FontSize->10], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.569613714259585*^9}], Cell[CellGroupData[{ Cell["Introduction", "Subsection", CellChangeTimes->{{3.569613748996591*^9, 3.569613754491609*^9}}], Cell[TextData[{ "I have recently been concerned on the one hand with partial traces, and on \ the other hand with \"quantum operations\" in the sense of Kraus. 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