QI_Documentation.nb

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function \!\(\*StyleBox[\\\"E\\\", \\\"TI\\\"]\) such that \
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returns a dynamical matrix of quantum \
channel\\n\!\(\*StyleBox[\\\"DynamicalMatrix\\\", \
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quantum channel given as a list of Kraus \
operators.\\n\!\(\*StyleBox[\\\"DynamicalMatrix\\\", \
\\\"Input\\\"]\)[\!\(\*StyleBox[\\\"fun\\\", \
\\\"TI\\\"]\),\!\(\*StyleBox[\\\"dim\\\", \\\"TI\\\"]\)]  - operates on a a \
function \!\(\*StyleBox[\\\"fun\\\", \\\"TI\\\"]\) acting on \
\!\(\*StyleBox[\\\"dim\\\", \\\"TI\\\"]\)-dimensional space. \\nSee also: \
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\!\(\*StyleBox[\\\"ChannelToMatrix\\\", \\\"Input\\\"]\).\"\>", 
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Cell[BoxData[
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\\\"Input\\\"]\)[\!\(\*StyleBox[\\\"K\\\", \\\"TI\\\"]\)] gives the image of \
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operators \!\(\*StyleBox[\\\"K\\\", \\\"TI\\\"]\). \
\\n\!\(\*StyleBox[\\\"Jamiolkowski\\\", \
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on \!\(\*StyleBox[\\\"dim\\\", \\\"TI\\\"]\)-dimensional space. See also: \
\!\(\*StyleBox[\\\"Superoperator\\\", \\\"Input\\\"]\), \
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\!\(\*StyleBox[\\\"MatrixSqrt\\\", \
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\!\(\*StyleBox[\\\"\[Rho]\\\", \\\"TI\\\"]\) acting on a bipartite \
(\!\(\*StyleBox[\\\"d\[Times]d\\\", \\\"TI\\\"]\))-dimensional system, \
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acting on a composite system with subsystem dimensions given in the list \!\(\
\*StyleBox[\\\"dims\\\", \\\"TI\\\"]\). List \!\(\*StyleBox[\\\"sys\\\", \
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Cell[BoxData[
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\\\"Input\\\"]\)[\!\(\*StyleBox[\\\"v\\\", \\\"TI\\\"]\)] returns projector \
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Cell[BoxData[
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\\\"Input\\\"]\)[\!\(\*StyleBox[\\\"\[Alpha]\\\", \
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of the pure state (as a state vector) for one qubit as (Cos[\[Alpha]] Exp[i\
\[Beta]], Sin[\[Alpha]]). This is equivalent to \
\!\(\*StyleBox[\\\"StateVector\\\", \\\"Input\\\"]\)[{\[Alpha],\[Beta]}]. See \
also: \!\(\*StyleBox[\\\"QubitPureState\\\", \\\"Input\\\"]\), \
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\!\(\*StyleBox[\\\"k\\\", \\\"TI\\\"]\) eigenvalues equal to 0. Thanks to \
Wojtek Bruzda. see Random Quantum Operations \
DOI[10.1016/j.physleta.2008.11.043].\"\>", "MSG"]], "Print", "PrintUsage",
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\\\"Input\\\"]\)[\!\(\*StyleBox[\\\"d\\\", \\\"TI\\\"]\)] - for integer \
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\!\(\*StyleBox[\\\"d\\\", \\\"TI\\\"]\)-dimensional space. See: T. Radtke, S. \
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\\\"RandomKet\\\", \\\"Input\\\"]\)[{\!\(\*StyleBox[\\\"d1\\\", \
\\\"TI\\\"]\),\!\(\*StyleBox[\\\"d2\\\", \\\"TI\\\"]\)}, \
\!\(\*StyleBox[\\\"type\\\", \\\"TI\\\"]\)] - for integers \
\!\(\*StyleBox[\\\"d1\\\", \\\"TI\\\"]\), \!\(\*StyleBox[\\\"d2\\\", \\\"TI\\\
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\\\"TI\\\"]\)-dimensional space with distribution specified by \
\!\(\*StyleBox[\\\"type\\\", \\\"TI\\\"]\). \\nThe parameter \
\!\(\*StyleBox[\\\"type\\\", \\\"TI\\\"]\) can be:\\n\t ''Sep'' - in this \
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case function returns maximally entangled random vectors,\\n\t \
\!\(\*StyleBox[\\\"l\\\", \\\"TI\\\"]\) list of positive numbers summing up \
to 1, the length of the list must be less or equal to the Min[\!\(\*StyleBox[\
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Cell[BoxData[
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Cell[BoxData[
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\\\"Input\\\"]\)[\!\(\*StyleBox[\\\"d\\\", \
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\!\(\*StyleBox[\\\"Bures\\\", \\\"TI\\\"]\)'' - gives a random state \
distributed according to Bures measure. \\nInteger \!\(\*StyleBox[\\\"K\\\", \
\\\"TI\\\"]\) - gives a random state generated with respect to induced \
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Cell[BoxData[
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\\\"Input\\\"]\)[\!\(\*StyleBox[\\\"d\\\", \\\"TI\\\"]\)] returns a random \
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\!\(\*StyleBox[\\\"QR\\\", \\\"TI\\\"]\) decomposition. See: F. Mezzadri,  \
NOTICES of the AMS, Vol. 54 (2007), 592-604.\"\>", "MSG"]], "Print", \
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Cell[BoxData[
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\"A\\\", \\\"TI\\\"]\)] is equivalent to \!\(\*StyleBox[\\\"Vec\\\", \
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Reshaping mapsmatrix \!\(\*StyleBox[\\\"A\\\", \\\"TI\\\"]\) into a vector \
row by row. Note, that this is different then thereshape operation in \
\!\(\*StyleBox[\\\"Matlab\\\", \\\"TI\\\"]\) or \!\(\*StyleBox[\\\"GNU Octave\
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\\nParameters {\!\(\*StyleBox[\\\"drows\\\", \
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Cell[BoxData[
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\!\(\*StyleBox[\\\"x\\\", \\\"TI\\\"]\),\!\(\*StyleBox[\\\"dim\\\", \
\\\"TI\\\"]\)] - accepts a vector or a matrix as a first argument and returns \
apropriate Schmidt decomposition. The second argument is optional and \
specifies the dimensions of subsystems.\\nIf \!\(\*StyleBox[\\\"x\\\", \\\"TI\
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\\\"TI\\\"]\) system as \\n\t \!\(\*StyleBox[\\\"sd\\\", \\\"TI\\\"]\) = \!\(\
\*StyleBox[\\\"SchmidtDecomposition\\\", \
\\\"Input\\\"]\)[\!\(\*StyleBox[\\\"mtx\\\", \\\"TI\\\"]\), {{\!\(\*StyleBox[\
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{\!\(\*StyleBox[\\\"c1\\\", \\\"TI\\\"]\), \!\(\*StyleBox[\\\"c2\\\", \
\\\"TI\\\"]\)}}];\\nand reconstruct the original matrix as\\n\t \
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\\\"TI\\\"]\)[[\!\(\*StyleBox[\\\"i\\\", \
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