Comment #5 on issue 3199 by [email protected]: Finish implementing
density operator/matrix
http://code.google.com/p/sympy/issues/detail?id=3199
Here is the summary of Trace/Partial Traces operations and related methods
that
would be needed. Please review.
Trace operation functionality in quantum module ( including partial trace )
a. A generic Tr expression that takes a matrix , as the operand. This will
inherit from Expr. ( we still need to determine a closest Expr to use as
template ).
Tr(matrix) = general trace formula, can use existing matrix function.
b. Tr( A \otimes B ) = Tr(A)Tr(B)
Same applies to > 2 tensor products.
The general density operator will have
______________________________________
1. Partial Trace function of following form in the density operator class:
TrPartial( density operator of set of tensor products , offset/offset
range to
trace)
eg. TrPartial( density( a_1 \otimes b_1, a_2 \otimes b_2, ..), 0) to
trace B
TrPartial( density( a_1 \otimes b_1 \otimes c_1, a_2 \otimes b_2
\otimes c_2, ..), 1,2) to trace BC
where a_i \in A, b_i in \B , c_i in C
(alternatively, should we create a partial trace expression?).
Qubit Density Operator
______________________
The qubit density operator,will also have a partial trace function
The qubit density operator can have sequence of 1-qubit states, n-qubit
states(as tensor products, or qubits)
1. TrPartial ( density_operator( ) , range of qubits to trace ).
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