Contents
1 Introduction
1.1 Acknowledgments
2
Using
Maxima
. features important for
qinf
3 Representation of states and operators
4 Creating instances of states
4
.
1
ketz
,
braz
,
ketx
,
brax
,
kety
,
bray
-- multipartite eigenstate kets and bras of
4
.
2
ket_n
,
bra_n
-- alternate form of
ketz
, etc
4
.
3
proj
-- Density matrix representation of a pure state (projection operator)
4
.
4
otimes
,
tensor_product
,
tensor_power
-- Creating state vectors with the tensor product
4
.
5
schmidt_ket
-- bipartite ket in Schmidt basis
4
.
6
bell
and
belln
-- Bell state kets in computational basis
4
.
7
ghz
and
ghzn
-- GHZ state kets
4
.
8
werner
-- Werner state density matrix
5 Creating and using operators
5.1 Pauli matrices
5
.
1
.
1
pauli
-- pauli matrices
5
.
1
.
2
pauli_product
-- tensor product of pauli matrices
5
.
1
.
3
pauliexp
-- expansion of operator in terms of tensor products of pauli matrices
5
.
1
.
4
invpauliexp
-- inverse of expansion in terms of tensor products of pauli matrices
5
.
1
.
5
correlation_tensor
-- retrieve component of correlation tensor by index
5
.
1
.
6
Using
pauliexp
and
invpauliexp
; an example
5
.
2
spinor_rotation
,
spinor_rotation_trig
5
.
3
insert_operator
-- insert single qubit operators in
-qubit operator
5.4 Gates
5
.
4
.
1
hadamard
operator
5
.
4
.
2
controlled_gate
-- gate with
control qubits
5
.
4
.
3
cnot
,
cphase
,
crot
5
.
4
.
4
swap
5
.
4
.
5
toffoli
5
.
4
.
6
fredkin
6 Entanglement
6
.
1
ptrace
,
ptracen
-- partial trace
6
.
2
entropy
-- von Neumann entropy
6
.
3
renyi_entropy
6
.
4
tsallis_entropy
6
.
5
purity
6
.
6
fidelity
6
.
7
concurrence
-- Wootter's concurrence
6
.
8
separable
-- test for separability
6.9 An entangled pure global state has mixed reduced states
7 More operators and functions
7.1 Predicate functions -- testing for properties
7.1.1 identitymatrixp
7.1.2 ketp, brap, braketp
7.1.3 square_matp
7.2 Miscellaneous
7.2.1 normalize_vector
7.2.2 normalize_matrix
8 Entanglement. longer examples
8.1 Entanglement swapping
Bibliography
Index
John Lapeyre 2008-09-02