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 $\sigma_x,\sigma_y,\sigma_z$
  • 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 $n$-qubit operator
  • 5.4 Gates
    • 5.4.1 hadamard operator$.$
    • 5.4.2 controlled_gate -- gate with $n$ 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