Introduction to Quantum Physics and Information Processing

List of Symbols and Notations

z

∗

Complex Conjugate, i →

−i of a complex number z

|ψi A general unknown quan-

tum state vector

|0i Single qubit basis state,

positive eigenstate of σ

z

|1i Single qubit basis state,

negative eigenstate of σ

z

|xi A generic computational

basis state

ˆ

A An operator, also repre-

sented as a matrix

ˆ

A

T

Transpose of the matrix A,

obtained by interchanging

the rows and columns

A

†

Adjoint, or complex conju-

gate transpose (A

∗

)

T

of a

matrix A

[A, B] Commutator AB − BA of

the given matrices

{A, B} Anti-commutator, AB +

BA of the given matrices

Tr(X) Trace of matrix X

Tr

A

(X) Partial trace over system A

P(r) Probability of occurrence

of value r

ˆ

P

i

Projection ...