Editing Full Quantum state tomography with Maximum Likelihood Estimation (section)

==Notation==
* <math>d</math>: Dimension of Hilbert space
* <math>\rho</math>: Density matrix of the prepared quantum state
* <math>E_j</math>: Different measurement operators of a selected basis, where <math>j = 1, ..., d^2</math>
* <math>A</math>: Select basis of measurement with the different measurement operators <math>E_j</math>
* <math>p_j</math>: Probability of the state corresponding to <math>E_j</math>
* <math>\bar{p_j}</math>: Expected value of <math>p_j</math>. <math>\bar{p_j} = N\langle\psi_j|\rho|\psi_j\rangle</math>
* <math>N</math>: normalization parameter which can be determined from the data. 
* <math>n</math>: Number of single shots corresponding to a measurement operator. This is used to calculate the probability
* <math>m_j</math>: Sample average of <math>N</math> single shot measurements of <math>E_j</math>. 
* <math>m_{ij}</math>: Outcome of the <math>i^{th}</math> measurement from <math>N</math> single shot measurements. <math>m_{ij} \in \{0,1\}</math>
* <math>E(m_j)</math>: Expected value of <math>m_j</math>
* <math>E(m_{ij})</math>: Expected value of <math>m_{ij}</math>
* <math>\hat{\rho_p}</math>: Manifestly physical density matrix of the prepared quantum sate. This is given by the formula <math>\hat{\rho_p}</math>, <math>\hat{\rho_p}(t) = \hat{T^{\dagger}}(t) \hat{T}(t) / tr\{ \hat{T}^{\dagger}(t) \hat{T}(t)\}</math>
* <math>\hat{T}(t)</math>: Formula for multiple qubits which is used in reconstructing <math>\hat{\rho_p}</math>
* <math>t</math>: Short form of <math>t_i, i=1, .., d^2</math>
* <math>L(t_1, t_2, ..., t_{n^2})</math>: Likelihood function