Tomographer::IndepMeasTomoProblem< MatrQ_, LLHValueType_, UseCLoopInstead > Struct Template Reference

Stores data for a tomography problem with independent measurements. More...

#include <tomographer/tomoproblem.h>

Public Types
typedef MatrQ_	MatrQ
typedef LLHValueType_	LLHValueType

Public Member Functions
	IndepMeasTomoProblem (MatrQ matq_)
	Constructs an IndepMeasTomoProblem instance. More...
LLHValueType	calc_llh (const typename MatrQ::VectorParamType &x) const
	Calculates the log-likelihood function. More...

Public Attributes
const MatrQ	matq
	The data types for this problem.
const int	dim
	The dimension of the Hilbert space.
const int	dim2
	The square of the dimension of the Hilbert space, dim2=dim*dim.
const int	Ndof
	The number of degrees of freedom, \( \text{Ndof} = \text{dim}\times\text{dim}-1 \).
LLHValueType	NMeasAmplifyFactor
	A factor to artificially amplify the number of measurements by.
MatrQ::VectorParamListType	Exn
	The POVM Entries, parameterized with X-param (param_herm_to_x())
MatrQ::FreqListType	Nx
	The frequency list, i.e. number of times each POVM effect was observed.
MatrQ::MatrixType	rho_MLE
	Maximum likelihood estimate as density matrix.
MatrQ::MatrixType	T_MLE
	Maximum likelihood estimate as T-parameterized density matrix. More...
MatrQ::VectorParamType	x_MLE
	X-Parameterized version of rho_MLE (param_herm_to_x())

Detailed Description

template<typename MatrQ_, typename LLHValueType_ = double, bool UseCLoopInstead = false>
struct Tomographer::IndepMeasTomoProblem< MatrQ_, LLHValueType_, UseCLoopInstead >

Stores data for a tomography problem with independent measurements.

Stores data corresponding to a tomography probem. This is given by

• a state space dimension
• a list of POVM effects
• a list of frequencies, i.e. how many times each POVM effect was observed
• a Maximum Likelihood Estimate, i.e. the density operator which maximizes the likelihood function

Additionally, we store also a factor by which to (artificially) amplify all the frequencies by, i.e. to effectively fake more measuremnts with the same statistics.

Definition at line 57 of file tomoproblem.h.

Constructor & Destructor Documentation

template<typename MatrQ_ , typename LLHValueType_ = double, bool UseCLoopInstead = false>

Tomographer::IndepMeasTomoProblem< MatrQ_, LLHValueType_, UseCLoopInstead >::IndepMeasTomoProblem ( MatrQ  matq_ )

inline

Constructs an IndepMeasTomoProblem instance.

Note

The members Exn and Nx are left uninitialized, because we don't know how many POVM effects there will be yet. This information will anyway probably be read later from an input file or such.

Definition at line 96 of file tomoproblem.h.

Member Function Documentation

template<typename MatrQ , typename LLHValueType , bool UseCLoopInstead>

LLHValueType Tomographer::IndepMeasTomoProblem< MatrQ, LLHValueType, UseCLoopInstead >::calc_llh ( const typename MatrQ::VectorParamType &  x ) const

inline

Calculates the log-likelihood function.

Returns

the value of the -2-log-likelihood function of this data at the point x, defined as

\[ \lambda(\texttt{x}) = -2\sum_k \texttt{Nx[k]}\,\ln\mathrm{tr}(\texttt{Exn[k]}\,\rho(\texttt{x})) . \]

Definition at line 179 of file tomoproblem.h.

Member Data Documentation

template<typename MatrQ_ , typename LLHValueType_ = double, bool UseCLoopInstead = false>

MatrQ::MatrixType Tomographer::IndepMeasTomoProblem< MatrQ_, LLHValueType_, UseCLoopInstead >::T_MLE

Maximum likelihood estimate as T-parameterized density matrix.

The T-parameterization is such that \( \rho = T T^\dagger \) .

Definition at line 86 of file tomoproblem.h.

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The documentation for this struct was generated from the following file:

• tomographer/tomoproblem.h (v1.1)