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- Deprecated function: SelectQuery::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
The accessible information is the amount of
classical information that can be extracted from a quantum system by an
optimal measurement when the information is encoded using a particular
ensemble
of quantum states.
More precisely, consider an ensemble ℰ = {(pX, ρX)}
where the probabilities come from the random variable X. Let YP be the random
variable that denotes the outcomes of the measurement described by a
POVM
P. The
mutual
information between X and
Y
I(X : YP) = H(X) − H(X|YP)
quantifies how much information Y contains about X. The accessible information is the
maximum of this when all possible POVMs are possible,
Iacc(ℰ) = maxPI(X : YP).
Bounds
The accessible information is upper bounded by the
Holevo
quantityHolevo1973,
Iacc(ℰ) ≤ χ(ℰ) = S(∑pXρX) − ∑pXS(ρX),
where S is the
von
Neumann entropy.
By substituting the von Neumann entropy in the Holevo quantity for
the
subentropy
Q, one gets a lower bound
JozsaRobbWootters1994,
Iacc(ℰ) ≥ χ(ℰ) = Q(∑pXρX) − ∑pXQ(ρX).
SOMIM (open-source code)
There is an open-source program code called SOMIM
(Search for Optimal
Measurements by an Iterative
Method), which calculates the maximal mutual
information (accessible information). For a given set of statistical
operators, SOMIM finds the POVMs that maximize the accessed information,
and thus determines the accessible information and one or all of the
POVMs that retrieve it. The maximization procedure is a steepest-ascent
method that follows the gradient in the POVM space, and also uses
conjugate gradients for speed-up.
The complete set of files including the codes and manual can be found
at the SOMIM website: http://www.quantumlah.org/publications/software/SOMIM/.
Category:Quantum
Information Theory
Last modified:
Monday, October 26, 2015 - 17:56
