MatsumotoFidelity

MatsumotoFidelity
Computes the Matsumoto fidelity of two density matrices
Other toolboxes required	none
Related functions	Fidelity
Function category	Norms and distance measures
Usable within CVX?	yes (concave)

MatsumotoFidelity is a function that computes the Matsumoto fidelity between two quantum states $\rho$ and $\sigma$, defined by \[F(\rho,\sigma) := \mathrm{Tr}(\rho\#\sigma),\] where \[\rho\#\sigma := \rho^{1/2}\Big(\rho^{-1/2}\sigma\rho^{-1/2}\Big)\rho^{1/2}.\]

Syntax

• FID = MatsumotoFidelity(RHO,SIGMA)

Argument descriptions

• RHO: A density matrix.
• SIGMA: A density matrix.

Examples

Pure states

If $\rho = |v\rangle\langle v|$ and $\sigma = |w\rangle\langle w|$ are both pure states then their Matsumoto fidelity simply equals 1 if they are parallel and zero otherwise:

>> v = RandomStateVector(4);
>> w = RandomStateVector(4);
>> MatsumotoFidelity(v*v',w*w')

ans =

   1.7454e-05

This highlights one slight limitation of this function: it is only accurate to 4 or so decimal places when both inputs are non-invertible (it is much more accurate if at least one input is invertible).

Source code

Click here to view this function's source code on github.