Meaning Of Quantum Fidelity

Take two copies of a state apply your implementation of a gate on one copy and apply the ideal gate on another copy this can be done on paper not in a lab and compute the fidelity between the two outputs.

Meaning of quantum fidelity. It does not refer to the space contained within a density matrix. Therefore i adapted the article to reflect this and use f as the main definition. Given two density operators and the fidelity is generally.

We analyze mean fidelity between random density matrices of size n generated with respect to various probability measures in the space of mixed quantum states. Hilbert schmidt measure bures. In the case of a density matrix fidelity represents the overlap with a reference pure state.

Fidelity as a distance measure between pure states used to be called transition probability. The existence of two. Fidelity is often used as a way of saying how good your source or quantum state preperation is by comparing the state of what you measure with what you ideally want.

The definition f is mainly propagated by the famous quantum information book by nielsen and chuang. The gate fidelity uses fidelity to decide how noisy a quantum gate is. Quantum fidelity fidelity is a popular measure of distance between density operators.

Moreover there are many fidelity bases distance measure s which can be used to define metrics on the space of density matrices 10. Quantum fidelity is the measure or precision of how close two quantum states are to each other of which the simplest example would be two qubits. Fidelity is a distance measure between quantum states.

In quantum information theory there are several inequalities relating the fidelity to other quantum state distinguishability measures 9. We propose a definition of fidelity for mixed quantum states in terms of uhlmann s transition probability formula f ϱ 1 ϱ 2 trace ϱ 1 ϱ 2 ϱ 1 1 2 2 and give new elementary proofs of its essential properties. Channel fidelity is a measure of how well information is retained within the channel and is related to quantum fidelity.