Quantum fidelity measures for mixed states

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum Physics

Background:

• Quantum technologies rely on performance metrics like fidelity for comparing quantum states.
• Fidelity measurement is complex for mixed quantum states, unlike simpler pure states.
• Numerous quantum fidelity measures have been proposed in scientific literature.

Purpose of the Study:

• To review and define the essential properties of quantum fidelity measures.
• To compare existing quantum fidelity measures based on these properties.
• To identify measures suitable for practical quantum applications.

Main Methods:

• Systematic review of proposed quantum fidelity measures.
• Analysis of mathematical properties required for fidelity measures.
• Comparative study of different fidelity measures with detailed proofs.

Main Results:

• Identified large classes of quantum fidelity measures satisfying all required properties.
• Demonstrated that multiple valid fidelity measures exist, analogous to norms and entropies.
• Provided detailed proofs for the properties of compared fidelity measures.

Conclusions:

• Several quantum fidelity measures are suitable for quantifying performance in quantum technologies.
• The choice of fidelity measure depends on specific application requirements.
• Understanding these measures is vital for advancements in quantum communication, computing, and simulation.