Coherence resource power of isocoherent states

Area of Science:

• Quantum Information Science
• Quantum Foundations

Background:

• Quantum states possess coherence, a key resource in quantum information processing.
• Comparing quantum states based on their coherence is crucial for understanding quantum resource theories.

Purpose of the Study:

• To investigate the comparability of quantum states with equal coherence values under incoherent operations.
• To determine if states with intermediate coherence are distinguishable based on their resource power.

Main Methods:

• Analysis of the preorder of incoherent operations on quantum states.
• Examination of pure states in quantum systems with dimensions greater than two.
• Consideration of well-behaved coherence measures, including relative entropy of coherence for qubit mixed states.

Main Results:

• States with null or maximum coherence are equivalent under incoherent operations.
• For dimensions greater than two, infinite incomparable pure states exist for any intermediate coherence value.
• Incomparable isocoherent states can exist for qubit mixed states, depending on the coherence measure used.

Conclusions:

• The comparability of quantum states based on coherence is highly dependent on the coherence value and system dimension.
• The existence of incomparable states highlights the complexity of quantifying and comparing quantum coherence as a resource.