Bounding the Benefit of Adaptivity in Quantum Metrology Using the Relative Fidelity

Area of Science:

• Quantum Information Science
• Quantum Communication
• Quantum Metrology

Background:

• Quantum protocols for channel discrimination and parameter estimation often use adaptive strategies or entangled probe states.
• The performance bounds for such protocols are challenging to establish due to these complexities.

Purpose of the Study:

• To introduce a new quantity, relative fidelity, for bounding the performance of quantum information protocols.
• To establish lower bounds on the fidelity of output states for general adaptive discrimination and parameter estimation protocols.

Main Methods:

• Definition of relative fidelity for pairs of channels and input states.
• Constraining input states by a minimum fidelity threshold.
• Minimizing relative fidelity over valid input state pairs to find the minimum relative fidelity.
• Deriving lower bounds on output state fidelity using minimum relative fidelity.
• Establishing a continuity bound for relative fidelity.

Main Results:

• A lower bound on the fidelity between output states is established in terms of the minimum relative fidelity.
• The performance of general adaptive quantum discrimination and parameter estimation protocols can be bounded.
• A continuity bound for relative fidelity confirms that N-use quantum Fisher information is at most N^2 times the one-shot QFI.

Conclusions:

• Relative fidelity provides a powerful tool for bounding the performance of adaptive quantum information protocols.
• The introduced framework allows for rigorous analysis of the ultimate limits in quantum channel discrimination and parameter estimation.
• This work contributes to understanding the fundamental capabilities and limitations of quantum information processing.