Adversarial Quantum Channel Discrimination

Area of Science:

• Quantum Information Theory
• Quantum Cryptography
• Statistical Decision Theory

Background:

• Quantum channel discrimination is crucial for quantum communication security.
• Existing methods often focus on "best-case" scenarios, leaving adversarial settings less understood.
• Asymmetric hypothesis testing is a key framework for analyzing error probabilities.

Purpose of the Study:

• To introduce a novel framework for quantum channel discrimination in an adversarial setting.
• To characterize the optimal type-II error exponent in this adversarial framework.
• To establish a connection between quantum cryptography and adversarial channel discrimination.

Main Methods:

• Development of a new quantum channel divergence measure (minimum output channel divergence).
• Application of asymmetric hypothesis testing to adversarial quantum channel discrimination.
• Reframing entropy accumulation as an adversarial channel discrimination problem.

Main Results:

• The optimal type-II error exponent is precisely characterized by the minimum output channel divergence.
• This result is a direct analog of the quantum Stein's lemma for adversarial settings.
• The optimal error exponent is achievable via simple nonadaptive adversarial strategies and is efficiently computable.

Conclusions:

• The new framework provides a complete understanding of the ultimate limits of quantum channel discrimination.
• The minimum output channel divergence offers a powerful tool for analyzing quantum channels in adversarial scenarios.
• This work establishes a significant link between quantum information theory and quantum cryptography through adversarial discrimination.