Discrimination Power of a Quantum Detector

Area of Science:

• Quantum Information Science
• Quantum Measurement Theory
• Statistical Inference

Background:

• Distinguishing quantum states is crucial for quantum information processing.
• Existing methods often optimize over measurements for fixed states, or vice-versa.
• Quantifying the intrinsic error of a measurement device is essential for its practical application.

Purpose of the Study:

• To determine the fundamental limits of a quantum measurement device's ability to discriminate between two quantum states.
• To quantify the intrinsic error associated with a measurement device.
• To explore the impact of multiple measurements and data processing on discrimination power.

Main Methods:

• Minimizing error probabilities (averaged and constrained) over all possible n-partite input states.
• Deriving asymptotic rates of error decrease for large numbers of measurements (n).
• Establishing Chernoff-type and dual Stein's lemma/Hoeffding bounds for discrimination limits.

Main Results:

• Identical copies of input states are optimal for asymptotic discrimination.
• Derived Chernoff-type bounds for averaged error rates, dual to standard Chernoff bounds.
• Obtained optimal asymptotic rates for constrained error probabilities, dual to Stein's lemma and Hoeffding's bound.
• Demonstrated that adaptive protocols do not enhance asymptotic discrimination rates.

Conclusions:

• The derived asymptotic rates quantify the ultimate discrimination power of any quantum measurement device.
• These findings provide fundamental benchmarks for the performance of quantum measurement devices.
• The study highlights the importance of state preparation in optimizing quantum discrimination tasks.