Strategies for single-shot discrimination of process matrices

Area of Science:

• Quantum Information Science
• Quantum Causality
• Process Matrices

Background:

• Causality is a growing area of interest in quantum information research.
• Process matrices offer a universal framework for defining causal structures.
• Distinguishing between different causal structures is crucial for quantum information processing.

Purpose of the Study:

• To develop an exact expression for the optimal probability of single-shot discrimination between process matrices.
• To explore the application of convex cone structure theory and semidefinite programming to this discrimination task.
• To analyze the discrimination of process matrices representing quantum combs, comparing adaptive and non-signalling strategies.

Main Methods:

• Derivation of an exact expression for optimal discrimination probability.
• Utilizing convex cone structure theory.
• Formulating the discrimination task as a semidefinite programming problem, leading to a trace norm quantification and an optimal realization.

Main Results:

• An exact expression for the optimal probability of distinguishing process matrices is provided.
• A semidefinite programming approach is developed to calculate the distance between process matrices using the trace norm.
• Two classes of perfectly distinguishable process matrices are identified.
• For quantum combs, the probability of distinguishing process matrices is independent of whether adaptive or non-signalling strategies are employed.

Conclusions:

• The study offers a robust method for quantifying the distinguishability of quantum causal structures.
• Semidefinite programming provides an efficient tool for analyzing process matrix discrimination.
• The choice of strategy (adaptive vs. non-signalling) does not impact discrimination success for quantum comb structures.