Quantum Sequential Hypothesis Testing

Area of Science:

• Quantum Information Processing
• Quantum Physics
• Statistical Inference

Background:

• Quantum hypothesis testing is crucial for distinguishing quantum states.
• Current methods often require a predetermined number of quantum state copies.
• Achieving high accuracy in state discrimination is computationally demanding.

Purpose of the Study:

• To introduce sequential analysis for quantum hypothesis testing.
• To determine the ultimate lower bounds on the average number of quantum state copies required.
• To develop strategies that achieve these lower bounds.

Main Methods:

• Sequential analysis applied to quantum hypothesis testing.
• Derivation of lower bounds on the average number of copies.
• Development of a block-sampling strategy.
• Analysis of strategies for qubit and general quantum states.

Main Results:

• Ultimate lower bounds on the average number of copies for quantum state discrimination were established.
• A block-sampling strategy achieves these bounds for certain state classes.
• Sequential strategies, especially for qubit states using local measurements, outperform collective measurements on fixed copies.
• For pure states, finite average samples are needed even for perfect discrimination (ε=0).

Conclusions:

• Sequential analysis provides an optimal approach to quantum hypothesis testing.
• The derived bounds offer fundamental limits on resources for quantum state discrimination.
• Practical strategies exist that can achieve these optimal bounds, improving efficiency.