Ultimate Limits for Quickest Quantum Change-Point Detection

Area of Science:

• Quantum Information Science
• Sequential Analysis
• Statistical Signal Processing

Background:

• Abrupt changes in data streams signal critical events requiring timely detection.
• Quickest change-point detection minimizes detection delay under bounded false alarm rates.
• Sequential analysis is fundamental for real-time data processing.

Purpose of the Study:

• To develop the quantum counterpart of quickest change-point detection for quantum data streams.
• To establish fundamental limits for detecting changes in quantum information.
• To explore strategies for online change-point detection in quantum channels.

Main Methods:

• Deriving a lower bound on the mean minimum detection delay for general quantum strategies.
• Analyzing adaptive collective measurements on growing quantum data strings.
• Developing block-based measurement strategies to approach the quantum limit.

Main Results:

• A lower bound on the mean minimum delay for quantum quickest change-point detection is established.
• Strategies achieving this lower bound are demonstrated, defining the ultimate quantum limit.
• The performance of online change-point detection in quantum channels is discussed.

Conclusions:

• The study establishes the theoretical limits for quantum quickest change-point detection.
• Practical strategies are proposed that asymptotically reach these quantum limits.
• This work lays the foundation for change detection in quantum information processing and communication.