Investigating quantum metrology in noisy channels

Area of Science:

• Quantum Information Science
• Quantum Metrology
• Quantum Communication

Background:

• Quantum entanglement is crucial for quantum information processing and metrology.
• Quantum Fisher Information (QFI) quantifies the precision of quantum measurements.
• Noisy quantum channels degrade entangled states and reduce QFI.

Purpose of the Study:

• To investigate the effect of decoherence channels on the QFI of N-qubit Greenberger-Horne-Zeilinger (GHZ) states.
• To analyze the impact of bit-phase flip (BPF) and generalized amplitude damping (GAD) channels on QFI.
• To explore strategies for mitigating decoherence and potentially enhancing QFI.

Main Methods:

• Determining the quantum evolution of N-qubit GHZ states under BPF and GAD channels.
• Calculating the eigenvalues of the evolved states.
• Deriving the Quantum Fisher Information (QFI) based on the state evolution and eigenvalues.

Main Results:

• In the absence of environmental interaction, the Heisenberg limit for QFI is achievable via specific rotations.
• In BPF channels, QFI initially decreases with increasing decoherence rate (pB) but revives symmetrically around pB = 0.5, leading to enhanced efficiency at higher noise levels (pB > 0.5).
• In GAD channels, QFI decays faster at finite temperatures compared to zero temperature, and QFI can be enhanced by adjusting environmental temperature.

Conclusions:

• Decoherence channels significantly impact the QFI of GHZ states, but the effect varies depending on the channel type and parameters.
• The study reveals counterintuitive findings, such as noise-induced efficiency enhancement in BPF channels.
• Environmental temperature is a critical factor in GAD channels, offering a potential control parameter for QFI optimization.