Naimark-dilated PT-symmetric brachistochrone

Area of Science:

• Quantum mechanics
• Quantum control
• Quantum information science

Background:

• The quantum brachistochrone problem seeks the fastest quantum evolution between two states.
• Parity-time (PT)-symmetric Hamiltonians offer unique properties in quantum systems.
• Previous theoretical work by Bender et al. proposed a PT-symmetric ultrafast brachistochrone regime.

Purpose of the Study:

• To provide a pathway for the experimental realization of PT-symmetric quantum brachistochrones.
• To reframe PT-symmetric systems as subsystems within a larger Hermitian framework.
• To enable ultrafast quantum control using entangled systems.

Main Methods:

• Naimark dilation of the PT-symmetric Hamiltonian.
• Reinterpretation of the PT-symmetric system as a subsystem of a Hermitian system in a higher-dimensional Hilbert space.
• Utilizing an entangled two-spin system for experimental implementation.

Main Results:

• Demonstrated a method to experimentally implement PT-symmetric quantum brachistochrones.
• Established a connection between PT-symmetric and Hermitian systems via Naimark dilation.
• Showcased the potential for ultrafast quantum control in entangled systems.

Conclusions:

• The Naimark dilation provides a viable route for experimental PT-symmetric quantum brachistochrone realization.
• This approach facilitates the study of PT-symmetric dynamics in controllable quantum systems.
• The findings pave the way for advancements in ultrafast quantum control and quantum information processing.