Unambiguous Quantum State Discrimination in a PT $\mathcal {PT}$ -Symmetric System of a Single Trapped Ion

Area of Science:

• Quantum Information Science
• Non-Hermitian Physics
• Quantum Computing

Background:

• Quantum state discrimination is crucial for quantum information processing.
• Non-Hermitian Hamiltonians with parity-time-reversal (PT) symmetry offer unique properties.
• Achieving unambiguous discrimination of non-orthogonal states remains a challenge.

Purpose of the Study:

• To experimentally demonstrate unambiguous quantum state discrimination.
• To investigate the role of PT-symmetric Hamiltonians in state discrimination.
• To explore the quantum brachistochrone dynamics for rapid state orthogonalization.

Main Methods:

• Experimental implementation using a single trapped 40Ca+ ion.
• Utilizing a non-Hermitian Hamiltonian with PT symmetry.
• Analyzing time evolution under PT-symmetric Hamiltonians in preserving and broken regimes.

Main Results:

• Achieved unambiguous discrimination of two non-orthogonal qubit states.
• Demonstrated that PT-symmetric Hamiltonians can drive non-orthogonal states to become orthogonal.
• Identified optimal Hamiltonian parameter ranges for fastest orthogonalization (quantum brachistochrone).

Conclusions:

• PT-symmetric non-Hermitian Hamiltonians provide a powerful tool for quantum state discrimination.
• This work highlights promising applications of non-Hermitian physics in quantum information processing.
• The findings offer a clear geometric picture and analytical understanding of the observed phenomena.