Adaptive State Fidelity Estimation for Higher Dimensional Bipartite Entanglement

Area of Science:

• Quantum Information Science
• Quantum Many-Body Systems
• Quantum Foundations

Background:

• Quantum state fidelity estimation is crucial for characterizing quantum systems.
• Higher-dimensional bipartite systems present unique challenges for state verification.
• Existing methods may not offer optimal precision for all entangled states.

Purpose of the Study:

• To establish an adaptive method for estimating quantum state fidelity in bipartite higher-dimensional systems.
• To develop state verifier operators adaptable to measurement statistics.
• To enable tighter bounds on state fidelity for Bell-type entangled states.

Main Methods:

• Construction of state verifier operators using local POVM operators.
• Adaptation of operators to measurement statistics in the computational basis.
• Explicit construction of verifier operators for Bell-type entangled states.

Main Results:

• An adaptive method for quantum state fidelity estimation is established.
• Lower and upper bounds on state fidelity for Bell-type entangled states can be estimated.
• Tighter fidelity bounds are achievable compared to previous methods by incorporating additional local POVM measurements.

Conclusions:

• The proposed adaptive method offers improved fidelity estimation for bipartite quantum states.
• The technique provides a flexible framework for state verification in higher dimensions.
• This work advances the characterization of entangled states in complex quantum systems.