Extendibility limits quantum-secured communication and key distillation

Area of Science:

• Quantum Information Theory
• Quantum Communication Security

Background:

• Secret-key distillation is crucial for private communication over quantum networks.
• Existing methods often require complex protocols or have limitations in efficiency.

Purpose of the Study:

• To develop efficient methods for secret-key distillation using local operations and one-way classical communication (LOCC).
• To establish computable upper bounds for private communication capacity over quantum channels, addressing an open question in the field.

Main Methods:

• Utilizing the resource theory of unextendible entanglement to analyze bipartite state transformations under one-way LOCC.
• Extending the formalism to include forward classical communication assistance for private communication over quantum channels.
• Employing semidefinite programming for computationally feasible bound calculations.

Main Results:

• Derived efficiently computable upper bounds on secret bits distillable from bipartite states via one-way LOCC.
• Obtained upper bounds on the one-shot forward-assisted private capacity of quantum channels.
• Demonstrated that these bounds apply to both one-shot and certain asymptotic settings, with error decreasing exponentially with channel uses.

Conclusions:

• The developed formalism provides a computationally feasible approach to understanding the limits of private communication over quantum networks.
• The findings offer significant advancements in quantifying secure key distillation and private capacity in quantum communication systems.