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This study explores generating ensemble coherence from quantum entanglement. Two methods are presented, linking ensemble coherence to entanglement and measurement uncertainty for quantum information applications.

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Area of Science:

  • Quantum Information Science
  • Quantum Foundations
  • Quantum Measurement Theory

Background:

  • The resource theory of coherence quantifies quantum properties in quantum systems.
  • Coherence measures for individual quantum states are well-established, but for ensembles, they remain an active research area.
  • An entanglement-based approach connects ensemble coherence to entanglement and measurement uncertainty via the measurement-ensemble duality principle and Born rule.

Purpose of the Study:

  • To present two novel methods for generating ensemble coherence from a fixed amount of entanglement in two-qubit systems.
  • To investigate the relationship between entanglement and ensemble coherence, particularly how much coherence can be extracted from a given entanglement resource.
  • To explore the application of these methods in quantum key distribution (QKD) protocols.

Main Methods:

  • Method 1: Applying a von Neumann measurement to one part of a non-maximally entangled bipartite state to generate non-orthogonal states.
  • Method 2: Utilizing a class of symmetric observables to generate ensembles relevant to various QKD protocols (B92, BB84, three-state QKD).

Main Results:

  • The first method demonstrates that the coherence of the generated non-orthogonal states can be equal to the initial entanglement.
  • The second method shows the generation of ensembles suitable for established QKD protocols, highlighting the role of symmetric observables.
  • Quantifies the amount of ensemble coherence obtainable from a specific quantity of entanglement.

Conclusions:

  • This work provides a deeper understanding of how ensemble coherence can be generated and quantified using entanglement as a resource.
  • The presented methods offer practical approaches for creating ensemble coherence, with implications for quantum information processing and secure communication.
  • Establishes a direct link between entanglement, measurement, and the generation of ensemble coherence.