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A Streltsov1,2, E Chitambar3, S Rana1

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This study introduces incoherent quantum state merging, distinguishing between operations that create coherence and those that don't. Results show entanglement and coherence cannot be gained simultaneously in this process.

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Area of Science:

  • Quantum Information Theory
  • Quantum Computation

Background:

  • Resource consumption in distributed quantum systems is a key area of study.
  • Standard quantum state merging treats entanglement as a resource and local operations as free.
  • Recent work distinguishes local operations based on their ability to create coherence.

Purpose of the Study:

  • To investigate incoherent quantum state merging, where one party uses only local incoherent operations.
  • To quantify resources in this scenario using pairs of entanglement and coherence.
  • To analyze the trade-offs between entanglement and coherence in quantum state merging.

Main Methods:

  • Development of novel tools for analyzing incoherent quantum state merging.
  • Application of these tools to various relevant quantum scenarios.
  • Derivation of a general lower bound for the sum of entanglement and coherence.

Main Results:

  • Quantum state merging cannot simultaneously increase entanglement and coherence.
  • A tight lower bound on the entanglement-coherence sum is established for all pure states.
  • An incoherent version of Schumacher compression is presented, with a compression rate linked to von Neumann entropy.

Conclusions:

  • Incoherent quantum state merging introduces a new perspective on resource quantification in quantum information.
  • The findings highlight fundamental limitations and trade-offs between entanglement and coherence.
  • The study provides a foundation for understanding resource costs in quantum information processing with restricted local operations.