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No Practical Quantum Broadcasting: Even Virtually.

Yunlong Xiao1,2, Xiangjing Liu3,4,5,6, Zhenhuan Liu7

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A new theorem shows that practical quantum information broadcasting is impossible. No linear process can efficiently and reliably distribute quantum states, limiting quantum communication technologies.

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Area of Science:

  • Quantum Information Science
  • Quantum Communication
  • Theoretical Physics

Background:

  • The no-broadcasting theorem fundamentally prohibits the exact copying of unknown quantum states.
  • Recent advancements in virtual operations offer new perspectives on quantum information distribution.
  • Practical constraints, like sample efficiency, are crucial for real-world quantum technologies.

Purpose of the Study:

  • To investigate the feasibility of practical quantum information broadcasting under realistic constraints.
  • To establish a 'no-practical-broadcasting' theorem by analyzing key requirements.
  • To explore the connection between virtual broadcasting and quantum spacetime frameworks.

Main Methods:

  • Proving that no linear process can satisfy sample efficiency, unitary covariance, permutation invariance, and classical consistency simultaneously.
  • Utilizing Schur-Weyl duality to identify and construct the canonical 1-to-N virtual broadcasting map.
  • Employing semidefinite programming to determine the sample complexity of the broadcasting map.
  • Analyzing the correspondence between virtual broadcasting and pseudodensity operators in a quantum spacetime.

Main Results:

  • A 'no-practical-broadcasting' theorem is established, demonstrating strict limits on distributing quantum information.
  • The unique canonical 1-to-N virtual broadcasting map satisfying specific conditions is identified and constructed.
  • The sample complexity of this map is determined.
  • The correspondence between virtual broadcasting and pseudodensity operators is shown to hold only for the 1-to-2 case.

Conclusions:

  • Practical quantum information broadcasting is fundamentally limited by the no-practical-broadcasting theorem.
  • The established virtual broadcasting map provides a theoretical benchmark for quantum information distribution.
  • The findings highlight fundamental asymmetries in quantum statistics within quantum spacetime frameworks.