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This summary is machine-generated.

Practical quantum communication requires balancing code rate, device size, and transmission fidelity, not just theoretical capacity. This study characterizes this trade-off for key quantum channels, introducing the quantum channel dispersion.

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Area of Science:

  • Quantum Information Theory
  • Quantum Communication Systems

Background:

  • The quantum capacity defines the maximum reliable communication rate over a quantum channel in the asymptotic limit.
  • Practical quantum communication is constrained by decoherence, limiting the manipulation of quantum systems.

Purpose of the Study:

  • To demonstrate the insufficiency of asymptotic quantum capacity for practical scenarios.
  • To characterize the trade-off between code rate, quantum device size, and transmission fidelity.

Main Methods:

  • Analysis of practical communication constraints imposed by decoherence.
  • Derivation of approximate and exact trade-off characterizations for specific quantum channels.
  • Development of general bounds for quantum channels, computable for small instances.

Main Results:

  • The asymptotic quantum capacity is insufficient for practical quantum communication.
  • An optimal trade-off exists between code rate, encoder/decoder device size, and transmission fidelity.
  • This trade-off is parameterized by channel capacity and quantum channel dispersion for dephasing, depolarizing, and erasure channels.

Conclusions:

  • Practical quantum communication necessitates a focus on achievable trade-offs beyond asymptotic capacity.
  • The quantum channel dispersion is a key parameter characterizing these practical trade-offs.
  • Developed bounds offer computational tools for analyzing quantum channel performance.