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We derived a formula for classical information transmission over noisy quantum channels. This formula quantifies the usefulness of entanglement resources for communication, even with limited receiver capabilities.

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Area of Science:

  • Quantum Information Theory
  • Quantum Communication

Background:

  • Classical information transmission over noisy quantum channels is a fundamental problem.
  • The role of quantum resources, such as entanglement, in enhancing communication capacity is an active area of research.
  • Previous models often assumed pure states for signal-ancilla pairs, limiting applicability.

Purpose of the Study:

  • To develop a capacity formula for classical information transmission over noisy quantum channels.
  • To characterize the utility of various entanglement resources for classical communication.
  • To analyze the impact of mixed states and limited receiver resources on channel capacity.

Main Methods:

  • Developing a capacity formula considering separable encoding and mixed signal-ancilla states.
  • Utilizing a
  • witness
  • to purify the signal-ancilla mixed state and analyze signal-witness correlations.
  • Deriving the formula for generalized covariant channels and applying it to quantum key distribution protocols.

Main Results:

  • A capacity formula for classical information transmission over noisy quantum channels with separable encoding and limited receiver ancilla resources.
  • The formula quantifies the utility of different forms of entanglement assistance.
  • The capacity formula is additive, even with entangled signals across multiple uses.
  • For generalized covariant channels, a simple closed-form capacity formula is obtained.
  • The formula provides an upper bound on information gain in two-way quantum key distribution protocols, identifying collective Gaussian attacks as most powerful for Gaussian protocols.

Conclusions:

  • The derived capacity formula provides a comprehensive tool for understanding classical communication over noisy quantum channels.
  • It highlights the nuanced role of entanglement and receiver resources in quantum communication.
  • The additivity of the formula simplifies analysis and has direct implications for the security of quantum key distribution protocols.