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Clean Quantum and Classical Communication Protocols.

Harry Buhrman1, Matthias Christandl2, Christopher Perry2

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This study introduces clean communication protocols, which ensure all registers reset after computation. Optimal protocols for inner product calculation require minimal qubits or bits, with general functions nearing maximal complexity.

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Area of Science:

  • Quantum Information Science
  • Theoretical Computer Science
  • Communication Complexity

Background:

  • Standard communication protocols often leave registers in altered states.
  • Clean communication protocols require all registers, except the output, to return to their initial states.
  • Understanding the cost of clean computation is crucial for efficient distributed information processing.

Purpose of the Study:

  • To determine the communication complexity of clean protocols for specific functions.
  • To establish bounds for clean communication complexity in both classical and quantum settings.
  • To explore the implications of clean protocols for distributed gate implementation.

Main Methods:

  • Development of novel clean communication protocols for computing the inner product of two n-bit strings.
  • Analysis of communication complexity for these protocols in the absence and presence of preshared entanglement.
  • Generalization of findings to a broader class of Boolean functions.

Main Results:

  • Clean inner product computation requires at most n+3 qubits (quantum) or n+O(sqrt[n]) bits (classical) without preshared entanglement.
  • Optimal distributed CNOT gate implementation is inspired by the quantum inner product protocol.
  • Nearly all Boolean functions exhibit maximal clean communication complexity: close to 2n bits classically and n qubits quantumly with preshared entanglement.

Conclusions:

  • Clean communication protocols introduce a significant but quantifiable overhead compared to standard protocols.
  • The derived bounds for inner product computation are near-optimal for both quantum and classical communication.
  • The study highlights the fundamental limits of clean information processing in distributed systems.