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In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
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Scattering And Absorption of Light in Planetary Regoliths
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Remote Sampling with Applications to General Entanglement Simulation.

Gilles Brassard1,2, Luc Devroye3, Claude Gravel4

  • 1Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, Montréal, QC H3C 3J7, Canada.

Entropy (Basel, Switzerland)
|December 3, 2020
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Summary
This summary is machine-generated.

This study introduces a distributed rejection sampling protocol for remote parties to sample discrete probability distributions. It enables exact simulation of quantum entanglement with efficient communication, especially for bounded systems.

Keywords:
classical simulation of entanglementcommunication complexityentropyexact samplingquantum theoryrandom bit model

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Area of Science:

  • Quantum Information Science
  • Distributed Computing
  • Probability Theory

Background:

  • Discrete probability distributions are essential in various computational tasks.
  • Simulating quantum entanglement typically requires significant communication overhead.
  • Existing methods for distributed sampling are often complex or inefficient.

Purpose of the Study:

  • To develop a method for exactly sampling discrete probability distributions across remote parties.
  • To enable efficient and exact simulation of general quantum entanglement.
  • To analyze the communication complexity of distributed sampling protocols.

Main Methods:

  • Adaptation of von Neumann's rejection algorithm into a distributed communication protocol.
  • Analysis of expected communication costs in terms of bits transmitted.
  • Investigation of trade-offs between communication rounds and initial data transmission.

Main Results:

  • A novel distributed sampling protocol is presented.
  • The expected number of communicated bits is analyzed.
  • A trade-off between protocol rounds and initial communication is demonstrated.
  • Efficient simulation of general quantum entanglement is achieved with O(m^2) bits for m parties under constant bounds.

Conclusions:

  • The proposed distributed rejection sampling offers an exact and efficient method for remote probability distribution sampling.
  • This approach significantly reduces communication complexity for simulating quantum entanglement.
  • The findings have implications for secure distributed computation and quantum information processing.