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Communication Tasks with Infinite Quantum-Classical Separation.

Christopher Perry1, Rahul Jain2, Jonathan Oppenheim1,2

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This summary is machine-generated.

Quantum communication offers significant advantages over classical methods. Utilizing quantum bits (qubits) and entanglement drastically reduces the information needed for secure data tasks between parties.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Foundations of Quantum Theory

Background:

  • Classical computation and communication have inherent limitations in efficiency and security.
  • Quantum resources, such as quantum computers and quantum communication, offer potential exponential advantages over classical counterparts.
  • Certain tasks, like function computation between two parties, can be performed with significantly less communication using quantum messages.

Purpose of the Study:

  • To investigate a specific information exclusion task between two parties (Alice and Bob) where quantum resources demonstrate superior power compared to classical resources.
  • To quantify the advantage of using quantum bits (qubits) over classical bits for communication in this task.
  • To explore the impact of entanglement on the communication complexity of the task.

Main Methods:

  • Analysis of an information exclusion task involving a string of length n.
  • Comparison of communication complexity using classical messages versus quantum messages.
  • Evaluation of the role of entanglement in reducing communication overhead.

Main Results:

  • When Alice sends classical messages, she must reveal nearly n bits of information.
  • When Alice sends quantum messages, the information revealed approaches zero as n increases, demonstrating a significant quantum advantage.
  • With entanglement, Alice needs to send only a constant number of bits, whereas without entanglement, the number of bits grows linearly with n.

Conclusions:

  • Quantum communication, particularly with qubits, offers exponential advantages in reducing information disclosure for specific tasks.
  • Entanglement further enhances communication efficiency, reducing the required information to a constant.
  • The task and its results are connected to foundational concepts in quantum theory, including the Pusey-Barrett-Rudolph theorem.