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Quantum protocols involving qubit state transmission and general measurements can be simulated classically using shared randomness and just two bits of communication. This minimal communication cost applies even to complex Bell scenarios with entangled states.

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Area of Science:

  • Quantum Information Science
  • Quantum Communication
  • Quantum Computing

Background:

  • Prepare-and-measure scenarios are fundamental in quantum information, involving transmitting quantum states (qubits) from one party (Alice) to another (Bob).
  • Bob can perform general quantum measurements, described by positive operator-valued measures (POVMs), to extract information from the received qubits.
  • Classical simulation of quantum protocols is a key area of research, aiming to understand the boundaries between classical and quantum information processing.

Purpose of the Study:

  • To determine the classical communication cost required to simulate general prepare-and-measure quantum protocols.
  • To establish the minimum number of classical bits necessary for a perfect simulation.
  • To extend these findings to Bell scenarios, analyzing the simulation of quantum correlations in entangled systems.

Main Methods:

  • Developed a theoretical framework to analyze general prepare-and-measure scenarios.
  • Utilized shared randomness and classical communication as simulation resources.
  • Applied the developed methods to analyze Bell scenarios with entangled two-qubit states and arbitrary local POVMs.

Main Results:

  • Demonstrated that any quantum protocol in a general prepare-and-measure setting can be perfectly simulated using shared randomness and two bits of classical communication.
  • Proved that two bits of communication represent the minimal cost for such a perfect classical simulation.
  • Showed that all quantum correlations in Bell scenarios, involving arbitrary local POVMs on entangled two-qubit states, can be simulated with two bits of communication.

Conclusions:

  • The computational power of general quantum prepare-and-measure protocols can be efficiently simulated classically, requiring only a small amount of communication.
  • This finding significantly reduces the communication overhead for simulating quantum correlations in specific, important scenarios like Bell tests.
  • The Toner and Bacon protocol is extended, showing that two bits are sufficient for simulating quantum correlations associated with arbitrary local POVMs on any entangled two-qubit state.