Classical Cost of Transmitting a Qubit

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.