Quantum Correlations Cannot Be Reproduced with a Finite Number of Measurements in Any No-Signaling Theory

Area of Science:

• Quantum Information Theory
• Foundations of Quantum Mechanics
• Bell Non-locality

Background:

• Bell inequalities test the limits of classical physics against quantum mechanics.
• No-signaling theories describe correlations without faster-than-light communication.
• Previous work has explored limitations on theories beyond quantum mechanics.

Purpose of the Study:

• To demonstrate that quantum theory necessitates an unbounded number of measurements in no-signaling theories.
• To establish a hierarchy of complexity for no-signaling theories based on measurement incompatibility.
• To identify specific Bell inequalities that highlight this unboundedness.

Main Methods:

• Constructing quantum correlations from n dichotomic measurements in a bipartite Bell scenario.
• Defining and utilizing linear Bell inequalities for (n-1)-wise incompatible measurements.
• Proving that these inequalities must hold in any no-signaling theory with limited measurement complexity.

Main Results:

• Existence of quantum correlations requiring more than (n-1) incompatible measurements for reproduction in no-signaling theories.
• Identification of specific Bell inequalities violated by quantum theory but obeyed by restricted no-signaling theories.
• Demonstration that no-signaling theories require an unbounded number of measurements to match quantum predictions.

Conclusions:

• Quantum correlations exhibit a complexity that cannot be captured by no-signaling theories with a finite bound on measurement incompatibility.
• This work establishes a fundamental difference between quantum correlations and classical or semi-classical correlations within the framework of no-signaling theories.
• The findings have implications for understanding the power of quantum resources and the limitations of alternative theories.