Local quantum measurement and no-signaling imply quantum correlations.

Area of Science:

• Quantum Information Theory
• Foundations of Quantum Mechanics

Background:

• Quantum mechanics posits local Hilbert spaces for parties.
• Nonlocal correlations beyond quantum mechanics are theoretically possible in some frameworks.
• The tensor product formalism is typically assumed for joint quantum systems.

Purpose of the Study:

• To demonstrate that the finite speed of information is the sole principle limiting correlations to quantum mechanical bounds.
• To explore the implications of local quantum mechanics without assuming the tensor product formalism.
• To show that any violation of quantum mechanical correlations would invalidate the theory locally.

Main Methods:

• Consideration of local quantum mechanics where each party has a Hilbert space.
• Analysis of local positive-operator-valued measurements.
• Investigation of joint systems not necessarily described by a tensor product Hilbert space.

Main Results:

• The finite speed of information fundamentally restricts all possible correlations between distant parties to be quantum mechanical.
• Local quantum mechanics, combined with the finite speed of information, naturally leads to quantum mechanical correlations.
• Any experimental evidence of nonlocal correlations exceeding quantum mechanical limits would falsify quantum theory, even at the local level.

Conclusions:

• The finite speed of information is a foundational principle underpinning the limits of quantum correlations.
• Local quantum mechanics is sufficient to derive quantum mechanical correlation bounds, provided information speed is finite.
• The study reinforces the robustness of quantum theory by showing local invalidation upon violation of its correlation structure.