Can quantum cryptography imply quantum mechanics? Reply to Smolin

TL;DR

This paper critiques Smolin's toy theory by showing it violates an independence condition essential for deriving quantum mechanics from information-theoretic axioms, reaffirming the CBH approach.

Contribution

It demonstrates that Smolin's counterexample fails to meet key independence assumptions, supporting the validity of deriving quantum mechanics from cryptographic principles.

Findings

Smolin's toy theory violates the independence condition.

The independence condition is crucial for the CBH derivation.

Acceptable physical theories should satisfy the independence condition.

Abstract

Clifton, Bub, and Halvorson (CBH) have argued that quantum mechanics can be derived from three cryptographic, or broadly information-theoretic, axioms. But Smolin disagrees, and he has given a toy theory that he claims is a counterexample. Here we show that Smolin's toy theory violates an independence condition for spacelike separated systems that was assumed in the CBH argument. We then argue that any acceptable physical theory should satisfy this independence condition.