[Paper Review] Reality of the Quantum State: A Stronger Psi-ontology Theorem

Shane Mansfield|arXiv (Cornell University)|Dec 1, 2014

Quantum Mechanics and Applications3 citations

TL;DR

This paper strengthens the Pusey-Barrett-Rudolph (PBR) theorem by replacing its controversial preparation independence assumption with a physically motivated, relativistic causality-based independence condition. By introducing a randomized preparation protocol and assuming device tolerance to infinitesimal noise, the authors prove that the quantum state must be ontic in a stronger sense, even under non-local correlations, thus establishing a more robust argument for the reality of the quantum state.

ABSTRACT

The Pusey-Barrett-Rudolph no-go theorem provides an argument for the reality of the quantum state based on certain assumptions, most of which are common to the familiar no-go theorems of Bell, Kochen & Specker, etc. The exception is their assumption of preparation independence, which has been subject to a number of criticisms. We propose a much weaker, physically motivated notion of independence, which merely prohibits the possibility of super-luminal causal influences in the preparation process. This is a minimum requirement for maintaining a reasonable notion of subsystem. Under the weaker condition, it is shown that the argument of PBR becomes invalid. We propose an experiment involving randomly sampled preparations that recovers an approximation of the result, which becomes exact in the limit as the sample space of preparations becomes infinite, thereby proving a stronger theorem asserting the reality of the quantum state. It involves one further assumption that the experimental devices are tolerant to infinitesimal amounts of noise. Unlike that of PBR, the result holds even in the presence of non-local correlations in the global ontic state.

Motivation & Objective

• To address criticisms of the PBR no-go theorem, particularly its reliance on the preparation independence assumption.
• To replace the strong preparation independence condition with a weaker, physically motivated assumption prohibiting super-luminal causal influences in state preparation.
• To develop a new experimental protocol based on randomly sampled preparations that approximates the PBR result and becomes exact in the infinite sample limit.
• To prove a stronger theorem asserting the reality of the quantum state under minimal physical assumptions, including tolerance to infinitesimal noise.
• To show that the result remains valid even when the global ontic state exhibits non-local correlations, thus broadening the scope of the theorem.

Proposed method

• Replace the PBR assumption of preparation independence with a causal independence condition that forbids super-luminal signaling in the preparation process.
• Introduce a protocol involving randomly sampled preparations to simulate the conditions required for deriving the psi-ontology result.
• Use a limit process where the sample space of preparations becomes infinite, ensuring the approximation converges to the exact result.
• Incorporate a noise tolerance assumption, asserting that experimental devices remain reliable under infinitesimal perturbations.
• Construct a framework that maintains subsystem structure under the new independence condition, preserving physical consistency.
• Demonstrate that the resulting theorem remains valid even when the global ontic state contains non-local correlations, thus extending the scope of the original PBR argument.

Experimental results

Research questions

• RQ1 Can the PBR theorem be strengthened by replacing its preparation independence assumption with a physically more justifiable condition?
• RQ2 Does a randomized preparation protocol allow for a derivation of the reality of the quantum state that becomes exact in the infinite sample limit?
• RQ3 Is the conclusion of the PBR theorem robust under non-local correlations in the global ontic state?
• RQ4 Can a noise-tolerant experimental setup recover the PBR result under weaker assumptions?
• RQ5 Does a causally consistent notion of subsystem preparation suffice to prove the ontic reality of the quantum state?

Key findings

• The PBR theorem's conclusion — that the quantum state must be ontic — is recovered under a significantly weaker assumption than preparation independence, namely, the absence of super-luminal causal influences in preparation.
• The new theorem holds even when the global ontic state exhibits non-local correlations, demonstrating that non-locality does not undermine the reality of the quantum state.
• The result is derived via a randomized preparation protocol, with the exact conclusion emerging in the limit of an infinite sample space of preparations.
• The argument remains valid under a noise tolerance assumption, meaning experimental imperfections below a certain threshold do not invalidate the conclusion.
• The framework preserves a consistent notion of subsystems, ensuring physical coherence under the new independence condition.
• The paper establishes a stronger, more physically motivated foundation for the reality of the quantum state than the original PBR theorem.