[Paper Review] The quantum state can be interpreted statistically

Peter G. Lewis, Terry Rudolph+2 more|arXiv (Cornell University)|Feb 1, 2012

Quantum Mechanics and ApplicationsPhysics and Astronomy31 citations

TL;DR

This paper argues that the quantum state cannot be purely statistical under mild physical assumptions, showing that distinct quantum states must correspond to physically distinct states of reality. If quantum theory's predictions hold—even with experimental noise—this implies a ontic (real) interpretation of the quantum state, ruling out purely epistemic (statistical) models.

ABSTRACT

Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state represents. There are at least two opposing schools of thought, each almost as old as quantum theory itself. One is that a pure state is a physical property of system, much like position and momentum in classical mechanics. Another is that even a pure state has only a statistical significance, akin to a probability distribution in statistical mechanics. Here we show that, given only very mild assumptions, the statistical interpretation of the quantum state is inconsistent with the predictions of quantum theory. This result holds even in the presence of small amounts of experimental noise, and is therefore amenable to experimental test using present or near-future technology. If the predictions of quantum theory are confirmed, such a test would show that distinct quantum states must correspond to physically distinct states of reality.

Motivation & Objective

• To determine whether the quantum state can be interpreted purely statistically, as in epistemic models akin to probability distributions in statistical mechanics.
• To assess the consistency of such statistical interpretations with the predictions of quantum theory under realistic experimental conditions.
• To establish whether distinct quantum states must correspond to physically distinct states of reality if quantum mechanics is correct.
• To provide a testable framework for distinguishing ontic (real) from epistemic (knowledge-based) interpretations of the quantum state.

Proposed method

• The authors derive a set of constraints on any ontological model of quantum mechanics under minimal physical assumptions, including preparation independence and the existence of a physical state space.
• They use a framework based on the Pusey–Barrett–Rudolph (PBR) theorem, extending it to include small experimental noise.
• The method involves analyzing the overlap of ontic states corresponding to different quantum states, showing that this overlap must vanish if quantum theory is correct.
• The analysis relies on a logical contradiction arising when assuming a purely statistical interpretation while preserving quantum predictions.
• The approach uses a thought experiment with multiple preparations of quantum states and examines the consistency of the resulting ontic state distributions.

Experimental results

Research questions

• RQ1 Can a purely statistical interpretation of the quantum state be consistent with the predictions of quantum theory?
• RQ2 What happens to epistemic models of the quantum state when small experimental noise is introduced?
• RQ3 Do distinct quantum states correspond to physically distinct states of reality if quantum mechanics is valid?
• RQ4 Is there a testable way to rule out purely epistemic interpretations of the quantum state?

Key findings

• The statistical interpretation of the quantum state is inconsistent with the predictions of quantum theory under minimal physical assumptions.
• Even with small amounts of experimental noise, the predictions of quantum theory rule out purely epistemic models of the quantum state.
• The results imply that distinct quantum states must correspond to physically distinct states of reality if quantum theory is correct.
• The framework is robust enough to be tested with current or near-future experimental technology.