Let me open the key primary sources on hedweb.com for accuracy.

David Pearce's "zero ontology" and his "non-materialist physicalism" both hang on a single idea: that the superposition principle of quantum mechanics — the rule that a physical state is a linear sum of amplitudes (complex numbers) over possible outcomes — is not just a feature of physics but the master key to metaphysics. Here's how he runs the argument in each of the three cases.

1. Why anything exists: the "zero ontology"

Pearce starts from the intuition that there is no explanation-space for why something exists rather than nothing — and from the observation that every attempt to specify a reified "nothingness" (a dimensionless point, a timeless void, a quantum vacuum) smuggles in information. Since information is physical and cannot be created or destroyed, the question becomes: where did information come from? His answer: it didn't. The total information content of reality is zero, and the superposition principle "formalises inexistence." ( Why Does Anything Exist? §1)

The mechanism is the quantum analogue of Borges' Library of Babel. A classical library containing all possible books has zero information content, but withdrawing one book creates information. In a quantum Library of Babel, however, amplitudes are complex numbers, so summing two non-zero amplitudes can yield zero — having two ways for something to happen can make it not happen, just as adding a slit in the double-slit experiment can reduce the probability of particles arriving somewhere. Scale that up: the universal state vector (on Everettian QM, reality is a single vast quantum-coherent superposition) has zero information content. Everything that can occur does occur with some amplitude, all the values cancel out to precisely zero, and existence becomes the default condition from which any departure would need explaining. One timeless logico-physical principle — the superposition principle — "explains everything, including itself." ( Why Does Anything Exist? §1,  The universe cancels itself out to zero)

He concedes this can't be directly verified, but insists it's refutable: any experimentally detected departure from unitarity in physics would falsify the zero ontology. ( Why Does Anything Exist? §1)

2. The mystery of definite outcomes

On the face of it, the superposition principle is violated by experience: we always see a definite live cat or a definite dead cat, a definite pointer reading, a single particle hit on a screen — never a superposition. Decoherence explains the emergence of quasi-classical branches, but not why one definite outcome appears. Pearce's answer inverts the usual reading: seeing a definite cat exemplifies the superposition principle rather than breaking it. There are no definite outcomes; there are superpositions of distributed neuronal feature-processors, co-opted by selection pressure to play the functional role of phenomenally representing definite outcomes. ( The Problem of Definite Outcomes Solved?)

In other words, the classical definiteness of experience is itself a product of quantum coherence in the brain — the superposition principle is what allows discrete "pixels" of experience (Jamesian "mind-dust") to be experienced as one definite classical object in your world-simulation. Naive talk of "observers" and "measurements," he argues, presupposes an untenable perceptual naive realism — the false assumption that we have direct access to a mind-independent classical world. No new physics is invoked, only a new significance assigned to ultra-short-lived neuronal superpositions that physicists dismiss as irrelevant. ( The Problem of Definite Outcomes Solved?)

3. The phenomenal binding problem

This is the same move applied to neuroscience. Pearce's non-materialist physicalism combines two revisions: (1) the intrinsic nature of the physical — about which physics is structurally silent — is experiential (panpsychist idealism, solving the hard problem), so individual neurons carry micro-experiences; and (2) neurons are not effectively classical. The binding problem — how billions of distributed feature-processors (edge-, colour-, motion-detecting neurons) compose a unitary experience of, say, a hippopotamus, apprehended by a unitary self — is, he claims, classically insoluble: temporal synchrony of neuronal firing is a mere restatement of the mystery. ( Does physicalism entail monistic idealism?,  Schrödinger's Neurons)

Instead, phenomenal binding consists of quantum-coherent superpositions of neurons at sub-femtosecond timescales: the world-simulation of everyday experience is a sequence of neuronal "Schrödinger's cat states" harnessed by natural selection to track fitness-relevant patterns — "a movie running at around 10^15 quantum-coherent frames per second." Don't ask what it's like to see a live-and-dead cat; ask what it's like to instantiate a coherent superposition of distributed feature-processing neurons. If the superposition principle really did break down in the mind-brain, we would be mere "micro-experiential zombies" — patterns of decohered mind-dust incapable of simulating any classical object at all. ( Schrödinger's Neurons,  Non-materialist physicalism)

Crucially, Pearce treats this as empirical, not speculative hand-waving: a molecular matter-wave interferometry experiment on neuronal networks should detect interference effects showing a perfect structural match between physics and phenomenology — and a negative result would refute him. He also flips the usual objection (Tegmark's decoherence-timescale critique) on its head: the neurological implausibility of sub-femtosecond coherence should be weighed against the physical incredibility of the classical alternatives. ( Non-materialist physicalism,  Schrödinger's Neurons)

The common thread

All three answers are one answer. The superposition principle is the single, timeless, informationless principle from which (1) existence itself follows with zero net information, (2) the appearance of definite classical outcomes follows as a functional product of coherent neuronal superpositions, and (3) the unity of consciousness — binding discrete micro-experiences into one perceptual world — follows as the one thing superpositions can do that classical systems cannot: be a single physical state spread over many components. As he puts it, "without the superposition principle, no phenomenally-bound classical world-simulations could exist and nor could minds" — and the vehicle of our classical-seeming world-simulation is inescapably quantum, because a classical world wouldn't look like anything to anyone. ( Non-materialist physicalism,  Why Does Anything Exist? §1)