On the Possibility of Quantum Circuits Part I: the Epistemic Level

TL;DR

This paper develops an epistemic formalism for quantum circuits that assesses their physical realizability and maintains Lorentz invariance, addressing paradoxes like Hardy's without contradictions.

Contribution

It introduces verification statements as epistemic assertions and a logical framework to evaluate quantum circuit realizability and consistency.

Findings

Formalism is Lorentz-invariant.

Prevents contradictory knowledge assertions.

Applied to Hardy's paradox successfully.

Abstract

We present a formulation of quantum circuits where the focus is set on whether a given circuit (made of unitary operators and projective measurements with definite outcomes) does reflect an actually realizable physical experiment. In order to do this, we introduce verifications statements which are purely epistemic assertions indicating whether a outcome is possible at some point and develop our formalism which, in the end, consists in a set of logical rules about verification statements. Finally, we argue that our formalism provides a Lorentz-invariant realistic formulation of quantum circuits and illustrate this by considering a circuit corresponding to Hardy's paradox and showing how our formalism prevents making contradictory assertions regarding our knowledge about the circuit.