Consistency of quantum computation and the equivalence principle

TL;DR

This paper argues that the equivalence principle must hold in quantum gravity to ensure the unitarity and consistency of quantum computations in gravitational fields, highlighting its importance for quantum information processing.

Contribution

It introduces a quantum variant of the equivalence principle necessary for consistent quantum computation in gravitational environments.

Findings

Without the principle, quantum evolution becomes non-unitary.

The principle is formulated in terms of gauge transformations.

Quantum phases acquired over loops are crucial for analysis.

Abstract

The equivalence principle, being one of the building blocks of general relativity, seems to be also crucial for analysis of quantum effects in gravity. In this paper we consider the question if the equivalence principle has to hold for consistency of performing quantum computation in gravitational field. We propose an analysis with a looped evolution consisting of steps both in the gravitational field and in the accelerated reference frame. We show that without the equivalence principle the looped quantum evolution cannot be unitary and looses its consistency. For this reasoning the equivalence principle is formulated in terms of the gauge transformations and is analyzed for particles acquiring an appropriate phases associated with the actions over the looped path. In consequence, to keep consistency of quantum operations in gravitational field, it is required to keep some quantum variant of the equivalence principle. This proves importance of the quantized versions of this fundamental gravitational principle for quantum information processing.