Finite-Memory Extension of Tegmark's Decoherence Bound in Biological Media

TL;DR

This paper extends Tegmark's decoherence bound to environments with finite memory, showing that decoherence dynamics are significantly altered by environmental correlations, especially in non-Markovian regimes.

Contribution

It introduces a finite-memory framework for decoherence, deriving exact equations for Ornstein-Uhlenbeck baths and revealing how decoherence scales with bath correlation time.

Findings

Decoherence is quadratic at short times in correlated environments.

Decoherence time scales as the square root of bath correlation time.

Tegmark's bound is recovered only in the memoryless limit.

Abstract

Tegmark's decoherence bound is derived under the assumption of a strictly memoryless environment. We show that this result corresponds to the singular limit of a finite-memory theory. For exponentially correlated environments decoherence is generically quadratic at short times and the decoherence time scales as the square root of the bath correlation time. For the Ornstein-Uhlenbeck bath we derive the exact non-Markovian coherence equation and verify the predicted scaling using an exact pseudomode mapping. Tegmark's bound is recovered only in the vanishing-memory limit.