Distinguishing Phases via Non-Markovian Dynamics of Entanglement in Topological Quantum Codes under Parallel Magnetic Field

TL;DR

This paper explores how non-Markovian dynamics of entanglement can distinguish topological phases in quantum codes under magnetic fields, revealing phase-dependent oscillations useful for noise-resilient quantum information processing.

Contribution

It introduces a measurement basis for optimizing localizable entanglement and analyzes its behavior near phase transitions under noise, providing new tools for topological phase detection.

Findings

Non-Markovian noise causes larger amplitude oscillations in entanglement bounds for nontopological phases.

The canonical measurement basis effectively bounds localizable entanglement in topological codes.

Entanglement dynamics can distinguish topological from nontopological phases under noise.

Abstract

We investigate the static and the dynamical behavior of localizable entanglement and its lower bounds on nontrivial loops of topological quantum codes with parallel magnetic field. Exploiting the connection between the stabilizer states and graph states in the absence of the parallel field and external noise, we identify a specific measurement basis, referred to as the canonical measurement basis, that optimizes localizable entanglement when measurement is restricted to single-qubit Pauli measurements only, thereby providing a lower bound. We also propose an approximation of the lower bound that can be computed for larger systems according to the computational resource in hand. Additionally, we compute a lower bound of the localizable entanglement that can be computed by determining the expectation value of an appropriately designed witness operator. We study the behavior of these lower bounds in the vicinity of the topological to nontopological quantum phase transition of the system, and perform a finite-size scaling analysis. We also investigate the dynamical features of these lower bounds when the system is subjected to Markovian or non-Markovian single-qubit dephasing noise. We find that in the case of the non-Markovian dephasing noise, at large time, the canonical measurement-based lower bound oscillates with a larger amplitude when the initial state of the system undergoing dephasing dynamics is chosen from the nontopological phase, compared to the same for an initial state from the topological phase. These features can be utilized to distinguish the topological phase of the system from the nontopological phase in the presence of dephasing noise.