Local convertibility of the ground state of the perturbed Toric code

Abstract

We present analytical and numerical studies of the behaviour of the $\alpha$-Renyi entropies in the Toric code in presence of several types of perturbations aimed at studying the simulability of these perturbations to the parent Hamiltonian using local operations and classical communications (LOCC) - a property called local-convertibility. In particular, the derivatives, with respect to the perturbation parameter, present different signs for different values of $\alpha$ within the topological phase. From the information-theoretic point of view, this means that such ground states cannot be continuously deformed within the topological phase by means of catalyst assisted local operations and classical communications (LOCC). Such LOCC differential convertibility is on the other hand always possible in the trivial disordered phase. The non-LOCC convertibility is remarkable because it can be computed on a system whose size is independent of correlation length. This method can therefore constitute an experimentally feasible witness of topological order.

19 Pages,11 Figures. Updated to the published version

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Cited by in corpus (8)

• Entanglement convertibility by sweeping through the quantum phases of the alternating bonds $XXZ$ chain
• Quantum critical phase transition between two topologically-ordered phases in the Ising toric code bilayer
• Quantum robustness and phase transitions of the 3D Toric Code in a field
• Thermalization of Topological Entropy after a Quantum Quench
• Detecting dimensional crossover and finite Hilbert space through entanglement entropies
• Long- and short-range interaction footprints in entanglement entropies of two-particle Wigner molecules in 2D quantum traps
• Stability of topological purity under random local unitaries
• Disorder-protected topological entropy after a quantum quench