Local convertibility of the ground state of the perturbed toric code

Abstract

We present analytical and numerical studies of the behaviour of the α-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 localconvertibility. In particular, the derivatives, with respect to the perturbation parameter, present different signs for different values of α 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.

Thermalization of topological entropy after a quantum quench

“…The eigenspace of H(λ) in 'τpicture' is a tensor product over the different chains. At this point, we show that P (t) can be calculated exactly by sum of correlation functions [58,62,81,82]. The details of the mapping and the solution in terms of correlation functions are shown in the Appendix.…”

“…In particular, let us see how the toric code with a certain arrangement of the external fields can be mapped into a system of free fermions [62,80]. We write V (λ) as the sum of external fields on the bonds, with a special arrangement: the field in the +z direction with magnitude of λ z on the horizontal(h) edges and the field in the +x direction with λ x on the vertical(v) edges.…”

Parity and Time-Reversal Violation in Atomic Systems

“…Much experimental work is currently under way that promises significant improvements in the measurements in the near future, e.g., in Xe [140], YbF [141,142], TlF [143] and ThO [144][145][146][147]. New experiments are also in preparation designed to measure the EDM of Xe [148] and Fr [149] at CYRIC in Tohoku, Ra at KVI [150] and Argonne laboratory [151,152], and Rn at TRIUMF [153] (see also [154]). Very recently, the SrF molecule was successfully trapped and cooled, demonstrating the the ability of this technique, which can be applied to molecular EDM and PNC experiments [118,119].…”

Long- and short-range interaction footprints in entanglement entropies of two-particle Wigner molecules in 2D quantum traps

“…The Hartley or max-entropy, S 0 = log 2 R, only depends on the Schmidt rank R of the spectrum distribution and is a measure of bipartite entanglement which serves as a criterion for efficient classical representation of the state [49]. The distribution of the entanglement spectrum can be better understood by computing the Rényi entropies for many different values of the parameter α [4].…”