Related papers: Layer-by-layer disentangling two-dimensional topol…
Since the long range entanglement is a universal characteristic of topological quantum states belonging to the same class, a suitable mathematical representation of the long range entanglement has to be also universal. In this Letter, we…
We study the entanglement structure of topological orders subject to decoherence on the bipartition boundary. Focusing on the toric codes in $d$ space dimensions for $d=2,3,4$, we explore whether the boundary decoherence may be able to…
Two topological phases are equivalent if they are connected by a local unitary transformation. In this sense, classifying topological phases amounts to classifying long-range entanglement patterns. We show that all 2D topological stabilizer…
Two gapped quantum ground states in the same phase are connected by an adiabatic evolution which gives rise to a local unitary transformation that maps between the states. On the other hand, gapped ground states remain within the same phase…
A hallmark feature of topologically ordered states of matter is the dependence of ground state degeneracy (GSD) on the topology of the manifold determined by the global shape of the system. Although the topology of a physical system is…
Spatially resolved local quantum geometric markers play a crucial role in the diagnosis of topological phases without long-range translational symmetry, including amorphous systems. Here, we focus on the nonlocality of such markers. We…
We study entanglement renormalization group transformations for the ground states of a spin model, called cubic code model $H_A$ in three dimensions, in order to understand long-range entanglement structure. The cubic code model has…
We demonstrate that two toric code layers on the square lattice coupled by an Ising interaction display two distinct phases with intrinsic topological order. The second-order quantum phase transition between the weakly-coupled…
Here we investigate the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of…
In this paper, the degenerate ground states of Z2 topological order on a plane with holes (the so-called surface codes) are used as the protected code subspace to build a topological quantum computer by tuning their quantum tunneling…
Topological models are characterized by a quantized topological invariant and provide a description of novel phases of matter that can exhibit localized edge states, corner modes, and chiral transport. We experimentally realize two 1-D…
Quantum entanglement is a particularly useful characterization of topological orders which lack conventional order parameters. In this work, we study the entanglement in topologically ordered states between two arbitrary spatial regions,…
A set of orthogonal multipartite quantum states is said to be distinguishability-based genuinely nonlocal (also genuinely nonlocal, for abbreviation) if the states are locally indistinguishable across any bipartition of the subsystems. This…
We investigate the topological-to-non-topological quantum phase transitions (QPTs) occurring in the Kitaev code under local perturbations in the form of local magnetic field and spin-spin interactions of the Ising-type using fidelity…
We present a two-part program for state space decomposition. States are classified into entanglement classes based on local unitary transformations, and then characterized as elements of topological spaces using the language of fibre…
The Greenberger-Horne-Zeilinger (GHZ) puzzle has been used to study quantum nonlocality and provide an all-or-nothing, no-go theorem for local hidden-variable models. Recent experiments using coincident-detected entangled photons prepared…
To a significant extent, the rich physical properties of photonic crystals are determined by the underlying geometry, in which the composed symmetry operators and their combinations contribute to the unique topological invariant to…
The multipartite Greenberger-Horne-Zeilinger (GHZ) state is a paradigmatic example of a highly entangled multipartite states with distinct quantum features. However, the GHZ state is very sensitive to generic decoherence processes, where…
Transitions between different topologically ordered phases have been studied by artificially creating boundaries between these gapped phases and thus studying their effects relating to condensation and tunneling of particles from one phase…
A prominent example of a topologically ordered system is Kitaev's quantum double model $\mathcal{D}(G)$ for finite groups $G$ (which in particular includes $G = \mathbb{Z}_2$, the toric code). We will look at these models from the point of…