Related papers: Local unitary transformation, long-range quantum e…
In this work we present some new understanding of topological order, including three main aspects: (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is…
A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular…
The preparation of long-range entangled states using unitary circuits is limited by Lieb-Robinson bounds, but circuits with projective measurements and feedback (``adaptive circuits'') can evade such restrictions. We introduce three classes…
In terms of the analysis of fixed point subgroup and tensor decomposability of certain matrices, we study the equivalence of of quantum bipartite mixed states under local unitary transformations. For non-degenerate case an operational…
The correspondence between local unitary equivalence of bipartite quantum states and simultaneous orthogonal equivalence is thoroughly investigated and strengthened. It is proved that local unitary equivalence can be studied through…
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…
We investigate the equivalence of quantum states under local unitary transformations. A complete set of invariants under local unitary transformations is presented for a class of mixed states. It is shown that two states in this class are…
We investigate the equivalence of quantum mixed states under local unitary transformations. For a class of rank-two mixed states, a sufficient and necessary condition of local equivalence is obtained by giving a complete set of invariants…
Local unitary invariants allow one to test whether multipartite states are equivalent up to local basis changes. Equivalently, they specify the geometry of the "orbit space" obtained by factoring out local unitary action from the state…
We propose a unifying framework for characterizing pure and mixed state phases of matter across equilibrium, non equilibrium, and metastable regimes. We introduce the concept of locally stable states, defined by the operational property…
A large class of quantum phase transitions for quantum lattice systems are characterized by local order parameters. It is shown that local order parameters may be systematically constructed from tensor network representations of quantum…
Motivated by link transformations of lattice gauge theory, a method for generating local unitary invariants, especially for a system of qubits, has been pointed out in an earlier work [M. S. Williamson {\it et. al.}, Phys. Rev. A {\bf 83},…
We investigate the relation between local unitary symmetries and entanglement invariants of multi-qubit systems. The Hilbert space of such systems can be stratified in terms of states with different types of symmetry. We review the…
Long-range entanglement--the backbone of topologically ordered states--cannot be created in finite time using local unitary circuits, or equivalently, adiabatic state preparation. Recently it has come to light that single-site measurements…
We derive a set of invariants under local unitary transformations for arbitrary dimensional quantum systems. These invariants are given by hyperdeterminants and independent from the detailed pure state decompositions of a given quantum…
The necessary and sufficient conditions for the equivalence of arbitrary n-qubit pure quantum states under Local Unitary (LU) operations derived in [B. Kraus Phys. Rev. Lett. 104, 020504 (2010)] are used to determine the different…
We present an approach of constructing invariants under local unitary transformations for multipartite quantum systems. The invariants constructed in this way can be complement to that in [Science 340 (2013) 1205-1208]. Detailed examples…
Topological phase transitions track changes in topological properties of a system and occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and…
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,…
One of the most striking features of quantum phases that exhibit topological order is the presence of long range entanglement that cannot be detected by any local order parameter. The formalism of projected entangled-pair states is a…