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n-Particle Quantum Statistics on Graphs
We develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantumExpand
Convexity of momentum map, Morse index, and quantum entanglement
We analyze from the topological perspective the space of all SLOCC (Stochastic Local Operations with Classical Communication) classes of pure states for composite quantum systems. We do it for bothExpand
Symplectic Geometry of Entanglement
We present a description of entanglement in composite quantum systems in terms of symplectic geometry. We provide a symplectic characterization of sets of equally entangled states as orbits of groupExpand
Universality of Single-Qudit Gates
We consider the problem of deciding if a set of quantum one-qudit gates $$\mathcal {S}=\{g_1,\ldots ,g_n\}\subset G$$S={g1,…,gn}⊂G is universal, i.e. if $${<}\mathcal {S}{>}$$ is dense in G, where GExpand
When is a pure state of three qubits determined by its single-particle reduced density matrices?
Using techniques from symplectic geometry, we prove that a pure state of three qubits is up to local unitaries uniquely determined by its one-particle reduced density matrices exactly when theirExpand
Non-abelian Quantum Statistics on Graphs
We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general frameworkExpand
How many invariant polynomials are needed to decide local unitary equivalence of qubit states
Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for the minimal number of invariant polynomials needed for solving local unitary (LU) equivalenceExpand
Universality of beamsplitters
  • A. Sawicki
  • Physics, Mathematics
  • Quantum Inf. Comput.
  • 29 July 2015
Using methods of control theory and some properties of rotations in three dimensions, it is proved that any nontrivial real 2-mode and "almost" any nontrevial real $3-mode beamsplitter is universal on $m\geq3$ modes. Expand
Classical nonintegrability of a quantum chaotic SU(3) Hamiltonian system
Abstract We prove the nonintegrability of a model Hamiltonian system defined on the Lie algebra s u 3 suitable for investigation of connections between classical and quantum characteristics of chaos.
Are scattering properties of graphs uniquely connected to their shapes?
This work considers scattering from a pair of isospectral microwave networks consisting of vertices connected by microwave coaxial cables and extended to scattering systems by connecting leads to infinity to form isoscattering networks and shows that the amplitudes and phases of the determinants of the scattering matrices of such networks are the same within the experimental uncertainties. Expand