It has recently been shown that quantum computers can efficiently solve the Heisenberg hidden subgroup problem, a problem whose classical query complexity is exponential. This quantum algorithm was discovered within the framework of using pretty-good measurements for obtaining optimal measurements in the hidden subgroup problem. Here we show how to solve the Heisenberg hidden subgroup problem u...

It is known that if $$d^2$$ vectors in a d-dimensional Hilbert space H form symmetric, informationally complete, positive operator-valued measure (SIC-POVM), then the tensor squares of these an equiangular tight frame symmetric subspace $$H\otimes H$$ . We prove that, for any SIC-POVM Weyl–Heisenberg group covariant type (WH-type), this can be obtained by projecting WH-type basis onto subspace....

We report magnetization, specific heat, muon spin rotation, and Na NMR measurements on the S=3/2 rhombohedrally stacked Heisenberg antiferromagnet NaCrO2. This compound appears to be a good candidate for the study of isotropic triangular Heisenberg antiferromagnets with very weak interlayer coupling. While specific heat and magnetization measurements indicate the onset of a transition in the ra...

We formulate an efficient method for characterizing and quantifying genuine multipartite entanglement in two-dimensional (2D) Heisenberg spin systems where the ground state is a large superposition obtained from nearest-neighbor dimer coverings on spin-1/2 lattices, the resonating valence bond (RVB) state. We find an analytical iterative method, the density matrix recursion method, to generate ...

The Heisenberg model is described. Some of the interesting behavior of Heisenberg antiferromagnets and its behavior as a function of dimension is described. One dimensional systems have no long range order, two dimensional systems order magnetically only at zero temperature, and three dimensional systems have a non-zero critical temperature. Assembling lower dimensional pieces into ladders and ...

This paper studies the problem of sequence-to-sequence alignment, namely establishing correspondences in time and in space between two di erent video sequences of the same dynamic scene. The sequences are recorded by uncalibrated video cameras, which are either stationary or jointly moving, with xed (but unknown) internal parameters and relative inter-camera external parameters. Temporal variat...

The membrane instanton superpotential for M-theory on the G 2 holonomy manifold given by the cone on S 3 × S 3 is given by the dilogarithm and has Heisenberg monodromy group in the quantum moduli space. We compare this to a Heisenberg group action on the type IIA hypermultiplet moduli space for the universal hypermultiplet, to metric corrections from membrane instantons related to a twisted dil...