Related papers: Thou Shalt Not Clone One Bit!
We present a binary code for spinors and Clifford multiplication using non-negative integers and their binary expressions, which can be easily implemented in computer programs for explicit calculations. As applications, we present explicit…
We show that if A is a subset of {1,...,N} contains no non-trivial three-term arithmetic progressions then |A|=O(N/ log^{1-o(1)} N). The approach is somewhat different from that used in arXiv:1007.5444.
We consider two different ways to encode quantum information, by parallel or anti-parallel pairs of spins. We find that there is more information in the anti-parallel ones. This purely quantum mechanical effect is due to entanglement, not…
The relevance of the pseudospin symmetry in nuclei is considered. New insight is obtained from looking at the continuous transition from a model satisfying the spin symmetry to another one satisfying the pseudospin symmetry. This study…
In this note we prove a representation theorem for the symmetric cone automorphisms in the spin algebra\, $\Ln$.
We prove a prime decomposition theorem for string links in a thickened surface. Namely, we prove that any non-braid string link $\ell \subset \Sigma \times I$, where $\Sigma$ is a compact orientable (not necessarily closed) surface other…
We explore various tree-level double copy constructions for amplitudes including massive particles with spin. By working in general dimensions, we use that particles with spins $s\leq 2$ are fundamental to argue that the corresponding…
We review model independent arguments showing that massless particles interacting with gravity in a Minkowski background space can have at most spin two. These arguments include a classic theorem due to Weinberg, as well as a more recent…
We have found a quantum cloning machine that optimally duplicates the entanglement of a pair of $d$-dimensional quantum systems. It maximizes the entanglement of formation contained in the two copies of any maximally-entangled input state,…
Spatially nonhomogeneously spin polarized nuclei are proposed as a new mechanism to monitor electron states in a nanostructure, or as a means to createn and, if necessary, reshape such nanostructures in the course of the experiment. We…
We conjecture an algorithm to construct spin multipartitions and prove that all the level one Fock spaces using our combinatorics are modules over the quantum enveloping algebra.
Using the Berezin-Marinov pseudoclassical formulation of spin particle we propose a classical model of spin noncommutativity. In the nonrelativistic case, the Poisson brackets between the coordinates are proportional to the spin angular…
Analyzing the properties of entanglement in many-particle spin-1/2 systems is generally difficult because the system's Hilbert space grows exponentially with the number of constituent particles, $N$. Fortunately, it is still possible to…
We introduce a spin polarization-scaling map for spin-$j$ particles, whose physical meaning is the decrease of spin polarization along three mutually orthogonal axes. We find conditions on three scaling parameters under which the map is…
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for by some realistic models with hidden variables. There are, however, two powerful…
We show that the non-commutative $CP^1$ model coupled with Hopf term in 3 dimensions is equivalent to an interacting spin-$s$ theory where the spin $s$ of the dual theory is related to the coefficient of the Hopf term. We use the…
We define the separability and entanglement notion for particle with spin $s=1$. We consider two cases. In the first the particle is composed of two fermions with $s_1=1/2$ and $s_2=1/2$. In the second case the state is the qutrit state…
Three apparently unrelated problems which have no solution using classical tools are described: the "N-strangers," "secret sharing," and "liar detection" problems. A solution for each of them is proposed. Common to all three solutions is…
We generalize the results of [B. Coecke, Helv. Phys. Acta 68, 396 (1995)] for the representation of coherent states of a spin-1 entity to spin-S entities with S>1 and to non-coherent spin states: through the introduction of 'hidden…
Each orthogonal group $\OO(n)$ has a nontrivial $\GL(1)$-extension, which we call $\GPin(n)$. The identity component of $\GPin(n)$ is the more familiar $\GSpin(n)$, the general Spin group. We prove that the restriction to $\GPin(n-1)$ of an…