Limits on entanglement in rotationally-invariant scattering of spin systems
N. L. Harshman
备注：
6 pages, no figures; v.2: sections added, edited for clarity, conclusions and calculation unchanged, typos corrected; v.3: new abstrct, revised first two sections, added references
This paper investigates the dynamical generation of entanglement in scattering systems, in particular two spin systems that interact via rotationally-invariant scattering. The spin degrees of freedom of the in-states are assumed to be in unentangled, pure states, as defined by the entropy of entanglement. Because of the restriction of rotationally-symmetric interactions, perfectly-entangling S-matrices, i.e. those that lead to a maximally entangled out-state, only exist for a certain class of separable in-states. Using Clebsch-Gordan coefficients for the rotation group, the scattering phases that determine the S-matrix are determined for the case of spin systems with $σ= 1/2$, 1, and 3/2.
We calculate the relative entropy of entanglement for rotationally invariant states of spin-1/2 and arbitrary spin-$j$ particles or of spin-1 particle and spin-$j$ particle with integer $j$. A lower bound of relative entropy of entanglement and an upper bound of distillable entanglement are presented for rotationally invariant states of spin-1 particle and spin-$j$ particle with half-integer $j$.
Computing the entanglement of formation of a bipartite state is generally difficult, but special symmetries of a state can simplify the problem. For instance, this allows one to determine the entanglement of formation of Werner states and isotropic states. We consider a slightly more general class of states, rotationally symmetric states, also known as SU(2)-invariant states. These states are invariant under global rotations of both subsystems, and one can examine entanglement in cases where the subsystems have different dimensions. We derive an analytic expression for the entanglement of form…
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We investigate the structure of SO(3)-invariant quantum systems which are composed of two particles with spins j_1 and j_2. The states of the composite spin system are represented by means of two complete sets of rotationally invariant operators, namely by the projections P_J onto the eigenspaces of the total angular momentum J, and by certain invariant operators Q_K which are built out of spherical tensor operators of rank K. It is shown that these representations are connected by an orthogonal matrix whose elements are expressible in terms of Wigner's 6-j symbols. The operation of the partia…
We present a general approach to calculating the entanglement of formation for superpositions of two-mode coherent states, placed equidistantly on a circle in the phase space. We show that in the particular case of rotationally-invariant circular states the Schmidt decomposition of two modes, and therefore the value of their entanglement, are given by analytical expressions. We analyse the dependence of the entanglement on the radius of the circle and number of components in the superposition. We also show that the set of rotationally-invariant circular states creates an orthonormal basis in t…
Local universality of non-local quantum resources in rotationally invariant scattering
InQubator for Quantum Simulation (IQuS) and Department of Physics, University of Washington（华盛顿大学量子模拟创新中心及物理系）；Institute for Quantum Information and Matter (IQIM) and Department of Physics, California Institute of Technology（加州理工学院量子信息与物质研究所及物理系）
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