Local Unitary Invariants of Quantum States

Abstract

We study the equivalence of mixed states under local unitary transformations in bipartite system and three partite system. First we express quantum states in Bloch representation. Then based on the coefficient matrices, some invariants are constructed in terms of the products, trace and determinant of matrices. This method and results can be extended to multipartite high dimensional system.

Maximally entangled Rydberg-atom pairs via Landau-Zener sweeps

“…Depending on the sweep rates and RRI strengths, various maximally entangled states are formed, and for a given set of parameters, the maximally entangled states change periodically. They are local unitary equivalent to the Bell states, and we explicitly verify that by calculating corresponding polynomial invariants for the two-qubit states [51][52][53][54]. Finally, considering the spontaneous emission, we show that the maximally entangled states via LZ sweeps can be realized using high-level rubidium Rydberg states.…”

“…the determinant of a matrix T 12 defined below [54] to be the same. Writing the two-qubit density matrix as…”

Detection of genuine tripartite entanglement based on Bloch representation of densitymatrices

“…In terms of the trace norm of linear combination of these matrices, we derive new criteria on GME. Let us briefly review the Schmidt decomposition [17] and LU equivalence [18,19] to explain our approach. Suppose |ϕ is a pure state of a composite system H d1 1 ⊗ H d2 2 .…”