Pairwise Concurrence in Cyclically Symmetric Quantum States

TL;DR

This paper characterizes pairwise entanglement in cyclically symmetric quantum states, showing that maximal entanglement depends on adjacent pairs and establishing monogamy bounds in 4 and 5 qubit states.

Contribution

It provides a novel analysis of pairwise concurrence in cyclically symmetric states and introduces explicit descriptions and monogamy bounds for 4 and 5 qubit X states.

Findings

Maximal entanglement is determined by adjacent pairs.

Explicit descriptions of states in 4 and 5 qubit X states.

Monogamy bounds restrict entanglement sharing in these states.

Abstract

We provide an initial characterization of pairwise concurrence in quantum states which are invariant under cyclic permutations of party labeling. We prove that maximal entanglement can be entirely described by adjacent pairs, then give explicit descriptions of those states in specific subsets of 4 and 5 qubit states - X states. We also construct a monogamy bound on shared concurrences in the same subsets in 4 and 5 qubits, finding that above non-maximal entanglement thresholds, no other entanglements are possible.