Quantum / CONCEPT

Generalized concentratable entanglement is not monotone under enlarging the subsystem

Liu, Knörzer, Wang and Tura (arXiv:2406.18517, Phys. Rev. Research 7, L032022) define the generalized concentratable entanglement C^{(K)}_psi(s) = (1 - 2^{-|s|} sum_{alpha in P(s)} Tr(rho_alpha^K)) / (K - 1) of an n-qubit pure state, with Tr(rho_emptyset^K) = 1, and conjecture that C^{(K)}_psi(s') <= C^{(K)}_psi(s) whenever s' is a subset of s, for every real K > 1. It fails at K = 5/2 for a four-qubit state with integer amplitudes: removing one qubit from {0, 1, 2} raises the value.