Generic incomparability of infinite-dimensional entangled states

Abstract

In support of a recent conjecture by Nielsen (1999), we prove that the phenomena of 'incomparable entanglement'-whereby, neither member of a pair of pure entangled states can be transformed into the other via local operations and classical communication (LOCC)-is a generic feature when the states at issue live in an infinite-dimensional Hilbert space.

Deterministic Local Conversion of Incomparable States by Collective LOCC

“…Vidal extended this to the case of probabilistic local conversion (SLOCC) of two pure bipartite entangled states [5]. Further, Morikoshi [6] investigated the recovery of entanglement loss in the process of local conversion and several other groups studied the possibility and impossibility of entanglement manipulation in different context [7,8,9,10,11,12,13,14,15,16].…”

Characterizing Incomparability in Quantum Information

“…Inconvertibility.-Nielsen conjectured that the probability of picking at random a pair of incomparable spectra in a d-system tends to 1 as d → ∞ [2]. It was established that densely many of these are in fact strongly incomparable [11]. Our objective is to find for a single spectrum its ratio of incomparable spectra in the Weyl chamber.…”

“…First educed by Nielsen [6], majorization incomparability was used to account for the restrictions placed on entanglement transformation. Work has been done to uncover its underlying nature [10][11][12][13], however such understanding is far from exhaustion. Here, we examine majorization incomparability under a quantum setting in hopes of facilitating such discussions.…”