Lower Bound for entanglement cost of antisymmetric states

TL;DR

This paper establishes a lower bound on the entanglement cost of antisymmetric states in bipartite d-level systems, clarifying uncertainties in previous claims about their entanglement measures.

Contribution

It provides a rigorous lower bound for the entanglement cost of antisymmetric states, correcting prior misconceptions and clarifying the actual entanglement lower limits.

Findings

Lower bound of entanglement cost is log_2(d/(d-1)) ebits.

For d=3, the entanglement cost is at least 0.585 ebits.

Previous claims about the entanglement being exactly one ebit are not supported by proof.

Abstract

This report gives a lower bound of entanglement cost for antisymmetric states of bipartite d-level systems to be log_2 (d/(d-1)) ebit (for d=3, E_c >= 0.585...). The paper quant-ph/0112131 claims that the value is equal to one ebit for d=3, since all of the eigenvalues of reduced matrix of any pure states living in N times tensor product of antisymmetric space is not greater than 2^(-N) thus the von Neumann entropy is not less than N, but the proof is not true. Hence whether the value is equal to or less than one ebit is not clear at this moment.