Entanglement Cost of Three-Level Antisymmetric States

Matthias Christandl, Norbert Schuch, Andreas Winter

Matthias Christandl, Norbert Schuch, Andreas Winter

Fumitaka Yura

We show that the entanglement cost of the three-dimensional antisymmetric states is one ebit.

Toshiyuki Shimono

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.

Keiji Matsumoto, Fumitaka Yura

We study the entanglement cost of the states in the antisymmetric space, which consists of ( d − 1) d -dimensional systems. The cost is always log 2 ( d − 1) ebits when the state is divided into bipartite . Combined with the arguments in [6], additivity of channel capacity of some quantum channels is also shown.

Lech Jakóbczyk