Quantum steering in infinite-dimensional systems: An anomalous case of the Hughston-Jozsa-Wootters theorem

Guang Ping He

Published 2017-08-30Version 1

According to the Hughston-Jozsa-Wootters (HJW) theorem, if two sets of quantum states have the same density matrix, then it is possible to construct a composite system, such that there are two measurements on one side of the system, which can collapse the other side into an element of the above two sets, respectively. Here we show that in infinite-dimensional systems, there exists two sets of states that the two corresponding measurements become identical. It means that the steering between these two sets of states is impossible. Also, for finite high-dimensional systems, our result reveals a kind of chaos effect. That is, the subtle change on the measurement result at one side of a composite system leads to a drastic difference in the resultant states of the steering at the other side.