Hidden teleportation for higher-dimensional quantum states

Jyun-Yi Li^1*, Gelo Noel M. Tabia², Yeong-Cherng Liang¹

¹Department of Physics, National Cheng Kung University, Tainan, Taiwan
²Department of Physics, National Tsing Hua Univerity, HsinChu, Taiwan

* Presenter:Jyun-Yi Li, email:L26064268@mail.ncku.edu.tw

An ideal quantum teleportation is a process by which an unknown d-dimensional quantum state is teleported intact from Alice to another distant party, Bob via the use of a shared maximally entangled resource and the communication of classical information. In contrast, if Alice and Bob only share a classical resource, such as a product state, the maximal average fidelity between the state Alice wants to teleport to Bob and the state Bob receives after the teleportation is at most f_c=2/(d+1). A shared quantum state is said to be useful for quantum teleportation if they can give an average fidelity larger than f_c. However, If Alice and Bob initially share an entangled state ρ with fidelity less than f_c, after appropriate local filtering, and conditioning on the success of the filtering process, the fidelity may be larger than f_c. In that case, we say that ρ has hidden teleportation power. The problem of whether any given two-qubit entangled state has hidden teleportation power has previously been solved. Here, we further investigate (1) the relation between the success probability of local filtering operation and the extent to which the maximal average fidelity can be increased, and (2) the hidden teleportation power of higher-dimensional quantum states. Specifically, we consider a d-dimensional one-parameter family of entangled states and derive an analytical expression giving the maximal overall teleportation fidelity when only real value local filters are considered.

Keywords: Quantum teleportation, Hidden teleportation, Fidelity