Quantum Inf Process (2013) 12:3607–3615
Classical communication and non-classical ﬁdelity
of quantum teleportation
Manik Banik · Md. Rajjak Gazi
Received: 22 May 2013 / Accepted: 25 July 2013 / Published online: 10 August 2013
© Springer Science+Business Media New York 2013
Abstract In quantum teleportation, the role of entanglement has been much discussed.
It is known that entanglement is necessary for achieving non-classical teleportation
ﬁdelity. Here we focus on the amount of classical communication that is necessary
to obtain non-classical ﬁdelity in teleportation. We quantify the amount of classical
communication that is sufﬁcient for achieving non-classical ﬁdelity for two indepen-
dent 1-bit and single 2-bits noisy classical channels. It is shown that on average 0.208
bits of classical communication is sufﬁcient to get non-classical ﬁdelity. We also ﬁnd
the necessary amount of classical communication in case of isotropic transformation.
Finally we study how the amount of sufﬁcient classical communication increases with
weakening of entanglement used in the teleportation process.
Keywords Quantum teleportation· Classical communication· Teleportation ﬁdelity
Quantum information theory, the generalization of classical information theory gov-
erned by the rules of quantum mechanics, has been a subject of much recent interest.
It is now known that various interesting communication schemes, like teleportation
[3,23,9] and dense coding [2,17,7], are possible when the laws of quantum mechan-
Recently our work has been extended to qudits in  by Weinar et al.
M. Banik (
) · Md.R.Gazi
Physics and Applied Mathematics Unit, Indian Statistical Institute,
203 B.T. Road, Kolkata 700108 , India
Md. R. Gazi