Quantum Inf Process (2016) 15:2661–2673
Quantum cloning disturbed by thermal Davies
· Jerzy Łuczka
Received: 3 September 2015 / Accepted: 16 February 2016 / Published online: 1 March 2016
© The Author(s) 2016. This article is published with open access at Springerlink.com
Abstract A network of quantum gates designed to implement universal quantum
cloning machine is studied. We analyze how thermal environment coupled to auxiliary
qubits, ‘blank paper’ and ‘toner’ required at the preparation stage of copying, modiﬁes
an output ﬁdelity of the cloner. Thermal environment is described in terms of the
Markovian Davies theory. We show that such a cloning machine is not universal any
more but its output is independent of at least a part of parameters of the environment.
As a case study, we consider cloning of states in a six-state cryptography’s protocol.
We also brieﬂy discuss cloning of arbitrary input states.
Keywords Cloning · Decoherence · Davies approach
Soon after recognizing that quantum information can be neither perfectly copied 
nor broadcasted , physicists have gone to any length to bypass this limitation. As it
has been a struggle against nature, their efforts could be only partially successful [3,4].
Possibility of quantum cloning, even though imperfect, has a great impact on security
of quantum data transmission [5,6]. References  and  can serve as two examples
of reviews summarizing theoretical and practical achievements of quantum cloning.
Institute of Physics, University of Silesia, 40-007 Katowice, Poland
Silesian Center for Education and Interdisciplinary Research, University of Silesia,
41-500 Chorzów, Poland