Physics Letters A 360 (2006) 251–255 www.elsevier.com/locate/pla Loss of entanglement after propagation in a quantum noisy channel modeled by a canonical unitary operation in two qubits Wellington Alves de Brito, Rubens Viana Ramos ∗ Department of Teleinformatic Engineering, Federal University of Ceara, Campus do Pici, 710, C.P. 6007, 60755-640 Fortaleza-Ceará, Brazil Received 19 June 2006; received in revised form 9 August 2006; accepted 11 August 2006 Available online 22 August 2006 Communicated by P.R. Holland Abstract In this work, we analyze the loss of entanglement of bipartite states after propagation in a noisy channel modeled by the interaction between the bipartite state and the environment through a canonical unitary form of a two-qubit gate. An analytic expression for the entanglement loss is found.  2006 Elsevier B.V. All rights reserved. PACS: 03.65.Ta; 03.67.-a; 03.65.Bz Keywords: Entanglement; Canonical unitaries; Quantum noisy channel Entanglement is a very important property of some composite quantum systems that plays a key role in many of the most important application of quantum computation and quantum information processing, as quantum key distribution [1,2] and quantum teleportation [3,4]. Despite of its importance for quantum information protocols, entanglement is a fragile property that is easily lost when the quantum system interacts with the environment, a process called decoherence [4,5]. Long distance quantum teleportation, for example, is limited by this effect. In fact, the quantum system–environment interaction represents a quantum noisy channel. The larger the noisy the faster the loss of entanglement and the increasing of entropy during channel propagation. Further, the lower the entanglement the larger (toward the value 0.5) the error rate in the quantum communication or computation systems. In this work, our aim is to analyze the entanglement variation of a bipartite state during propagation in a quantum noisy channel. A similar task was realized in [6]. However, differently from their approach, we will use for the quantum noisy channel model the system–environment interaction through a unitary evolution. The unitary evolution considered here is the canonical unitary evolution discussed in [7]. Having this, we have been able to find an analytical expression for the loss of entanglement during channel propagation. Basically, the quantum noise appears due to the fact that one cannot access all existing variables, being required to trace out part of the whole system. Hence, we can see a quantum noisy channel for a bipartite state as a unitary interaction between the bipartite state and a single qubit representing the environment and, after the interaction, tracing out the environment. Hence, we are going to analyze the bipartite state obtained from a pure tripartite C 2 ⊗ C 2 ⊗ C 2 state. Let us consider the quantum noisy channel modeled as shown in Fig. 1. * Corresponding author. E-mail addresses: wbrito@deti.ufc.br (W. Alves de Brito), rubens@deti.ufc.br (R. Viana Ramos). 0375-9601/$ – see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2006.08.039